Civil Engineering

The PUC-Rio graduate program in Civil Engineering was the first M.Sc. program in the field implemented in Brazil. Currently, the Civil Engineering department offers degrees in Structural (M.Sc. since 1965; Ph.D. since 1985) and Geotechnical (M.Sc. since 1967; Ph.D. since 1985) engineering. The program has a widely acknowledged teaching and research excellence. Its graduates have leading roles as professors, in the main Brazilian universities and in several foreign ones as well (in Latin America, the USA and Canada), and also as engineering professionals and entrepreneurs.

The graduate program offers advanced studies and provides the opportunity of interaction with foreign institutions to carry out joint research and academic exchange programs.

In the field of Structural Engineering, our department produces theoretical and experimental studies on static, dynamic, instability and collapse behavior of structures. New experimental and computer modeling techniques (with use of numerical methods and computer graphics) are developed for use in advanced methods of analysis and design. These techniques are applicable to structures made of concrete, steel and other materials (including non-conventional materials), as well as to biomechanics and nanotechnology.

In the field of Geotechnical Engineering, the program emphasizes theoretical and experimental research on the behavior of soils, rocks, and geosynthetics, with applications to dams, excavations, foundations, slope stability, mining, waste disposal, environmental geotechnics, engineering geology, soil dynamics, underground water hydrology, petroleum geomechanics, and field instrumentation of earthworks, among other areas.

Additional information can be found at the Department’s site and, in Portuguese, here.


Syllabus: Algebra of vectors and matrices, determinants, inverse, solution of a system of linear algebraic equations, quadratic forms, eigenvalues and eigenvectors. Ordinary differential equations, linear equation systems, approximation by series, orthogonal polynomials and stability. Initial and boundary value problems. Partial differential equations: mathematical physics. Method of separation of variables; boundary and initial conditions. Variational calculus: the Euler equation. The delta operator. Functionals of several functions and with higher-order derivatives. Natural and forced boundary conditions. Restrictions and Lagrange multipliers. Variational principles in mechanics. Functionals with two or more independent variables

Bibliography: Kreyszig, Erwin – Advanced Engineering Mathematics – John Wiley & Sons, New York, USA, 2011. Hildebrand, Francis P. – Advanced Calculus for Applications – Prentice-Hall, New York, USA, 2nd edition, 1976. Greenberg, Michael D. – Foundations of Applied Mathematics – Prentice Hall, New York, USA, 1978. Goldberg, Jack L. – Matrix Theory with Applications – McGraw-Hill, New York, USA, 1991. Boyce, William E. and DiPrima, Richard C. – Elementary Differential Equations and Boundary Value Problems – Wiley New York, USA, 9th edition, 2008. Elsgoltz – Ecuaciones diferenciales y cálculo variacional. Wan, Frederic Y.M. – Introduction to the Calculus of Variations and its Applications – Chapman & Hall, New York, USA, 1st edition, 1994

Syllabus: General linear transformations in and between force and displacement coordinate systems. Matrix expression of energy theorems. Two- and three-dimensional analysis of shear-deformable, curved beams with variable cross sections. Generic load cases and equivalent nodal forces. Flexibility and stiffness methods. Matrix flexibility and stiffness formulations for frame structures considering generalized loading and support conditions. Computer implementations

Bibliography: Introduction to the finite element method. W. McGuire, R. H. Gallagher and R. D. Ziemian, Matrix Structural Analysis, 2nd Edition, John Wiley & Sons, New York, 2000. L. P. Felton and R. Nelson, Matrix Structural Analysis, John Wiley & Sons, 1997. M. B. Kanchi, Matrix Methods of Structural Analysis, Halsted Press, 1994. N. A. Dumont, Lecture notes. Selected papers

Syllabus: Tensor operations. Kinematics. Small and large deformation and strains. Cauchy and Piola-Kirchhoff I and II stress definitions. General equations of elasticity. Three-dimensional problems. Two-dimensional problems in Cartesian and polar coordinates. Torsion. Other topics

Bibliography: Little, R. W., 1973, Elasticity, Prentice-Hall; Boresi, Ap.; Chong, K.P., 1987, Elasticity In Engineering Mechanics, Elsevier; Shames, I.H.; Cozzareli, F. A., 1992, Elastic And Inelastic Stress Analysis, Prentice-Hall

Syllabus: Phenomenological aspects. Basic definitions. One-dimensional plasticity. Flow criteria, hardening laws, flow rules. Classical rate-independent plasticity. Maximum dissipation principle. Computational aspects. Solution of the initial value problem. Stress projection algorithms. Introduction to the continuum damage mechanics

Bibliography: Simo, J. C.; Taylor, R., 1999, Computational Plasticity and Visco-plasticity, Springer -Verlag; Lubliner, J., 1990, Plasticity Theory, MacMillan; Lemaitre, J.; Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press; Chen, W.F.; Han, D.J., 1988, Plasticity for Structural Engineers

Syllabus: Structural stability theory: basic concepts and definitions. Stability criteria: static, dynamic and energy criteria. Physical and geometric nonlinearity. Equilibirum paths. Limit and bifurcation points. Critical and post-critical behavior. Imperfection sensitivity. Multiple bifurcations and modal coupling. Vibrations of structural elements liable to buckling. Structural stability problems: slender columns, the elastica. Plate stability. Shell stability. Stability of beams and frames in the plane. Spatial buckling of beams. Stability of arches and rings. Systems subjected to nonconservative loads. Stability of inelastic systems. Computational modeling of stability problems. Approximate methods: Ritz, Galerkin, etc. Eigenvalues problems and use of finite elements. Geometric matrices for different structural elements. Nonlinear analysis. Identification of limit and bifurcation points and determination of equilibrium paths

Bibliography: Croll and Walker, Elements of Structural Stability, Macmillan, London, 1972. Brush and Almroth, Buckling of Bars, Plates and Shells, Mcgraw-Hill, 1975. Bazant and Cedolin, Stability of Structures, Oxford, 1991. El Naschie, Stress, Stability and Chaos, Mcgraw-Hill, 1990. Thompson and Hunt, Elastic Instability Phenomena, Wiley, 1984. Allen and Bulson, Background to Buckling, Mcgraw-Hill, 1980. Cook, Malkus and Plesha, Concepts and Applications of Finite Element Analysis, Wiley, 1989. Timoshenko and Gere, Theory of Elastic Stability, McGraw-Hill, 1961

Syllabus: Overview of structural dynamics. Single-degree-of-freedom systems: formulation of the equations of motion, undamped and damped free vibration response, response to harmonic, periodic and impulsive loads, response to general dynamic loads, Duhamel integral, numerical integration of the equations of motion and response spectra. Multi-degree-of-freedom systems: formulation of the equations of motion, mass, damping and stiffness matrices, undamped and damped free vibrations, orthogonality conditions, modal analysis, forced vibrations. Distributed parameter systems: partial differential equations of motion, eigenvalues and eigenfunctions, beam flexure, free and forced vibrations, Ritz and Galerkin method

Bibliography: Clough and Penzien, Dynamics of Structures McGraw-Hill, 1993. Meirovitch, Elements of Vibration Analysis, McGraw-Hill, 1975. Craig, Structural Dynamics, Wiley, 1981. Thompson, Teoria da Vibração, Interciência, 1973. Beanaroya, Mechanical Vibration, CRC Press, 2010. Rao, Mechanical Vibrations, Addison-Wesley, 1986. Weaver and Johnston, Structural Dynamics by Finite Elements, Prentice-Hall, 1987

Syllabus: Cartesian tensors. Vector analysis in index notation. Analisys of stress and strain. Static and dynamic equations of continuous media. Energy and mass conservation theorems. Ideal and viscous fluids. Applications. Elastic waves in solids. Viscoelasticity. Viscoelastic models. Relaxation. Thermodynamics of deformation. Thermoelasticity

Bibliography: Frederic and Chang, Continuum Mechanics, A. Bacon; G. E. Mase. Continuum Mechanics, Schaum

Syllabus: Plate theory equations. Boundary conditions. Circular plates subjected to symmetric loads. Rectangular plates subjected to different loading types and various edge conditions. Continuous plates. Bending of anisotropic plates. Bending of plates under combined action of lateral loads and forces in the mid-plane of the plate. Plates with large deformations. Prismatic laminar structures

Bibliography: Szilard, 1974, Theory of Plates, Prentice-Hall Inc; Jawad, M.H., 1994, Theory and Design of Plate and Shell Structures, Chapman & Hall; Ciarlet,, P.G., 1997, Mathematical Elasticity: Theory of Plates, North-Holland; selected technical papers

Syllabus: Principle of the minimum total potential energy. Virtual displacement principle in two and three dimensions. Convergence criteria. Consistent nodal loads. Isoparametric elements. Numerical integration. Kirchhof and Mindlin plate elements. Locking. Incompatible elements. Static condensation. Hybrid formulation

Bibliography: Zienkiewicz, O. C. & Taylor, R. L., 1998, The Finite Element Method, 4th Edition, vol. 2, McGraw-Hill; Bathe, K-J, 1995, Finite Element Procedures, Prentice-Hall Inc.; Cook, R. D., Malkus, D. S., & Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, 3rd Edition, John Wiley & Sons

Syllabus: Generalized variational principles. Hamilton´s principle. Energy methods for stability analysis. Torsion. Bending of prismatic bars. Axisymmetric problems. Half-space problems. Wave propagation in elastic media

Bibliography: Little, R. W., Elasticity, Prentice-Hall; Mello e Souza, Métodos de Energia, Interciência

Syllabus: Probability theory. Analysis in the frequency domain. Random processes:definition and characterization. Differentiation and integration. Weakly stationary process. Power spectrum and power spectrum density function. Gaussian distribution. Poisson and Markov. Distribution of the Rayleigh and Vanmarcke peaks. Analysis of single- and multi-degree-of-freedom systems. Linear systems. Approximate methods for the analysis of nonlinear systems. Classical probabilistic risk and reliability analysis. Applications to simple systems

Bibliography: Lin.Y.K., Probalistic Theory of Structural Dynamics, Krieger, 1976. Lin, YlK., Cai, G.Q., Probabilistic Structural Dynamics: Advanced Theory and Applications, Mcgraw-Hill, 1994. Clough, R.W., Penzien, J., Dynamics of Structures, Mc-Graw-Hill, 1993. Newland, D.E., An Introduction to Random Vibrations, Spectral and Wave Analysis, Addison-Wesley Longman, 1996. Vlasta Molak, Fundamentals of Risk Analysis and Risk Management, Lewis Publishers, 1996. Melchers, R.E., Structural Reliability, John Wiley & Sons, 1987

Syllabus: Continuous systems. Approximate methods for evaluation of vibration frequencies and vibration modes. Lagrangian formulation of the equations of motion. Analysis in the frequency domain. Structural analysis problems:Linear and nonlinear systems. Vibrations due to base excitation. Seismic loads. Generation of artificial earthquakes. Soil-structure interaction. Moving loads in beams. Wave forces on offshore structures

Bibliography: Clough, R.W. Penzien, 1993, Dynamics of Structures, McGraw-Hill; Bathe, K.J., 1995, Finite Element Procedures, Prentice-Hall Inc.; Das, B.M., 1993, Principles of Soil Dynamics, PWS-Kent Publishing Company; Newland, D.E., 1996, An Introduction to Random Vibrations, Spectral and Wavelet Analysis, 3rd edition, Addison-Wesley Longman, selected journal papers

Syllabus: Introduction. Simplified models for inelastic materials. Classical models for viscoelastic behavior of materials. Classical plasticity models. Plastic analysis of beams, frames and other structures. Stability considerations. Computational models for plasticity. Computational models for concrete and brittle materials

Bibliography: I.H. Shames e F.A. Cozarelli, Elastic and Inelastic Stress Analysis, Prentice-Hall, 1992. Flügge, Viscoelasticity. M.R. Horne, Plastic Theory of Structures, T. Nelson, 1971

Syllabus: Limit states design criteria, In-plane behaviour, Local buckling and postbuckling strength of plates, Uniform and non-uniform torsion, warping properties of sections, beams, columns and beam-columns, connections

Bibliography: Galambos, T.V., 1968, Structural Members and Frames, Prentice Hall; Norm CAN/CSA – S16.09 – Design of Steel Structures, 2009; Norm NBR-8800/2008 Projeto de Estruturas de Aço e de Estruturas Mistas de Aço e Concreto de Edifícios, 2008; Guide to Stability Design Criteria for Metal Structures, 5th edition, edited by Galambos, T. V., John Wiley, 1998; Lecture notes and technical papers

Syllabus: Limit states design of steel structures philosophy. Second order differential equations, Composite construction: Composite beams, composite trusses, stub-girder construction, composite columns, Connections, Bracing design. Plate girders, Plastic design principles

Bibliography: Galambos, T.V., 1968, Structural Members and Frames, Prentice Hall; Norma NBR-8800/2008 Projeto de Estruturas de Aço e de Estruturas Mistas de Aço e Concreto de Edifícios, 2008; Owens, G.W. and Cheal, B.D., 1989, Structural Steelwork Connections, Butterworths; Norm CAN/CSA – S16.09 – Design of Steel Structures, 2009; Faella, C., Piluso, V. & Rizzano, G., 1998, Structural Steel Semirigid Connections, CRC Press; Lecture notes and technical papers

Syllabus: Introduction. Principles for structural safety: serviceability and ultimate limit states according to NBR6118, MC2010-FIB and ACI318. Mechanical properties of concrete and steel. Bond between concrete and steel bars. Ultimate limit state design of sections under combined axial load and bending. Columns and bracing structures: design of short and slender columns according to NBR6118 and MC2010-FIB, moment-curvature relationship, general method for analysis of slenderness effects. Shear: behavior of beams and slabs failing in shear. Verification of serviceability limit states of cracking and deflections of beams. Strut-and-tie models

Bibliography: MacGregor, J.G., 1988, Reinforced Concrete – Mechanics and Design, Prentice-Hall; Nilson, A.H. & Winter, G., 1991, Design of Concrete Structures, McGraw-Hill International Editions; Fusco, P.B., 1981, Estruturas de Concreto – Solicitações Normais, Editora Guanabara Dois; Selected technical papers; lecture notes

Syllabus: Introduction. Principles for structural safety: serviceability and ultimate limit states according to NBR6118, MC2010-FIB and ACI318. Mechanical properties of concrete and steel. Bond between concrete and steel bars. Ultimate limit state design of sections under combined axial load and bending. Columns and bracing structures: design of short and slender columns according to NBR6118 and MC2010-FIB, moment-curvature relationship, general method for analysis of slenderness effects. Shear: behavior of beams and slabs failing in shear. Verification of serviceability limit states of cracking and deflections of beams. Strut-and-tie models

Bibliography: MacGregor, J.G., 1988, Reinforced Concrete – Mechanics and Design, Prentice-Hall; Nilson, A.H. & Winter, G., 1991, Design of Concrete Structures, McGraw-Hill International Editions; Fusco, P.B., 1981, Estruturas de Concreto – Solicitações Normais, Editora Guanabara Dois; Selected technical papers; lecture notes

Syllabus: General concepts, classification and types of prestressing. Principles for structural safety of prestressed concrete. Mechanical properties of concrete and prestressing steel. Analysis and design of sections for flexure in non-cracked and cracked linear stages and at the ultimate limit state. Forces and moments due to prestress: equivalent loading, primary and secondary moment, shear and axial force, linear transformation and concordancy of cables. Losses of prestress. Shear in prestressed beams. Bearing at anchorage zones. Prestressed concrete slabs

Bibliography: Lyn, T.Y. and Burns, N.H., 1982, Design of Prestressed Concrete Structures, John Wiley & Sons; Collins, M.P. & Mitchell, D., 1987, Prestressed Concrete Basics, Canadian Prestressed Concrete Institute; Pfeil, W., Concreto Protendido, Livros Técnicos e Científicos Editora S.A.; Selected technical papers

Syllabus: Introduction to the optimal project. Linear programming: Simplex algorithm. Application to the limit analysis of trusses and beams. Non-linear programming with no restrictions: optimal conditions and algorithms. Application to the non-linear analysis of structures. Non-linear programming with restrictions: Kuhn-Tucker conditions, direct and indirect algorithms. Duality. Applications to the optimal project

Bibliography: Vanderplaats, G., 1984, Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill; Haftk, R. T. & Gürdal, Z., 1992, Elements of Structural Optimization, 3rd edition, Kluwer Academic Press; Lecture notes and technical papers

Syllabus: Revision of the probability theory. Introduction, history and situation. Concepts and definitions. Uncertainty and threat characterization. Identification and classification of the methodologies available. Probability risk analysis for complex engineering systems: objectives. Structural reliability theory. Evaluation of failure probability. Time dependent probabilistic and statistical methods. Events and failure trees. Risk control. Application of the probabilistic risk analysis to the case of extreme environmental actions

Bibliography: Molak, V., 1996, Fundamentals of Risk Analysis and Risk Management, Lewis Publishers; Melchers, R.E., 1987, Structural Reliability, John Wiley & Sons.; Budnitz R.J, Apostolaskis G., Boore D.M., Cluff L.S., Coppersmith K.J., Cornell C.A. e Morris P.A., 1997, Recommendations for Probabilistic Seismic Hazard Analysis, NUREG/CR-6372 U.S. Nuclear Regulatory Commission, Washington, D.C., UCRL-ID122160 vol.1

Syllabus: Introduction. Pathology of: Concrete Structures; Steel Structures; Wood Structures; Masonry Structures; Buildings of Historic Interest; Structures Affected by Fire; Soil-Structure Interaction; Maintenance, Rehabilitation, Repair and Strengthening of Structures

Bibliography: De Souza, V.C.M. e Ripper, T. – Pathology, Rehabilitation and Strengthening of Structures, PINI; fib – Model Code for Service Life Design, 2006; fib – Model Code 2010; Selected Papers

Syllabus: Continuum mechanics, potential and elasticity problems, fundamentals of differential geometry, fundamental solutions and Green’ functions; numerical integration; generalized inverse matrices and structural analysis. The stationary total potential energy: from the virtual work principle to displacement, force and mixed formulations; strong, weak and inverse formulations; weighted residual methods. The conventional boundary element method; numerical implementations for potential and elasticity problems of finite and open domains; integration and linear-algebra issues. The hybrid boundary element method: The Hellinger-Reissner potential, mixed and hybrid virtual-work concepts; integration and linear-algebra issues; simplified versions of the method; application to some particular cases; numerical implementations. Application to fracture mechanics and time-dependent problems, among other problems

Bibliography: A. E. H. Love, A Treatise of the Mathematical Theory of Elasticity, 4th ed., Cambridge Univ. Press, 1927. C. A. Brebbia, J. C. F. Telles, L. C. Wrobel, Boundary Element Techniques, Springer-Verlag, 1984. A. Ben-Israel, T. N. E. Greville, Generalized Inverses: Theory and Applications, Robert E. Krieger Publ. Co. New York, 1980. K. Washizu, Variational Methods in Elasticity and Plasticity, 2nd ed., Pergamon Press, 1973. N. A, Dumont, technical papers, lecture notes

Syllabus: Fundamentals of Nonlinear Structural Analysis. Review of continuum mechanics. Types of non-linear formulations. Total Lagrangean formulation. Geometrically Nonlinear Finite Elements : bar, beam, continuum. Solution methods for non-linear systems. Critical points. Finite deformations. Introduction to non-linear material behavior

Bibliography: Klaus, J.B., 1996, Finite Element Procedures, Prentice Hall; Belytschko T.; Liu, W.K. & Moran, B., 2001, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons; Crisfield, M.A., 2001, Nonlinear Finite Element Analysis for Solids and Structures vol. I & II, John Wiley & Sons Ltd

Syllabus: Finite Element Method: basic concepts; Finite Element Process; 3D Modeling of structures; Linking Modeling and Analysis; Rigid Links, Constraints and Offsets; Modeling Building Structures; Modeling Bridges; Structural Dynamics in the Finite Element Method; Thermal Loads and their Effect

Bibliography: R. D. Cook, D. S. Malkus and M. E. Plesha, Concepts and Applications of Finite Element Analysis, Fourth Edition, John Wiley & Sons, Inc., 2002. W. McGuire, R.H. Gallagher, and R.D. Ziemian. Matrix Structural Analysis, 2nd Edition. John Wiley & Sons, Inc., 2000. D. L. Logan. A First Course in the Finite Element Method, 3rd Edition. PWS Publishing Co., 2002. R. D. Cook. Finite Element Modeling for Stress Analysis. John Wiley & Sons, Inc., 1995. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: Volume 1, Basic Formulation and Linear Problems, 4th Edition. McGraw-Hill, 1975. W. F. Carroll. A Primer for Finite Elements in Elastic Structures. John Wiley & Sons, Inc., 1999. N. Ottosen and H. Petersson. Introduction to the Finite Element Method. Prentice Hall 1992. S. P. Timoshenko and J. N. Goodier. Theory of Elasticity, 3rd Edition. McGraw-Hill, 1970. L. P. Felton and R. B. Nelson. Matrix Structural Analysis. John Wiley & Sons, Inc., 1997

Syllabus: Engineering workflow; Business models in the AEC industry; The concept of BIM; Computational systems to support BIM activity; Electronic data management systems; Constructibility; Interoperability

Bibliography: Eastman, C., Teichols, P., Sacks, R., & Liston, K. BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers, and Contractors. Second Edition, John Wiley & Sons, Inc., 2011. Hardin, B., BIM and Construction Management: Proven Tools, Methods, and Workflows, Wiley Publishing, Inc., 2009. Krygiel, E., Nies, B., & McDowell,S. Green BIM: Successful Sustainable Design with Building Information Modeling, Wiley Publishing, Inc., 2008. Read, P., Krygiel, E. & Vandezande, J., Autodesk Revitt Architecture 2012 Essentials, John Wiley & Sons, 2011. Lima, C. C., Autodesk, Revit Architecture 2013 – Conceitos e Aplicações, Ed. Erica, 2012

Syllabus: Programming in C and data structures. Notions of graphics hardware architecture. Event driven graphics interface programming. Two-dimensional graphics systems architecture. Plane and space geometric transformations. Parallel and perspective projections. Three-dimensional visualization techniques. Finite-element visualization techniques. Development of interactive-graphics programs for finite-element models

Bibliography: Rogers, D.F., Adams, J.A., 1990, Mathematical Elements for Computer Graphics, second Edition, McGraw-Hill International Editions, Computer Series; Rogers, D.F., 1985, Procedural Elements for Computer Graphics, McGraw-Hill International Editions, Computer Series; Foley, J.D., Van Dam, A., Feiner, S., Hughes, J., 1995, Computer Graphics: Principles and Practice, Second Edition in C, Addison-Wesley; Woo M., Neider J. & Davis T., 1998, OpenGL 1.2 Programming Guide. The Official Guide to Learning OpenGL, Addison-Wesley; Angel E., 1997, Interactive Computer Graphics: a Top-Down Approach with OpenGL, Addison-Wesley; selected technical articles

Syllabus: Object-oriented programming. Graphics systems with interactive input data. Geometric modeling. Curves and surfaces. Finite element mesh generation. Scientific Visualization

Bibliography: B. Stroustrup, 2000, The C++ Programming Language, Addison-Wasley, 3rd edition; Rogers, D.F., Adams, J.A., 1990, Mathematical Elements for Computer Graphics, second Edition, McGraw-Hill International Editions, Computer Series; Rogers, D.F., 1985, Procedural Elements for Computer Graphics, McGraw-Hill International Editions, Computer Series; Foley, J.D., Van Dam, A., Feiner, S., Hughes, J., 1995, Computer Graphics: Principles and Practice, Second Edition in C, Addison-Wesley; Woo M., Neider J. & Davis T., 1998, OpenGL 1.2 Programming Guide. The Official Guide to Learning OpenGL, Addison-Wesley; Angel E., 1997, Interactive Computer Graphics: a Top-Down Approach with OpenGL, Addison-Wesley; selected technical articles

Materials Engineering and Chemical and Metallurgical Processes

Versatility is one of the main characteristics of the graduate program offered in the Department of Materials Engineering. The M.Sc. and D.Sc. programs, implemented in 1971 and 1991 respectively, receive students from a large variety of related areas to pursue studies on the wide range of materials and industrial processes addressed by our Department and to integrate their research with environmental issues.

The program caters for both graduates holding a degree in Materials and for professionals of other areas, since the professors are involved in research that covers diverse areas of Materials Engineering as well as Chemical and Metallurgical Processes, encompassing such fields as mineral technology, environmental technology, the chemical processing of raw materials for the production of materials and for the analyses of structural and mechanical properties.

Because of its association with the industry, the Program of Materials Engineering and Chemical and Metallurgical Processes also focuses on issues concerning the control and preservation of the environment.

Additional information can be found, in Portuguese, here


Syllabus: Student presentations of their research progress
Syllabus: Laws of thermodynamics; phase equilibrium in one component systems; behavior of gases and chemical reactions involving gases; reactions involving gas and condensed phases, solid and liquid solutions; equilibrium diagrams and Gibbs energy; reactions involving ionic solutions

Bibliography: DeHoff, R. T., Thermodynamics in Materials Science, McGraw-Hill, Inc., New York, 1993

Syllabus: Chemical bonds. Crystalline and amorphous materials. Polymorphism. Atomic disorder in solids. Point defects. Line defects: the principles of dislocations theory and plastic flow. Grain boundary and polycrystals. Metallic phases. Introduction to the Fe-C diagram. Hardening. Fundamentals of the elasticity theory. Metallic, ceramics., polymeric and composite materials. Principles of failure analysis: fracture and corrosion

Bibliography: W. D. Callister, Materials Science and Engineering – An Introduction, John Wiley, 1994

Syllabus: The field transformations dimensional nano, micro and mesoestruturals in materials. Diffusion. Nucleation and growth. Recrystallization. Solidification. Difusional transformations: spinodal decomposition. Precipitation from solid solution, stability and phase transition kinetics, thermo mechanical processing. Adifusional transformations: martensite

Bibliography: W. D. Callister, Materials Science and Engineering – An Introduction, John Wiley, 1994

Syllabus: Function of one variable; limit; derivative; integral. Functions of Several Variables, partial derivative, differentials. Linear regression. Basic Statistics

Bibliography: Gonçalves, M. B. e Flemmin, D. M; Cálculo A: funções, limite, derivação, integração; São Paulo, Markron, 1999. Craizer, M. ; Tavares, G. . Cálculo Integral a Várias Variáveis. 1. ed. Rio de Janeiro: Editora PUC-Rio, 2002. Costa, A. F. B. ; Epprecht, E. K. ; Carpinetti, L. C. R. . Controle Estatístico de Qualidade. 2. ed. São Paulo – SP: Atlas, 2005

Syllabus: Laws of thermodynamics. Thermodynamic equilibrium criteria. Thermodynamic stability criteria. Chemical reactions, solutions and phase diagrams. Statistical thermodynamics and condensed and gaseous solutions models. Relation between Gibbs energy and the phase diagram

Bibliography: DeHoff, R. T.,Thermodynamics in Materials Science, McGraw-Hill, Inc., New York, 1993. Graetzel, M. and Infelta, P., The Bases of Chemical Thermodynamics, vol. 1 e 2, Universal Publishers, Parkland, FL, 2000. Lupis, C. H. P.; Chemical Thermodynamics of Materials, North-Holland, New York, 1983

Syllabus: Thermodynamic equilibrium in multi-component systems. Gibbs phase rule. Gibbs energy versus composition and phase diagrams. Introduction to the Thermo Calc. Systems one, two or more components; Calculation of binary, ternary, isopleth, predominance and Pourbaix diagrams. Applications in materials development and environmental control

Bibliography: Rhines, F.N., Phase diagrams in metallurgy : their development and application, McGraw-Hill Publishing Co., New York, 1956. Hillert, M.; Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis, Cambridge University Press, Cambridge, 1998

Syllabus: Description of a fluid in motion. Conservation of mass. Conservation of momentum. Conservation of energy. Laminar flow of Ideal and viscous fluids. Turbulent flow. Flow in closed conduits. Steady-state conduction. Unsteady-state conduction, Convective heat transfer. Radiation heat transfer. Steady-state molecular diffusion. Unsteady-state molecular diffusion. Convective mass transfer. Convective mass transfer between phases

Bibliography: Welty, J.R., Wicks, C.E., Wilson, R.E. and Rorrer, G., Fundamentals of Momentum, Heat, and Mass Transfer, 4th Edition, John Wiley & Sons, 2001. Gaskell, D.R., An Introduction to Transport Phenomena in Materials Engineering, Macmillan, 1992. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., Transport Phenomena, John Wiley & Sons, 1960. Incropera, F.P., Dewitt, D. P., Fundamentos de Transferência de Calor e de Massa, 5ª Edição, Livros Técnicos e Científicos Editora S.A., 2003

Syllabus: Optical spectroscopy. Mass spectroscopy. Atomic absorption and emission. X-Ray Fluorescence Microprobe. Calorimetry, and other characterization techniques

Bibliography: Metals Handbook, Vol 10, Ninth edition, Microstuctural Characterization, ASM , 1986. Brandon, D. and Kaplan, W. D., Microstuctural Characterization of Materials, J. Wiley, 1999

Syllabus: Introduction to analytical electron microscopy (AEM), electron sources and detectors. Alignment and calibration. Types of Images in AEM: bright field, dark field, electron diffraction, energy dispersive spectroscopy, enegy loss spectroscopy, scanning transmission electron microscopy (STEM), convergent beam and microdiffraction

Bibliography: Williams, D.B. and Carter, C.B., Transmission Electron Microscopy (a textbook for Materials Scienece, Plenum, 1996. Hirsch, P., Howie, A., Nicholson, R. B., Pashley, D. W. and Whelan, M. J., Electron Microscopy of Thin Crystals, R. Krieger, 1977

Syllabus: Digital image processing sequence. Sampling and quantization. Types of scanners. Image files. Point operations. Algebraic operations. Local operations. Geometric operations. Fourier Transform and its properties. Discrete Fourier transform and fast Fourier transform. Image segmentation. Thresholding and edge detection. Morphological operations. Attribute Extraction, size measurement, shape, position, intensity and texture. Pattern classification and recognition

Bibliography: Russ, J.C., Computer-Assisted Microscopy, Plenum Press, 1991 e The Image Processing Handbook, CRC, 1992. Gonzalez, R.C. and Woods, R., Digital Image Processing, Addison-Wesley,1993. Castleman, K. R., Digital Image Processing, Prentice Hall,1979. Paciornik, S. and Mauricio, M.H.P., Digital Imaging, in ASM Handbook: Metallography and Microstructures, 2004. Gomes, O., Processamento e Análise de Imagens aplicados à Caracterização Automática de Materiais, Dissertação de Mestrado, PUC-Rio, 2001

Syllabus: Microscopic techniques for characterization of materials. Quantitative data from microscopy. Optical microscopy, contrast, diffraction and resolution. Scanning electron microscopy, image formation, secondary and back-scattered electrons. Spectroscopy of X-Ray emission. Transmission electron microscopy fundamentals, image formation, diffraction and phase contrast, bright field, dark field. Images acquisition, processing and digital analysis. Digital microscopy

Bibliography: Microscopia óptica, Goldstein, J.I., Scanning Electron Microscopy and X-Ray Microanalysis, Kluwer Academic/Plenum Publishers, 2002. Williams, D. and Carter C. B., Transmission Electron Microscopy, Kluwer Academic/Plenum Publishers, 1997

Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: Reflection and diffraction of X-rays. Crystallography, symmetry and description of a crystal by asymmetrical positions. Equations diffracted intensity. Equations of reflection of X-rays. The Rietveld method and its applications. Introduction to structure determination by X-ray diffraction

Bibliography: Elements of X-Ray Diffraction, 2a Edição, B. D. Cullity, Addison-Wesley Pub. Co., Reading, MA, 1978. The Rietveld Method, R. A Young (ed.), Oxford Science Publications e International Union of Crystallography, Oxford, 1995. X-Ray Diffraction in Crystals, Imperfect Crystals and Amorphous Bodies, A Guinier, Dover Publications, New York, 1994

Syllabus: Condensed matter fundamentals. Periodicity and crystallographic symmetry. Diffraction in crystals. Reciprocal lattice. Dislocation theory. Point and planar defects. Defects interaction. Movement of dislocations. Applications to deformation processes

Bibliography: Kittel, C., Introduction to Solid State Physics, John Wiley and Sons, 2005. Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Holt Rinehart and Winston, International edition,1987. Weertman, J. and Weertman, J. R., Elementary Dislocation Theory, Oxford University Press, 1992

Syllabus: Detailed solutions of Fick’s laws on stationary and transients systems. Diffusion mechanisms in metallic materials, ceramic, polymer, liquid and amorphous solids. Phenomenological model of diffusion: mobility and chemical activity. Diffusion in dilute and concentrated alloys. Diffusion in multi-component systems. Materials with high diffusivity: thin films, nano-crystalline materials, materials with plastic deformation

Bibliography: Shewmon, P.G., Diffusion in Solids, 2a Edição, McGraw-Hill, New York, 1998. Crank, J.; The Mathematics of Diffusion: 2a Edição, Clarendon Press, Oxford, 1975

Syllabus: Driving force in the phase transformation. Nucleation and growth theory. Spinodal decomposition. Transformations controlled by diffusion or reaction at the interface. Models of microstructure evolution. Martensitic transformations

Bibliography: Martin, J. W., R. Doherty, D. and Cantor, B., Stability of Microstructure in Metallic Systems, Cambridge, 1997. Christian, J., The Theory of Transformations in Metals and Alloys, Pergamon, 1975

Syllabus: Elastic behavior of solids. Dynamics of dislocations and flow mechanisms in crystalline materials. Mobility of dislocations in imperfect crystals. Plastic deformation in mono and poly-crystals. Hardening mechanisms. Thermo-mechanical treatments. Materials composites. Behavior at high work temperatures. Fluency. Behavior in cryogenic condition. Brittle fracture. Fracture under monotonic and dynamic loadings

Bibliography: Dowling, N. E., Mechanical Behavior of Materials, Prentice-Hall, 1993. Courtney, T. H., Mechanical Behavior of materials. McGraw Hill, New York, 1990. Dvorak, G. J., Research Trends in Solid Mechanics. Elsevier Science, Oxford, 2000. Broek, D., The Practical Use of Fracture Mechanics. Kluwer Academic Publishers, Dordrecht, 1989

Syllabus: Theoretical fracture resistance of structural materials. Effect of discontinuities. Crack nucleation. Thermodynamic aspects of the fracture. Loading modes. Factor elastic stress concentration. The crack extension force. Plastic zone. Unstable fracture. Tenacity test. Dugdale, Wells and Rice Theories. CTOD Parameters (Crack Tip Opening Displacement) and J-Integral. Stable crack growth. Resistance curves. Micro-mechanisms of fracture. Microstructure and fracture resistance. Models of fracture. Fatigue. Fluency. Mechanisms of accumulation of damage in advanced materials

Bibliography: Broek, D., Elementary Engineering Fracture Mechanics. Kluwer Academic Publishers, Dordrecht, 1986. Anderson, T. L., Fracture Mechanics – Fundamentals and Applications. CRC Press, New York, 1995. Suresh, S., Fatigue of Materials. Cambridge University Press, Cambridge, 1994. Rossmanith, H. P., Teaching and Education in Fracture and Fatigue. Chapman & Hall, London. 1996. D. F. Socie and G. B. Marquis, Multiaxial Fatigue. SAE International, Warrendale, 2000

Syllabus: Origin and nature of residual tensions. Formation of residual tension in welded joints. Surface Treatments. Techniques for evaluating residual tension. Interaction between primary and secondary tensions. Influence of residual tension on the integrity of structural and mechanical components. Fatigue in the presence of fields of residual tension. Effect of residual tension in the stress corrosion cracking. Numerical analysis of the fields of residual stresses. Residual stress relief

Bibliography: Macherauch, E. and Kloos, K. H., Residual Stresses in Science and Technology. DGM Publication, Oberursel, 1997. Throop, J. F. and Reemsnyder, H. S., Residual Stress Effects in Fatigue. ASTM Publication, Warrendale, 1991. Allen, J. S. et al., Residual Stresses and Their Effect. The Welding Institute Publication, Cambridge, 2001

Syllabus: Fracture resistance of structural materials. Parameters K, CTOD and J. Evaluation of fracture behavior of structural components. Tests on large plates. Evaluation of fracture risk in welded joints. Microstructural and mechanical heterogeneities. Effect “mis-match” and “pop-in” behavior. Defects importance. Integrity of structural components. CTOD curves for projects. Failure analysis diagrams. Document R6. Engineering modeling. The master curve for determining the transition temperature structural steels. Based risk inspection

Bibliography: Jones, D. R. H., Failure Analysis – Case Studies, Elsevier Science, Oxford, 1998.CEGB, Application of the CEGB Failure Assessment Procedure R-6 to Structural Integrity – Research Report R88, Central Electric of Great Britain, Gloucester, 1992. BSI, Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures / BS 7910:1999, British Standard Institution, London, 1999. Edwards, J. H. et al., Structural Integrity in the 21st Century, EMAS Publishing, Solihull, 2000. API, Fitness-for-Service – API Recommended Practice 579, American Petroleum Institute, Washington D.C., 2000. API, Risk-Based Inspection – API Recommended Practice 580, American Petroleum Institute, Washington D.C., 2002

Syllabus: Ceramic materials atomic bonds. Crystal structures, atomic packing and interstices. Glasses and their properties. Point defects and their influence on the electrical properties of ceramic materials. Ceramics phase equilibrium diagrams. The effect of microstructure on thermal and mechanical properties. Reactions involving solids, diffusion, grain growth and phase transformation in ceramic systems

Bibliography: Chiang, Y-M., Birnie, D. and Kingery, W. D., Physical Ceramics, Wiley-MIT, 1997. Kingery, W. D., Bowen, H. K. and Hulman, D. R., Introduction to Ceramics”, J. Wiley, 1976

Syllabus: Definition and classification of polymeric materials. Polymerization reactions. Characteristics of the macromolecular structure. Structural parameters: polymerization grade, crystallinity, molecular weight. Mechanical properties. Deformation processes versus time. Additives. Manufacturing processes. Recycling

Bibliography: Billmayer Jr., F. W., Textbook of Polymer Science, Interscience Publishers, New York, 1982. Mano, E.B., Introdução a Polímeros, Ed. Edgard Blücher, São Paulo, 1985. Elias, H.G., An Introduction to Polymer Science, VCH Publishers, New York, 1997

Syllabus: Definition and classification of composite materials. Elasticity theory review for anisotropic, orthotropic and isotropic materials. Macro-mechanical behavior. Laminate Composites. Analysis of laminated structures. Failure criteria

Bibliography: Chawla, K. K., Composite Materials, Science and Engineering, Springer Verlag, 1998. Jones, R. M., Mechanics of Composite Materials, Taylor and Francis Inc., 1999. Agarwal, B.D., Broutman, L. J. and Chandrashekhara, K., Analysis and Performance of Fiber Composites, John Wiley and Sons Inc., 2006. Gibson, R. F., Principles of Composite Materials Mechanics, McGraw-Hill, 1994

Syllabus: Classification of welding processes. Fusion welding. Solid state welding. Welding thermal cycle. Heat affected zone. Ferrous alloys Weldability. Non-ferrous alloys Weldability. Microstructural transformations. Brazing. Welding of Plastics. of Composites union. Ceramic union. Principles of adhesion

Bibliography: Schwartz, M. M., Joining of Composite Matrix Materials, ASM International, 1994. Linnert, Welding Metallurgy, vol.1, AWS, 1994. Granjon, H., Fundamentals of Welding Metallurgy, Abington Publishing, 1994. Easterling, K. E., Introduction to the Physical Metallurgy of Welding, 1985. O’Brien, R.L. (Editor), Welding Handbook, vols. 1, 2, 3 e 4, AWS, 8th edition,1996

Syllabus: Interactions between electron beam and matter. Electron optics of TEM. Reciprocal lattice and electron diffraction process. Selected area and convergent beam diffraction. TEM images types and properties. Kinematic and dynamic theory. Planar defects and interfaces. Dislocations. Phase contrast image. Moiré fringes. High resolution Microscopy. The transfer function and the atomic scale resolution. Applications

Bibliography: D.B. Williams and C.B. Carter, “Transmission Electron Microscopy (a textbook for Materials Science”, Plenum, 1996

Syllabus: Fundamentals of Corrosion phenomena. Galvanic corrosion. Selective corrosion. Pitting corrosion and cracks. Stress corrosion and hydrogen embrittlement, corrosion under fatigue. Inter-granular corrosion. Atmospheric corrosion. Corrosion by ground. Corrosion in concrete. General aspects of corrosion protection. Protection by metallic and organic coatings. Corrosion Inhibitors. Cathodic Protection. Kinetics of metal bio-corrosion processes. Bio-film formation. Mechanisms, inhibition, detection, and prevention of bio-corrosion

Bibliography: Ramanathan, L. V., Corrosão e seu Controle, Hemus Editora Limitada, Brasil, 1994. Fontana, M. G., Corrosion Engineering, 3th Edition, McGraw-Hill, 1987. Roberge, P. R., Handbook of Corrosion Engineering, McGraw-Hill; 2000

Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: Fluids. Statics, kinematics and dynamics of fluids. Fluid masses subjected to acceleration. Fluid-solid systems. Drag forces. Fixed and movable bed. Fluidization. Pneumatic transport. Fluid flow in “dry” and “drained” porous beds. Fluidization diagrams. The fluid dynamics in process engineering. Case studies

Bibliography: Vennard, J. K., Elementary Fluid Mechanics, John Wiley & Sons, 1995. Fox, R. W. and McDonald, A. T., Introduction to Fluid Mechanics, John Wiley & Sons, 2005. Kunii, D. and Levenspiel, O., Fluidization Engineering, Butterworth-Heinemann; 2006. Szekely, J. and Themelis, N. J., Rate Phenomena in Process Metallurgy, John Wiley & Sons, 1971

Syllabus: Overview on mineral processing. Mineral liberation and Mineral liberation spectra. Fundamentals on Comminution; primary, secondary and tertiary crushing / grinding. Flowsheets design Screening and Classification in Hydrocyclones, Mineral Concentration: gravity concentration, flotation, magnetic and electrostatic separation. Dewatering: thickening. Examples of mineral processing flow sheets

Bibliography: Wills, B.A.; Mineral Processing Technology, Elsevier Ltd, 2006. Fuerstenau, M. C. and Han, K. N.; Principles of Mineral Processing, Soc for Mining Metallurgy and Explorations, 2003

Syllabus: Thermodynamics and kinetics fundamentals. Reactors mole balances. Industrial reactors. Conversion and reactor sizing. Rate laws and stoichiometry. Isothermal reactor design. Analysis of experimental results. Heterogeneous reactions, mechanisms and controlling step. Characteristics of heterogeneous reactions. Fluid-solid reactions. Kinetic modeling

Bibliography: Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice-Hall International, 1996. Levenspiel, O., Engenharia das Reações Químicas, Edgard Blucher Ltda, 1974. Smith, J. M., Chemical Engineering Kinetics, McGraw-Hill Book Company, 1981. Szekely, J., Evans, J. W. and Sohn, H. Y., Gas-Solid Reactions, Academic Press, 1976. Sohn, H.Y. and Wadsworth, M.E., Rate Processes of Extractive Metallurgy, Plenum Press, 1979

Syllabus: Fundamentals of Aqueous Solutions Physical-Chemistry. Thermodynamic stability diagrams. Speciation in aqueous solutions. LogC x pH and Eh x pH diagrams. Bio and Hydrometallurgical processes: leaching, bioleaching, ion exchange resins, solvent extraction, precipitation processes of metals in solutions. Fundamentals of Electrowinnig and eletrorefining Case studies

Bibliography: Butler, J. N.; Ionic Equilibrium, John Wiley and Sons Inc., 1998. Han, K. N.; Fundamentals of Aqueous Metallurgy, Soc for Mining Metallurgy and Explorations, 2002. Jackson, E., Hydrometallurgical Extraction and Reclamation (Ellis Horwood Series In Industrial Metals), Halsted Press, Chichester, 1986

Syllabus: Fundamentals of electrochemistry. Thermodynamic Fundamentals. Nernst equation. Overpotentials. Electrochemical kinetics. Electrometallurgical processes for extracting metals. Electrorefining and electrowinning. Electrochemical applied to effluent treatment and metal removal

Bibliography: Bockris, J. O’M. and Reddy, K. N. A; Modern Electrochemistry 1: Ionics, Plenum Publishers, 1998. Bockris, J. O’M. and Reddy, K. N. A; Modern Electrochemistry 2A: Fundamentals of Electrodics, Plenum Publishers, 2000. Bockris, J. O’M. and Reddy, K. N. A; Modern Electrochemistry 2B: Electrodics in Chemistry, Engineering, Biology and Environmental Science, Plenum Publishers, 2000

Syllabus: Physical-chemistry of high temperature reactions: Equilibrium composition diagrams applied to processes. High-temperature operations: roasting, smelting, oxidation and reduction. Synthesis of materials. Methods of metals refining. Environmental considerations

Bibliography: Hayes, P., Process Principles in Minerals & Materials Production, Hayes Publishing Co; 3rd edition, 2003. Moore, J.J., Chemical Metallurgy, Butterworth-Heinemann; Reprint 2nd edition, 1993

Syllabus: Study of surfaces and interfaces. Surface Chemistry Fundamentals. Surface tension. Evaluation methods of surface tensions. Adsorption on Interfaces. Adsorption isotherms. Physical and chemical adsorption. Electrical double layer. Aqueous systems. Industrial applications: colloids, homogeneous precipitation, nanoparticles, foams and flotation

Bibliography: Hunter, R.; Foundations of Colloid Science, vol. I & II – Oxford University Press, 2001. Adamson, A. W., Physical Chemistry of Surfaces, 6th Edition, Jonh Wiley & Sons, New York, 1997. Jolivet, J.-P. Metal Oxide Chemistry and Synthesis: From Solution to Solid State, Jonh Wiley & Sons, New York, 2000

Syllabus: Thermodynamic of Iron & Steelmaking processes. Diagrams: Fe-O, Fe-C-O, Fe-H-O and Fe-C-H-O. Slags. Elements behavior in refining. Desulphurization, Dephosphorization and Deoxidation. Kinetics of Iron & Steelmaking processes. Models and mechanisms. Fundamentals of new technologies. Case studies

Bibliography: Von Bogdandy, L. and Engell, H. J., The Reduction of Iron Ores, SV Berlin Heidelberg, 1971. Turkdogan, E. T., Fundamentals of Steelmaking, The Institute of Materials, London, 1996. Ghosh, A., Secondary Steelmaking, CRC Press, 2000. Fruehan, R. J. (editor), The Making, Shaping and Treating of Steel, Iron making & Steelmaking vols, 11th. ed, AIST Steel Foundation, 1998. Omori, Y., and Nihon, T. K., Blast Furnace Phenomena and Modeling, Elsevier, London

Syllabus: Industrial wastewater treatment processes. Pretreatment and primary treatment: equalization, neutralization, settling, filtration, oil-water separation, flotation. Coagulation and flocculation. Chemical precipitation. Biological treatment operations. Ion exchange. Chemical oxidation. Industrial reuse of water. Waste gas scrubbing

Bibliography: Eckenfelder, W.W., Industrial Water Pollution Control, 2nd. edition, McGraw-Hill, 1989

Syllabus: Generation of wastewater in industry. Legal conditions for wastewater disposal. Physical-chemistry of aqueous solutions. Equalization and Neutralization. Degradation of organic matter: biological oxidation, adsorption, chemical oxidation. Removal of heavy metals: Precipitation, Coagulation and Flocculation. Oxidation of sulfides/sulphites, nitrites and cyanides. Fluoride removal. Reverse osmosis. Ion exchange. Advanced oxidation processes. Industrial reuse of water. Sedimentation and filtration

Bibliography: Eckenfelder, W.W., Industrial Water Pollution Control, 2nd. edition, McGraw-Hill, 1989. Lora, E.E.S., Prevenção e Controle de Poluição nos Setores Energético, Industrial e de Transporte, Interciência, 2a. Edição, Rio de Janeiro, 2002

Syllabus: Uses of water in industry. Water permits, reuse of water in industry. Conventional treatment: coagulation, flocculation, decantation, filtration, disinfection. Anti-scaling treatments. Anti-corrosive treatments. Softening. Purification. Advanced treatments

Bibliography: Mierzwa, J.C. e Hespanhol, I., Água na Indústria – Uso Racional e Reuso, Oficina de Textos, S. Paulo, 2005. Pereira, C., Tratamentos Físico-Químicos de Águas, Vol. 1, UERJ – Campus Regional de Resende, 2001

Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The subject depends on the interest of the department
Syllabus: The students must register in this course after having completed the necessary credits for Masters Degree
Syllabus: The students must register in this course after having completed the necessary credits for Doctorate Degree
Syllabus: Students must register in this course to attend the Doctorate qualifying exam
Syllabus: Students must register in this course to defend his Doctorate Thesis Proposal
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses
Syllabus: Teaching activities in undergraduate courses

Production Engineering

The M.Sc. program in Production Engineering, which started in 1967, is the oldest of its kind in Brazil. In 1992, the Ph.D. program was implemented. The graduate programs of the Department of Industrial Engineering focus on the analytical and quantitative study of production systems in the areas of Operations and Production Planning, Transportation and Logistics Planning, Production and Operations Scheduling and Control, Transportation and Logistics Scheduling, Capital Markets and Corporate Finance.

The investigation of management issues that are relevant for Brazilian enterprises and the focus on research applied to organizations provide the preparation of highly qualified managerial personnel for the industry, as well as excellent professionals with an academic profile for teaching and research..

Additional information can be found at the Department’s site, in Portuguese, here.


Syllabus: Introduction to stochastic processes. Markov chains. Birth-death processes. Queueing Theory. Single-server models. Steady-state solution. Transient behavior. Other queueing models: multiple servers, system with limited capacity, finite source, general distribution of service times. Practical issues (determining the distributions of arrival and service times, models for dimensioning queueing systems). Introduction to simulation of queueing systems

Bibliography: 1)Wayne L. WINSTON: OPERATIONS RESEARCH: APPLICATIONS AND ALGORITHMS. Hamdy A. TAHA:OPERATIONS RESEARCH: AN INTRODUCTION Editora: Macmillan. Averill M. LAW & W. David KELTON: SIMULATION MODELING AND ANALYSIS McGraw-Hill Series in Industrial Engineering and Management Science

Syllabus: Basic concepts on graphs: Connectivity, Paths, Chains, circuits and cycles; trees and arborescences. Optimal trees and arborescences. Representation of graphs in computers. Shortest Paths Models. Methods for networks with positive and negative costs. Calculation from one origin to all destinations and between all origins and destinations. Network flow assignments. Assignment models with and without congestion. Network equilibrium problems. Optimality Conditions. Multimodal Multiproduct assignment. Maximum Flow and Minimum Cost Problems

Bibliography: Ahuja, R.K, Magnanti, T.L, Orlin, J.B (1993). Network Flows. Prentice Hall, New Jersey

Syllabus: Probability: axioms and theorems. Conditional probability. Independence. random variables, mass probability function, probability density, distribution function. Moments and properties. Moment generating function. Most important discrete and continuous distributions. Random vectors. Joint, marginal and conditional distributions. Covariance and correlation. Conditional expected value. Independent random variables. Functions of random variables. Sum and linear combination of random variables. Central Limit Theorem. Normal approximations. Sampling. Estimators and properties. Estimation methods. Sampling distributions. Confirdence intervals. Hypothesis testing

Bibliography: Montgomery, Douglas C., e Runger, George C.: Estatística Aplicada e Probabilidade para Engenheiros. 2a edição, LTC Editora, Rio de Janeiro, 2003

Syllabus: Basic concepts of Mathematics: linear systems, vector spaces, and convexity. Non-linear optimization with and without constraints: function of one and several variables. Optimality conditions. Lagrange multipliers. Linear optimization: graphical solution, the Simplex Method, duality, sensibility analysis, dual-simplex method, revised simplex, Dantzig-Wolfe decomposition, and column generation. Linear integer programming: cutting plane, branch and bound methods, and applications

Bibliography: Pizzolato, Nelio D. and Gandolpho, André A. Técnicas de Otimização. 1. ed. Rio de Janeiro: LTC – Livros Técnicos e Editora LTDA. 2009. v. 1, 227 p

Syllabus: Time value of money and theories of interest rates. Capital budgeting criteria. Cash-flow calculations. Long-term financial debt and leasing. Structure of the cash-flow for economic projects analysis. Operating leverage and break-even point: cost-volume-profit analysis. More advances techniques for economic projects analysis: sensibility analysis, monte carlo simulation and decision tree. Risk, return and uncertainty. Portfolio theory: diversification, the efficient frontier and the choice of optimal portfolio. Financial market equilibrium and the capital asset pricing model (CAPM) and its extensions. The cost of capital. Financial leverage, capital structure and the MM theorems. Operating and financial performance of companies. Valuation techniques. Options contracts and basic properties. Valuation of options, binomial model, risk-neutral pricing, Black-Scholes formula. Real option analysis and the value of intangibles and flexibilities of investment projects

Bibliography: Copeland, T.E; Weston, J.F; “Financial Theory and Corporate Policy”, Addison Wesley- 4th Edition- 2005. Brealey & Myers; “Principles of Corporate Finance”, McGraw-Hill.- 9th Edition 2008

Syllabus: Black and Scholes Model of Option Pricing. Geometric Brownian Motion, Itó Process and Log Normal Distribution. Cox and Ross Risk Neutral Model. Cox, Ross and Rubinstein Binomial Model. Exotic Options. Rational Option Pricing Theory of Merton

Bibliography: Black, F. and Scholes, M., 1973, “The Princing of Options and Corporate Liabilities”, Journal of Political Economy, 81,637-659; Cox, J. C. and Ross, S.A., 1976, “The Valuation of Options for Alternative Stochastic Processes”, Journal of Financial Economics, 3(1/2), 145-166; Cox, J.C., Ross, S.A., and Rubinstein, M., 1979, “Option Pricing: A Simplified Approach”, Journal of Financial Economics, 7(3) 229-263; Merton, R.C., 1973b, “Theory of Rational Option Pricing”, Bell Journal of Economics and Management Science, 4(I), 141-183; Shreve, Steven E., Stochastic Calculus for Finance, New York: Springer – Verlag, 2004; Hull, John., Options, Futures and Other Derivatives Securities, 5th Edition, New York: Prentice-Hall, 2000

Syllabus: Basics of options and real options; arbitrage; parity and symmetry of options. Early exercise premium and dividends. Real options in discrete time: risk-free portfolio, risk-neutral measure; binomial method; complete and incomplete market; hypothesis of market efficiency. Uncertainty and stochastic processes: Geometric Brownian motion, mean reversion, jumps and other processes; seasonality; futures market. Itô-Doeblin formula, optimization under uncertainty and option valuation in continuous time: deduction of the Black-Scholes-Merton differential equation and solution options; integral method optimization and perpetual options. Extensions of the basic model of real options: temporary stopping option; abandonment option, interactions between options and hysteresis option model (entry-exit compound options). Monte Carlo simulation to solve real options: real and risk-neutral simulations; practical cases with correlated stochastic processes. Optional item (if we have time): Technical uncertainty and learning options

Bibliography: Dixit, A.K. & R.S. Pindyck (1994): “Investment under Uncertainty”.Princeton: Princeton University Press, 468 pp. (chapters 3 a 7, 10 e 12); Dias, M.A.G. (2013): “Análise de Investimentos com Opções Reais – Teoria e Prática” (Analysis of Investments with Real Options – Theory and Practice). Textbook in preparation; some parts (chapters) of the book will be provided. Slides, lecture notes, articles and additional materials complement the bibliography

Syllabus: Arbitrage Theorem and Arrow Debreu Security. Markov Process. Martingales Stochastic Differentiation and Integration. Weiner Process and Jump Process. Ito’s Lemma. Black and Scholes Model of Option Pricing. Girsanov’s Theorem. Feyman-Kac Formula

Bibliography: Neftci, S., An Introduction to the Mathematics of Financial Derivatives; London: Academic Press, 2000; Black, F. and Scholes, M., “The Pricing of Option and Corporate Liabilities”, Journal of Political Economy, vol.8 (June 1973), 637-89; Aiube, Fernando A.L., Modelos Quantitativos em Finanças, Porto Alegre: Bookman, 2013

Syllabus: Value; Present Value and the cost of capital; Valuing cash flows in certain and uncertain environments; The multiperiodic CAPM and Projects Valuation; The Value of Information and Monte Carlo Simulation; Decision Trees and Project Valuation Problems in Capital Budgeting; The Theory of Real Options and Capital Budgeting

Bibliography: Dixit, A.A. & Pindyck, R.S. Investment under uncertainty. Princeton University Press, 2004

Syllabus: Individual Decision Making; Choice Rules, Consumer Choice; Demand Functions and Comparative Staties; Classical Demand Theory; The Utility Maximization Problem; Duality; Welfare Evaluation of Economic Changes; Equilibrium and its Basic Welfare Properties; The Production Theory; Efficient Production; The Geometry of Cost and Supply; Profit Maximization and Cost Minimization; The Market Power; Monopoly Pricing; Oligopoly and Static Models; Externalities; Equilibrium and its Basic Welfare Properties

Bibliography: Mass-Colell, A.; Whinston, M.D., Green, J.R. – Microeconomic Theory. Oxford University Press, 1995

Syllabus: Historical approach to the capitalist organisation of work, from craft to mass production: steps in the evolution of organisations; traditional production systems; management and the division of labor; the mass production system. New production systems and paradigm change; lean production; mass customisation; product variety; vertical integration and outsourcing; small and medium companies; industrial clusters and local/regional development; integration and manufacturing flexibili

Bibliography: Braverman,H. – Labor and Monopoly Capital: The Degradation of Work in the Twentieth Century, 1974. Pine II, B.J. – Mass Customization: The New Frontier in Business Competition, Harvard Business School Press, 1993. Piore, M. / Sabel, C. – The Second Industrial Divide, Basic Books Inc., 1984

Syllabus: The strategic aspect of operations management: production of goods and services. Conceptual framework for operations strategy: production strategy, competition in the global level. The search for competitiveness. Changes in technology and work organization. Life cycle of products and their relation to production processes and managerial priorities: life cycle of the product development process, matrix-process product. Learning curves. Economic aspects of production process and planning of investment in capacity and production technology, uncertainty and risk. Demand forecasting: components time series models and estimation methods for long and short term forecast control. Statistical process control: basic concepts, process capability. Charts: fundamentals and main control charts for variables and attributes, performance measures. Factorial experiments: definitions and basic principles

Bibliography: Nahmias, S. Production and Operations Analysis, fifth edition.New York:McGraw-Hill. 2005. Montgomery, D. C., Introduction to Statistical Quality Control, Fourth edition. New York: Wiley. 2001. Silver, E. A., Pyke, D. F. and Peterson, R., Inventory Management And Production Planning and Scheduling, third edition. New York: Wiley.1998. Montgomery, D. C. Design and Analysis of Experiments, 5th ed. New York:Wiley. 2001

Syllabus: To address concepts and stages of production planning and control of some production systems, focusing on the procedures of sales and operations planning for mid- term horizon. Typical problems of inventory and production planning are modeled as mathematical programming problems, which will be solved by a commercial software package. Concepts and stages of production planning and control. Typical problems of inventory and production planning; costs and resources comprehension, as well as constraints of production systems. Mathematical modeling of planning problems into linear and mixed linear programming problems. Mathematical modeling language. Use of the package AIMMS or a similar software package available

Bibliography: Inventory Management and Production Planning and Scheduling, E.A.Silver, D.F.Pyke E R. Peterson, John Wiley and Sons, 3rd edition, 1998; Production Planning by Mixed Integer Programming, Y. Pochet e L.A. Wolsey, Springer, 2006

Syllabus: Analysis of variance with one or more factors. Analysis of the fixed effect model. Model adequacy. Factorial experiments: definitions and basic principles. Fractional factorial experiments. Analysis of response curves and surfaces: estimation and parameters validation. Model adequacy. The method of steepest ascent. Response surface analysis of second order model. Experiments for response surface. Advanced topics on statistical process control: CUSUM and EWMA charts, autocorrelated process control; multivariate statistical process control. Other research topics on statistical process control

Bibliography: Montgomery, D. C. (2001). Design and Analysis of Experiments, 5th ed. Wiley. Myers, R. H. e Montgomery, D. C. (2002). Response Surface Metodology, Wiley. Montgomery, D. C. (2001). Introduction to Statistical Quality Control,4th ed. Wiley

Syllabus: Introduction to Demand Forecast Models. Four steps Model: application to passengers and freight. Freight Transportation modes characteristics. Fleet calculation. Transportation mode and Shipper selection. Introduction to logistics. Design of elements of logistic systems. Spatial metrics and calculation of central points. Design of physical distribution systems. Vehicle Cycle analysis. Considering demand and service stochastic aspects. Districting and fleet definition. Vehicle routing. Logistics costs

Bibliography: Novaes, Antonio Galvao: Sistemas Logisticos. Ed. Bluecher, 1989. Daganzo, Carlos. Logistics Systems Analysis. Springer Verlag, 1996. Bowersox, D.J.; Closs, D.J. Logistical Management. Mcgraw-Hill, 1996

Syllabus: Mathematical programming models applied to logistics, transportation, production planning and control, supply chain management and finances.  Hands-on approach and real cases models. Use of modeling systems. Explicit and Symbolic representation. Linear, Integer and Non-linear programming. Stochastic Programming. Risk and Decision Analysis


Syllabus: The physical distribution systems and the materials management. Components and levels of service. The use of operations research models in the physical distribution systems. The location problem in the plane and in networks. The minimum-spanning tree problem. The inventory control and the production sequencing problem. Design, packing and internal movement. The production system: the production planning, the service to the client, and the channels of distribution. Communications and control: the flow of information, the purchasing cycle and the control of the system

Bibliography: Class notes on: historical development of logistics; inventory control; and sequencing. Larson, Richard C. e Amadeo R. Odoni, Urban Operations Research, Prentice-Hall, Englewood Cliffs, New Jersey, 1981. Nelio D. Pizzolato, Fernanda P. Raupp e Guina Sotomayor Alzamora; Revisão de Desafios Aplicados em Localização com Base em Modelos da p-Mediana e suas Variantes; PODES, Vol. 4, No 1, 2012, pp. 13-42

Syllabus: Supply Chain Definition. Challenges and opportunities of its management. Main enablers: information technology, organizational structure and relationships types/ partnerships. Supply Chain and product Design. Chain analysis and mapping/ Outsourcing. Procurement. Industrial applications and current industry practices. Logistics games

Bibliography: SIMCHI-LEVI, D., KAMINSKY, P, SIMCHI-LEVY, E. Cadeia de Suprimentos: Projeto e Gestão. Bookman, 2003. ISBN: 85-363-0119-8; FAWCETT, S.T, ELLRAM, L.M., OGDEN, J.A. Supply Chain Management: From Vision to Implementation. Pearson/Prentice Hall, 2007. ISBN: 0-13-101504-4; 3)LAMBERT, D. M. Supply Chain Management: Process, Partnerships, Performance. Supply Chain Management Institute, 2004. ISBN: 0-9759949-0-5

Syllabus: The problem of Weber. Discrete models for the location in networks. Location-routing models. Consumers in competitive location models. Meta heuristics and genetic algorithms for the p-median problem. Software for location and interface with geographic information systems. Stochastic demand models. Hub location models

Bibliography: Zvi Drezner e Horst W.Hamacher, editors, Facility Location: Theory. Springer, Berlin 2004; Galvão, R. D., “The use of Lagrangian relaxation in the solution of uncapacitated facility location problems”, Location Science, Vol. 1, pp. 57-70. ReVelle, C.S. e H. A. Eiselt, “Location analysis: a synthesis and survey”, European Journal of Operational Research, Vol 165, 2005,pp. 1-19. Farahani, R.Z. and Hekmatfar (editors) (2009). Facility Location: Concepts, Models, Algorithms and Case Studies: Contributions to Management Science. Physica-Verlag Heidelberg

Electrical Engineering

The activities of the Department of Electrical Engineering started in 1947 when the undergraduate course was first offered. The pioneering M.Sc. program started in 1963 and the Ph.D. program was launched in 1981.

The graduate programs, funded mainly by governmental agencies since the 70’s, have been recognized by scholars and professionals, both nationally and abroad, as a leading force in this field.

This program aims to prepare highly qualified human resources in addition to developing and transferring innovative scientific and technological knowledge to the academic and business world. More than 900 students have graduated with a Master’s degree and 180 have been awarded a Ph.D. over the years. There are currently more than 200 students enrolled in the undergraduate courses.

As Electrical Engineering is a privileged field for interaction with the industrial sector, the program comprises a large diversity of research initiatives lead by its highly qualified faculty members, graduated from top-ranked institutions.

The strongest areas of research are Applied Electromagnetism, Decision Aid Methods, Signal Processing and Control, Communication Systems and Electric Power Systems.

Additional information can be found at the Department’s site, in Portuguese, here.

  • Telecommunications

The Center for Telecommunications Studies (CETUC) is an additional unit created in 1965 to carry out research, to coordinate and conduct teaching activities both in the undergraduate and graduate programs and to develop projects in the area of Telecommunications.

Its teaching activities are achieved through the Department of Electrical Engineering and, in order to fund its research, CETUC maintains agreements with government agencies and contracts with industry. It also provides consulting services and personnel training for telecommunication professionals.

Additional information can be found, in Portuguese, here.

  • ETDs and the Maxwell System

ETDs – Electronic Theses and Dissertations is the international designation of theses & dissertations made available as full-text works from digital libraries or institutional repositories all over the world.

ETDs became mandatory at PUC-Rio from August 01, 2002 on. Before this date, some graduate programs had been using the Maxwell System to publish their ETDs.

The Maxwell System is an institutional repository that hosts and makes available scholarly communication of the university; ETDs are one of the contents on the system.  This system is a product of LAMBDA – Laboratório de Automação de Museus, Bibliotecas Digitais e Arquivos of the Departamento de Engenharia Elétrica. It has been in operation since 1995.

As far as ETDs are concerned the system complies to metadata specifications for these works: MTD-BR – Modelo Brasileiro de Metadados para Teses e Dissertações, the Brazilian National Standard, and ETD-ms – An Interoperability Metadata Standard for Electronic Theses and Dissertations, the international standard. The system is an OAI-PMH – Open Archives Initiative Protocol for Metadata Harvest data provider. Due to these characteristics, PUC-Rio’s ETDs are haversted, indexed and made available from union catalogs all over the world. PUC-Rio joined the MetaArchive Cooperative to assure the digital preservation of the ETD collection hosted by the Maxwell System.

The graduate programs of CTC – Centro Técnico Científico are responsible for more than 50% of the almost 5 thousand ETDs in the collection. Some programs published works presented before 2002  and Electrical Engineering engaged in retrospective digitization of its complete collection, dating back to 1966.

The Maxwell System can be visited here.


Syllabus: Fabrication methods of nanodevices. Electronic and optoelectronic devices based on semiconductor nanostructures. Optical microcavities with quantum dots as active media. Single electron transistor. Single photon source. Devices based on carbon nanotubes and organic materials. Photonic devices
Syllabus: Plane waves: general properties. Spectral decomposition, reflection and refraction. Spectral representation of elementary sources. Green’s functions. Propagation and scattering in circularly and spherically symmetric regions. Approximate methods: WKB solution and geometric optics. Elementary sources in stratified media
Syllabus: Radio wave equation. Optical solution. Eikonal equation. Refractive index of the troposphere. Equivalent radius of the earth. Tropospheric ducts. Radio meteorological parameters. Propagation at frequencies over 10 GHz. Rain attenuation. Crosspolarization due to rain
Syllabus: Fields due to dipoles in the presence of a conducting plane Earth: space and surface waves; Norton approximation. Fields due to dipoles in the presence of a conducting spherical Earth: interference region and the divergence coefficient; shadow region and the residue series. Propagation in stratified media: geometrical optics and WKB solutions. Diffraction of plane waves by a perfectly conducting half-plane. Applications to the analysis of the effects of terrain irregularities on propagation of radio waves. Rain attenuation and scattering: Mie’s theory; particle distributions; determination of the specific attenuation
Syllabus: Introduction. Fundamentals of VHF and UHF propagation. Propagation over irregular terrain. Propagation in built-up areas. Characterization of multipath phenomena. Wideband channel characterization. Specific mobile radio channels. Sounding, sampling and simulation. Man-made noise and interference
Syllabus: Scalar and vector theories of diffraction. Aperture radiation; effects of illumination law and phase errors. Methods of evaluation of radiation integrals. Physical-optics approximation. Sectorial, pyramidal and diagonal horns. Propagation in corrugated waveguides; corrugated horns. Synthesis and analysis of single and dual reflector antennas in symmetric and off-set configurations
Syllabus: High-frequency asymptotics and ray optics. Geometrical optics and geometrical theory of diffraction. High-frequency scattering and applications to the analysis of reflector antennas and ray tracing in cellular environments. Complex rays and evanescent waves
Syllabus: Introduction: Helmholtz equation and the parabolic differential equation approximation; boundary conditions. Finite difference method: approximation of differential operators; solution of parabolic and elliptic differential equations; solution of eigenvalue problems; application to radio wave propagation in the presence of irregular terrain and to the determination of cutoff frequencies of waveguides with arbitrary cross sections. Finite element method: variational and weighted residual formulations; finite elements and local representation of potentials; mesh generation; application to the solution of Helmholtz equation and to the determination of cutoff frequencies of waveguides with arbitrary cross sections. Integral equations for radiation, scattering and propagation problems. Method of moments: expansion and test functions; Galerkin and collocation methods; application to radiation of linear antennas, to scattering of plane waves by cylinders with arbitrary cross sections and to radio wave propagation in the presence of irregular terrain
Syllabus: Signals and Systems discrete in time: classification, invariance, causalty and stability. Representation of discrete signal and Systems. Z transform, discrete-time Fourier transform: definition, properties and couvergence. Discrete Fouries transform: definition and properties. Fast Fourier transform algorithms. Random discrete time signals; concepts, errors and power spectral estimation
Syllabus: Introduction: Review of basic discrete time processing techniques, results and applications, Digital Filter Structures, Digital Filter Design, Software Implementation, Finite Word-Length Effects, Multirate Digital Signal Processing, Applications
Syllabus: Cameras; Geometric Camera Models; Camera Calibration; Epipolar Geometry; Fundamental Matrix Estimation; Matching; Stereoscopy; Structure from Motion; Tracking
Syllabus: Digital Image Fundamentals;  Image Transformations; Enhancement; Restoration; Morphological Image Processing; Segmentation; Features Extraction; Classification
Syllabus: Process modeling and identification practice. Application of reduced order observers and models. Digitalization techniques and their application in control algorithms. Case study: ON-OFF, PID and variations, cacade and feedforward. Process control hardware: AD and DA converters, data input and output, process variables, architecture of dedicated mini and microcomputers, numerical control. Operational systems and languages for process control. Distributed processing. Case study
Syllabus: Linear Graphs: two and four terminals passive elements; variables definitions in several domains; graph generation and equations determination. Bond Graphs: elements of one, two and several ports, definition of constitutive equations, graph generation and equations determination
Syllabus: Basic Features: Learning, Association, Generalization and Robustness; History; Structure of the Artificial Neuron; Artificial Neural Network Topologies; Learning Strategies: Supervised and Unsupervised; Learning Algorithms: Perceptron, Delta Rule, Back Propagation and variations, Self-Organizing Maps, Probabilistic Neural Networks, Radial Basis Function Networks; Applications
Syllabus: Basic concepts; Evolution and natural selection; Genetic Algorithms (GAs) components; Population size; reproduction methods; selection; crossover; mutation; Traditional Genetic Algorithm; GAs Techniques and Parameters; Prisoners Dilemma (Machine Learning); Mathematical Foundations of GAs; Schema Theory; Deception; Epistasis; Combinatorial Problems; Scheduling Problems; Genetic Programming; Evolvable Hardware; GAs Developing Systems; Parallel GAs; Applications
Syllabus: Definitions; Basic Features; Types of Imprecision; Fuzzy Sets, Properties and Characteristics; Logical Operations; T-norms and T-conorms; Hedges; Fuzzy Relations and Compositions; Propositional Logic, Modus Ponens; Fuzzy Logic, Generalized Modus Ponens; Fuzzy Systems: Rule Base, Inference, Fuzzification, and Defuzzification modules; Fuzzy Control; Applications
Syllabus: Data cleaning and integration; data transformation; variables selection; modeling ensembles for classification and forecasting; performance measures; Dealing with uncertainty; Applications
Syllabus: Modeling population dynamics; modeling infectious diseases; population genetics and evolution; molecular biology; metabolic pathways; immunology; pattern formation; tumor modeling
Syllabus: The planning of the distribution systems. The equipment dimensioning of the distribution systems. The operation of the distribution system. The billing of the distribution systems
Syllabus: The restructuring of the electricity sector. The transmission tariff usage. The allocation of the transmission losses
Syllabus: Matrix models of components and systems in steady state. Short-circuit studies. Power flow studies: Gauss-Seidel, Newton-Raphson and decoupled load flow methods, application to multiterminal dc/ac systems. Contingency analysis. Application of sparsity techniques in the solution of electrical networks. Static network equivalents: Ward and REI types
Syllabus: Phenomena characterization by maximum transmission existence and voltage control effect. Voltage stability assessment: critical operating point and power margin. Voltage stability reinforcement by operative actions
Syllabus: Power system stability problem. Synchronous machine representation in stability studies. Load modeling in stability studies. Small-signal stability analysis. Transient stability analysis. Methods of improving stability
Syllabus: Introduction: the optimization problem. Linear programming: the simplex method and duality. Dynamic programming. Non-linear programming: constraints, Lagragean multipliers, KKT conditions, the gradient method, penalty functions. Applications in power systems
Syllabus: Generating unit characteristics. Load-frequency control. Power interchange among areas. Operative reserves
Syllabus: Review of probability theory and stochastic processes. Digital communication system models. Vector representation of signals. Optimum receivers for Gaussian channels. Introduction to coding: channel capacity and coded systems
Syllabus: Detection and estimation theory. Stochastic processes representation. Signal detection. Parameter and random variable estimation. Linear estimation. Wiener and Kalman filters
Syllabus: Information measures (entropy, mutual information). Lossless source coding (coding theorem; coding techniques – Hoffman, Lempel-Ziv). Channel capacity. Channel coding theorems. Channel coding techniques (block codes, correlation codes)
Syllabus: Analysis of satellite communication systems under statistical communication theory. Baseband processing, modulation and multiple access in satellite communication systems. Satellite channel impairments, interference and intermodulation analysis
Syllabus: Introduction to the main features and challenges of cellular communications. Concept of frequency reuse. Common channel access techniques: FDMA, TDMA and CDMA. Mobile network architecture and protocol structure, review of common channel signaling protocol SS7. Air interface characteristics. Description of first (AMPS) and second generation wireless systems standards (GSM, IS-95 and IS-136), including logical channel structure, modulation techniques, source and channel coding algorithms. Low-tier systems. Radio resource management techniques: power control, handoff algorithms and channel allocation techniques. Mobility management in cellular systems
Syllabus: Baseband transmission. Error probability evaluation. Intersymbol interference: equalization. Regenerative systems: “jitter” and line coding. Modulation techniques for digital bandpass transmission. External interferences in radio systems
Syllabus: Elements of computer networks. Protocols: concepts and hierarchies. The OSI reference model. The data link, access, transport, and application layers. Packet-switched networks. Network analysis and design
Syllabus: Cellular and wireless communications systems – basic concepts. Wireless LAN and cellular systems technologies. Propagation channel models. Coverage planning. Capacity planning.
Syllabus: Compound Semiconductors. Alloys and Heterostructures. Pn and pin junctions. Carrier confinement. Radiative recombination and optical absorption. Bandgap engineering. Structures with quantum confinement. Structures of high carrier mobility. Superlattices and strained layers. Processing of semiconductor structures: photolithography, eletring and polishing
Syllabus: Introduction and basic concepts. Main parts of an optical system. Optical fibers. IM/DD optical systems. IM/DD digital signals. IM/DD cable TV systems. Coherent optical systems. Systems using optical amplifiers. Solitonic optical communication systems
Syllabus: Fundamentals of quantum physics. Two-level systems (qubits). Quantization of the electromagnetic field. Quantum correlations and non-locality. Non-classical light. Light-matter interaction. Applications to quantum communications and quantum computation
Syllabus: Ray optics. Wave optics, Gaussian beams. Electromagnetic optics. Polarization. Resonant optical cavities. Statistical optics. Photons and atoms. Lasers
Syllabus: Semiconductor optics. Semiconductor optical sources. Photodetectors. Electro-optics. Acousto-optics. Applications of optoelectronic devices
Syllabus: Guided waves. Optical fibers: attenuation, dispersion, scattering, nonlinear effects. Passive and active optical devices. Instruments and measurement techniques. Applications of fibers and optical devices
Syllabus: Plain old telephone networks. Circuit switching, packet switching, hubs, and switches. Intelligence layer 2 and intelligence layer 3. ADSL and WDM technologies. Considerations on the IEEE 802.3 standard and the optical ethernet as carrier-grade technologies. Class of service (COS) and quality of service (QOS). PBB (provider backbone bridge) and PBT (provider backbone transport) networks. New-generation networks and the OTN-G709 (optical transport network). Switches and routers in the 100 Gbps environment using the OTN-G709 standard
Syllabus: Introduction to materials and components. Dispositives, transmission lines and waveguides over Si, Ge, SiGe, GaAs, InPh, CMOS, SiCMOS, SiGeCMOS. Logical circuits, gates ECL, LVDS, CML and flip-flops in the Terahertz domain. Differential scattering parameters. Mux and Demux applications in 100 Gbps. MIC and MMIC technologies and on-chip and off-chip connections. Very Large Scale Integration (VLSI) applications in 100 Gbps and the IEEE P802.3ba
Syllabus: Linear Spaces, Linear Manifolds, Linear Independence, Hamel Basis, Linear Transformations, Isomorphisms, Isomorphic Equivalence, Direct Sum, Projections, Metric Spaces, Convergence and Continuity, Open Sets and Topology, Equivalent Metrics and Homeomorphisms, Closed Sets and Closure, Dense Sets and Separable Spaces, Complete Spaces, Continuous Extension and Completion, Baire Category Theorem, Compact Sets, Sequential Compactness, Normed Spaces, Banach Spaces, Subspaces and Quotient Spaces, Bounded Linear Transformations, Open Mapping Theorem and Continuous Inverses, Equivalence and Finite-Dimensional Spaces, Continuous Linear Extension and Completion, Banach-Steinhaus Theorem and Operator Convergence, Compact Operators, Hahn-Banach Theorem and Dual Spaces
Syllabus: Inner Product Spaces, Hilbert Spaces, Orthogonality, Orthogonal Complement, Orthogonal Structure, Unitary Equivalence, Summability, Orthonormal Basis, Fourier Series Theorem, Orthogonal Projection, Riesz Representation Theorem and Weak Convergence, Adjoint Operator, Self-Adjoint Operators, Square Root and Polar Decomposition, Normal Operators, Spectrum of an Operator, Spectral Radius, Numerical Radius, Examples of Spectra, Spectrum of a Compact Operator, Spectral Theorem for Compact Normal Operators, Spectral Theorem for Normal Operators
Syllabus: Review of probability theory. Random variables. Sequence of random variables, convergence, law of large numbers, central limit theorem. Stochastic processes, stationarity, autocorrelation, power spectral density, continuity, differentiation, integration and ergodicity. Stochastic processes through linear systems (time and frequency domain), Gaussian, Markov and Poisson processes
Syllabus: Probability space. Markov chain and Markov processes. Branching processes. Counting processes. Poisson and Renewal processes. Martingales. Wiener processes. White noise, stochastic integrals. Stochastic differential equations
Syllabus: Generalization; Architecture Limits and its relation with available Data; Introduction to Reinforcement Learning; Learning by Interaction; Dynamic Programming; Temporal Differences Method: TD, TD(?), Q-Learning, SARSA and AHC; Recurrent Neural Networks; Support Vector Machines; Applications
Syllabus: Introduction, Main Applications, Feature Vectors; Supervised and Non Supervised Classifiers; Bayesian Decision Theory, Discriminant Functions and Decision Surfaces, The Gaussian Distribution Case; Supervised Methods: Bayesian Learning, Bayes Classifier and Maximum Likelihood Estimation, Classification Capacity and Dimensionally Problem, Parzen Window and Nearest Neighbor Methods, Multiple Fisher Discriminant, Generalized Discriminant Functions, Perceptron Algorithm, Non Separable Behavior, Minimum Square and Pseudo Inverse, Relation to the Fisher Discriminant, Widrow-Hoff and Stochastic Approximation Methods; Non Supervised Density Mixture Methods, Non Supervised Bayesian Learning, Similarity Measures, Iterative Non Supervised Classification Methods, Kohonen and Hybrid Methods
Syllabus: Descriptive statistics, multivariate normal distribution, sampling from a Multivariate Normal Distribution, Maximum Lilkelihood Estimation, Inferences about the mean, multivariate analysis of variance, principal components and factor analysis, linear discriminante analysis, cluster analysis
Syllabus: Inference; Bayes Theorem. Congugacy; Choise of non-informative priors. Dynamic Linear Models; Constant; Linear growths and basic seasonal model. Specification of discount factors and the Bayes factor. The software BATS and case studies with BATS. Non-Gaussian formulations. Gibbs sampling; Makov Chain. Obtaing the posterior via Gibbs sampling. Forecasting applications
Syllabus: ARIMA modeling; stylized facts of returns series; a framework for non linear time series models; non linear models for the conditional mean; non linear models for the conditional variance; state space models and stochastic volatility; risk measures: Var and CVar; risk and extreme values; multivariate dependence in time series models via copulas and its use in risk measure
Syllabus: Components of a GLM; estimation; hypothesis tests; residuals and diagnostics; models for count data (Poisson and negative binomial); models for binary data (Bernoulli and Binomial); models for distributions with constant coefficient of variation (gamma); quasi likelihood models
Syllabus: Descriptive techniques; concepts of seasonality, trend, stationarity and auto-correlation. Stochastic models for time series. Moving-average (MA) and auto-regressive (AR) processes; mixed ARMA and integrated ARIMA models. Forecasting. Spectral Analysis. Multivariate formulations. Linear Systems. Comparisons with state-space formulations
Syllabus: Models and tests for non-stationary time series. Non observed components models: trend, seasonals and cycles; State space models; Non observed components and regressors in state space form; The Kalman filtering; Smoothing algorithm; Maximum likelihood estimation; Goodness of fit and residuals diagnostics
Syllabus: Market risk and other types of risk. Stylized facts of financial returns. Value-at-risk: Normal model, Delta normal model, non parametric method. Statistical tests to verify VaR. Volatility models: GARCH and SV
Syllabus: Linear systems descriptions (state equations, transfer functions, fatorizations, VARMA models). Linear systems properties (contrlability, observability, Liapunov stability, input-output stability, poles and zeros). Change of basis and canonical forms Internal structure (minimal realizations, Kalman decomposition, Wolovich’s structure theorem, equivalent descriptions). Servomecanisms (definitions, design using state regulators and diophantine equations). Application to time series and to others subjects of interest
Syllabus: Geometric theory (EDO’s, phase space, equilibrium, Liapunov stability, Liapunov functions, limit circles). Approximated methods (describing functions), geometric methods (local coordinates, controllability and observability, central manifold theorem, linearization – exact and approximated, servomecanisms and decoupling) input-output relations (systems as non-linear operators, series of Volterra-Fliess, input-output stability, small gain theorem & passivity and consequences – circle and Popov theorems). Particular systems (bilinear systems, polynomial systems)
Syllabus: Mathematical modeling of convex problems; The simplex Method; Duality Theory; Sensitivity Analysis; Decomposition Methods for Large-Scale Problems
Syllabus: Review of Numeral Methods for Unconstrained Problems, Descent Methods and Linear Search. Methods for Constrained Problems. Optimality Conditions. Quadratic Programming. Interior Point Methods. Convergence Analysis
Syllabus: Mathematical modeling of non-convex problems with binary and integer variables, Polyhedral Theory, Dynamic Programming, Valid inequalities, Duality and Relaxations. Branch-and-Bound Algorithms, Cutting Planes, Branch-and-Cut, Decomposition Methods for Large-Scale Problems
Syllabus: Geometric optimal control theory (calculus of variations, Pontryagin maximum principle for continuous and discrete time, relations with Mathematical Programming, problems with constraints – bang-bang control, linear quadratic problem, state feedback, Riccati equations). Wiener-Hopf control (criteria, Youla parametrization, basic H2 geometry, analyticalsolutions). H-infinity control (including relation between Riccati and factorization problems). Numerical methods for resolution of optimal control problems
Syllabus: Introduction to Graph Theory, Design and Analysis of Algorithms, Computational Complexity. Optimal Paths and Trees, Maximum Flow Problem, Minimum Cost Flow Problem, Optimum Matching Problems, Matroids, Multicommodity Flow Problem
strong>Syllabus: Interior Point Methods, Semi-definite Programming, Constraint Programming, Approximation Algorithms
Syllabus: Lagrangian Relaxation for Combinatorial Optimization Problems. Dual Methods for Separable Large-Scale Problems. Solution Methods for Non-Differentiable Optimization Problems: Subgradients, Cutting Planes and Bundle Methods. Relation with the Dantzig-Wolfe method

Mechanical Engineering

Since its foundation in 1964, the graduate program of the Department of Mechanical Engineering keeps high standards in teaching and research. With significant interaction with the national and international scientific communities, the program has always been rated the maximum grade by CAPES, the national agency that regulates the graduate programs in Brazil.

The Department of Mechanical Engineering acts in research and development in the areas of applied mechanics, thermosciences, oil and energy. It was one of the first departments in the country to offer a graduate program in Engineering. Joint projects with various industry sectors — such as the automotive, aeronautic, naval, and especially the energy sector — contribute to the continuous development of products, removal of technological barriers, modernization of laboratories, and placement of highly qualified professionals in the job market. The graduate program in Mechanical Engineering also promotes advanced studies and fosters joint research and exchange programs with several renowned foreign institutions.

Additional information can be found at the Department’s site and, in Portuguese, here


Syllabus: Exposition of topics of interest of the mechanical engineering department
Syllabus: Exposition of topics of interest of the mechanical engineering department
Syllabus: Non-linear Dynamics Unidimensional flows and bifurcations. Bi-dimensional flows: Phase plane, limit cycles, bifurcations classification. Chaos: Lorenz equations, uni-dimensional maps, fractals, attractors. Non-linear behavior of mechanical systems: Poincaré sections, Lyapunov exponents, escape from potential wells

Bibliography: Nonlinear Dynamics and Chaos, Strogatz, S.H., Addison Wesley 1994; Introduction to Experimental Nonlinear Dynamics, Virgin, L.N., Cambridge Univ. Press 2000

Syllabus: Partial differential equations approximation methods: finite differences, finite volumes and finite elements. Sparse matrices: graph representation, data structure and storage techniques, basic operation in sparse matrices. Linear algebra basic concepts. Linear system solution by direct, iterative and projection methods. Eigenvalue problems and solutions by power and projection methods. Preconditioning

Bibliography: Matrix Computations, Golub, G.H. e Van Loan, John Hopkins Univ Press, 1989; Iterative Methods for Sparse Linear Systems, Saad, Y.,; Numerical Methods for Large Eigenvalue Problems,  Saad, Y., http://www-; Numerical Linear Algebra, Trefethen, L.N. e Bau III, D., SIAM, 1997

Syllabus: Rotordynamics Rigid rotor, flexible rotor: Laval (Jeffcott) rotor dynamics in rigid bearings; unbalance versus rotor bow; influence of internal and external damping; bearing orthotropy; resonance crossing; blade loosening, gyroscopic effect. Hydrodynamic bearings: horizontal machines, vertical machines. Damping devices, non-axisymmetric rotors

Bibliography: Gasch, Nordmann, Pfutzner, Rotordynamik, Spinger 2002; Genta, Dynamics of Rotating Systems, Springer 2005

Syllabus: Exposition of topics of interest of the mechanical engineering department
Syllabus: Newtonian mechanics of particles, systems of particles, systems with varable mass. Moving reference frames. Lagrangean formulation and applications. Variational calculus in Mechanics. Hamilton’s Principle and Hamilton’s equations. Kinematics and Dynamics of rigid bodies and applications

Bibliography: Introduction to the geometric theory and stability of autonomous systems. Bibliografia: Principles of Dynamics, Greenwood, D.T., Prentice-Hall, 1965; Methods of Analytical Dynamics, Meirovitch, L., McGraw-Hill, 1970

Syllabus: Ordinary Differential Equations (ODE). Systems of ODE. Applications of ODE to Mechanical Engineering. Fourier series and integrals. Laplace Transform. Partial Differential Equations (PDE): classification, analytical solutions and applications to Mechanical Engineering. Bessel functions and Legendre polynomials. Analytic functions of a complex variable. Conformal mappin

Bibliography: Advanced Engineering Mathematics, Wylie, C.R. e Barrett, L.C., 5ª ed., McGraw-Hill, 1982; Advanced Calculus for Applications, Hildebrand, F.B., Prentice-Hall, 1982; Advanced Calculus, Spiegel, M.R., Schaum’s Outline Series; Laplace Transform, Spiegel, M.R., Schaum’s Outline Series; Differential Equations, Ayres Jr., F., Schaums’s Outline Series

Syllabus: The finite element method – basic principles: virtual work and minimum power. Equilibrium equations. Numerical integration techniques and discretization. Solid element formulations for one, two and three-dimension and structural elements: bars, beams, plates and shells. Modeling considerations and generalized degrees-of-freedom. Numerical solution techniques for steady, transient and eigenvalue problems. Implementation of a finite element numerical analysis code

Bibliography: Finite Element Procedures, Bathe, K.J, , Prentice-Hall, 1996; The Finite Element Method Zienkiewicz, O.C, , McGraw-Hill, 1979; The Finite Element Method, Hughes, T.J.R, , Prentice-Hall, 1987

Syllabus: Tensor Theory. Analysis of Strain and Stress. Equations of Elasticity. Boundary Value Problems, two and three dimensional Elastostatic Problems. Variational Methods
Syllabus: Stress and strain analysis. Dimensional Analysis and Similitude of Models. Uncertainty Analysis. Electrical Resistance Strain Gages. Electrical Circuits for Strain Gages. Strain Gages Based Transducers. Photoelasticity 2D and 3D. brittle Coating. Moiré. Thermoelasticity. Fiber Optic Strain Gages. Residual Stress Measurement. Stress Intensity Factor Determination.  Digital image Correlation

Bibliography: Experimental Stress Analysis, J,W. Dally e W.F. Riley, 4th ed., College House Enterprises, LLC, 5713 Glen Cove Drive, Knoxville Tennessee, EUA, 2006; Springer Handbook of Experimental Solid Mechanics, 1st Edition, editor: William N. Sharpe, Society for Experimental Mechanics, Springer, 2008

Syllabus: Systems. Properties of Systems. Heat. Work. Systems not PVA. First Law of Thermodynamics. Control volumes deformable and non-deformable. Control volumes accelerated. Second Law of Thermodynamics. Reversibility and irreversibility. Entropy. Energy availability. Loss of power availability. Applications. Third Law of Thermodynamics. Partial derivatives in thermodynamics. Real gases. Properties tabulated

Bibliography: Fundamentals of Thermodynamics, 6th edition, Van Wylen, Sonntag, Borgnakke, Editora Ltda. EdgardBlucher,2003

Syllabus: Fundamental concepts. Uncertainty and its use in experiment planning. Data acquisition and processing. Temperaure:scales and standards. Resistance temperature sensors, thermocouples, thermistors. optical methods for temperature measurement. Temperature errors in sensor installation. Pressure measurement: standards and transducers. Flow visualization. Fluid flow measurement: Pressure-based sensors, hot-wire sensors, Laser-Doppler velocimetry, Particle Image Velocimetry. Flow measurement: standards, positive displacement devices, Venturi, Orifice plate and nozzles

Bibliography: Fundamentals of Temperature, Pressure and Flow Measurement, Benedict, Wiley Interscience, 1989, Experimental Methods for Engineers, Holman, McGraw-Hill, 2000, Fluid Mechanics Measurements, Goldstein, Taylor and Francis, 1996, Particle Image Velocimetry, Adrian and Westerweel, Cambridge University Press, 2011

strong>Syllabus: Continuum hypothesis. Conservations equations. Constitutive equations. Navier-Stokes equations. Exact and approximate solutions of the conservation equations. Introduction to asymptotic solutions, lubrication theory, creeping flows. Low Reynolds number convection. Laminar boundary layer theory. Turbulence fundamentals

Bibliography: Advanced Transport Phenomena – Fluid Mechanics and Convective Transport Processes, L. Gary Leal, Cambridge, 2007. Advanced Transport Phenomena: Momentum, Energy, and Mass Transfer in Continua, John C. Slattery, 3rd ed., 1996. Transport Phenomena, Bird, R. B.; Stewart, W. E.;Leighfoot, E. N., John Wiley, 1960

Syllabus: Mechanism of transport. Fundamental equation of transport. Constitutive equations of heat transport. Energy equation. Constitutive equations of mass transport. Multicomponent system. Dimensional analysis of the transport equations. Similarity between heat and mass transfer: heat and mass transport in solids or stationary fluids, in laminar flow inside the boundary layer and turbulent flows. Transport of heat and mass transfer between phases: film coefficient, mass transport coefficient, Nusselt and Sherwood numbers. Macroscopic balances for energy and mass

Bibliography: Momentum, and Energy Transfer in Non Continues, JC Slattery, McGraw-Hill, 1972; Diffusional Mass Transfer, nd H.P. Skelland, Wiley Interscience, 1974

Syllabus: Discretization Methods. Discretization schemes for diffusion equation and diffusion and convection. Numerical viscosity. Methods for solving the algebraic system: direct and iterative. Techniques to accelerate convergence. Transient explicit and implicit methods. Velocity-pressure coupling: the stream function-vorticity and primitive variables. Use of commercial software

Bibliography: Numerical Heat Transfer and Fluid Flow, Patankar, SV; Hemisphere Publishing Corporation, 1980; Computational Fluid Mechanics and Heat Transfer, J.C. Tannehill; DA Anderson and R.H. Pletcher, Taylor and Francis, 1997, 2nd. Ed. Mechanics and Heat Transfer Computational Fluid, C.R. Maliska, LTC Press, 2nd. Ed., 2004

Syllabus: Glassy liquids. Polymer gels. Particulate gels. Electro- and magnetoresponsive suspensions. Foams, emulsions and blends. Liquid-crystalline polymers. Surfactant solutions. Block co-polymers

Bibliography: Larson RG (1999) The Structure and Rheology of Complex Fluids, Oxford; Barnes HA (2000) A Handbook of Elementary Rheology, published by the Institute of Non-Newtonian Fluid Mechanics, University of Wales, UK; Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, J. Wiley, 2nd ed., Vol. 1: Fluid Mechanics

Syllabus: Open Reciprocating Compressors; Rotary and Orbital Compressors; Hermetic Compressors; Air-cooled Condensers and Air-source Evaporators; Water Condensers and Evaporators; Fixed Area Expansion Devices; Expansion Valves; Ancillaries; Operation in Transient Regime; Cooling Towers

Bibliography: International Journal of Refrigeration; ASHRAE Transactions; International Institute of Refrigeration Informatory Notes; Notes on the Simulation of Refrigeration, Parise, J.A.R

Syllabus: Solution of complex problems involving fluid flow, heat transfer, mass transfer and chemical reaction. Advanced models for turbulence and computational implications

Bibliography: Numerical Heat Transfer and Fluid Flow, Pantakar, S.V.; Hemisphere Publishing Corporation, 1980

Syllabus: Solar radiation characteristics. Incident radiation on horizontal and tilted surfaces. Solar radiation data in Brazil. Solar collector materials and heat transfer analysis. Performance analysis of thermal systems as a function of different parameters. Performance simulation and design. Economic analysis. Photovoltaic cells for electric energy generation : system performance analysis and design

Bibliography: Solar Engineering of Thermal Processes, Duffie & Beckman, Wiley Interscience, 2006

Syllabus: Tensor analysis. Continuum hypothesis. Kinematics of fluid flow. Velocity gradient tensor. Reynolds Transport Theorem. Basic laws. Conservation of mass. Momentum equation. Stress tensor. Angular momemtum equation. Energy equation. Second law of thermodynamics. Constitutive equations. Stokes Fluid. Newtonian fluid and the Navier-Stokes equation. Potential flow. Vorticity equation and dynamics. Classical solutions of the Navie-Stokes equation. Low Reynolds number flows. Introduction to hydrodynamic lubrication theory

Bibliography: Incompressible Flow, Panton, John Wiley, 2005. Fundamental Mechanics of Fluids, I.G., Currie, 1993,  An Introduction to Fluid Dynamics, G.K. Batchelor, 1967; Physical Fluid Dynamics, D.J. Tritton, 1988

Syllabus: Navier-Stokes equation; Exact solutions; Creeping Flow; Concept of boundary layer; Laminar boundary layers.; Boundary layers similar and non similar methods of solution; Approximate method of von Kármán and Pohlhausen; Turbulent flow concepts; Introduction to boundary layer stability; Transition to turbulent flow; Models for turbulent flow; Turbulent flow in ducts

Bibliography: Transport Phenomena ou Fenômenos de Transporte, R.B. Bird, W.E. Stewart e E.N. Lightfoot, 2a. edição; Boundary Layer Theory, H. Schlichthing, 1994; Viscous Flow, F.S. Sherman, 1990; An Introduction to Fluid Dynamics, G.K. Batchelor, 1967

Syllabus: Basic concepts and definitions of multiphase flow. Equations of motion – continuous phase. Equations of motion – disperse phase. Equations of motion for the mixture and homogeneous model. Friction losses in separated flow. Non-ideality of physical properties. Real gases behavior. Joule-Thomson coefficient. Flow patterns. Bubble flow. Slug flow. Stratified flow. Annular flow

Bibliography: M. Ishi, T. Hibiki, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Springer, New York, 2006; Bertola, V., Modelling and Experimentation in Two-Phase Flow, Ed. Springer-Verlag, New York, 2003; Wallis, G.B., One-Dimensional Two-Phase Flow, McGraw Hill Co., New York, 1969


Syllabus: General equation for the conduction heat transfer : integral and differential formulations. Steady state and transient heat conduction problems. Numerical formulation. Radiation heat transfer. Surface properties. Radiative heat transfer between gray, diffuse and specular surfaces. General equation. Participant media. Monte Carlo method. Combined convection and radiation heat transfer

Bibliography: Conduction of Heat in Solids, Carslaw, H.S. and Jaeger, J.C., Oxford University Press, Oxford, 2000. Heat Conduction, Ozisik, M.N, John Wiley & Sons, Inc, N.Y., 1993, Radiative Heat Transfer, Ozisik, M.N., John Wiley, 1981

Syllabus: Convection in laminar flows. Hydrodynamic and thermal boundary layer. Similar solutions in forced and natural convection. Moxed convection. Internal flows. Tubes and channels. Graetz problem. Convection in turbulent flows. Analogies

Bibliography: Convective Heat and Mass Transfer, Kays, W.M., McGraw-Hill, 1980; Convective Heat Transfer, L. C. Burmeister, John Wiley & Sons, 1983; Convection Heat Transfer, A. Bejan, , John Wiley & Sons, 1984

Syllabus: Introduction. Historic facts. Definitions: usual air pollutants, legislation, sources and effects of air pollutants, concentration measurement. General properties of particulate air pollutants: particle characterization, fluid particle interactions, drag force, physical processes important in the collection of particulates. Equipment used in the collection of particulate air pollutants: gravitational devices, cyclones, electrostatic precipitators, filtration, air washers. General properties for gas mixtures. Equipment for the control of gaseous air pollutants: incinerators, adsorption systems, absorption systems. Control of Sulfur oxides. Control of Nitrogen oxides

Bibliography: Air Pollution Control. A Design Approach, C. D. Cooper and F. C. Alley

Syllabus: Introduction. Composition of the atmosphere. Interactions of the solar radiation with the atmosphere. Energy Balance. Temporal and spatial scales for the atmospheric processes. Pollutants in the atmosphere. Global cycles and residence time. Fundamentals of atmospheric chemistry. Aerosols. Meteorology applied to air pollution. Atmospheric dispersion. Natural removal processes. Discussion on the most recent/relevant problems in atmospheric pollution

Bibliography: From Air Pollution to Climate Change, J.H. Seinfeld e S.N. Pandis, Wiley-Interscience. Air Pollution Meteorology, J.R. Eagleman, Trimedia Publishing. Atmospheric Chemistry and Physics of Air Pollution, J.H. Seinfeld, John Wiley & Sons

Syllabus: Introduction to complex fluids. Basic forces. Polymers. Particulate suspensions. Liquid crystals

Bibliography: Larson RG (1999) The Structure and Rheology of Complex Fluids, Oxford; Barnes HA (2000) A Handbook of Elementary Rheology, published by the Institute of Non-Newtonian Fluid Mechanics, University of Wales, UK; Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, J. Wiley, 2nd ed., Vol. 1: Fluid Mechanics

Syllabus: Modeling of Refrigeration Systems, Fundamentals of Thermodynamics; Fundamentals of Refrigeration – The Vapor Compression Cycle; Heat Pumps; Compressors – Basic Theory; Heat Exchangers – Basic Theory; Expansion Devices Basic Theory; Refrigerant Properties; Simulation of the Vapor Compression Refrigeration Cycle;

Bibliography: ASHRAE Transactions, International Journal of Refrigeration, Bulletin of the International Institute of Refrigeration, 2009 ASHRAE Handbook – Fundamentals; Notes on the Simulation of Refrigeration, Parise, J.A.R

Syllabus: Introduction (history, basics, fundamentals). Design considerations (thermal load calculation; types of storage). Equipment (storage tanks, control types). Control strategies. Sizing accumulation capacity. Economic evaluation. Comparison of storage technologies

Bibliography: Design Guide for Cool Thermal Storage, C. E. Dorgan, J. S. Elleson, ASHRAE, 1993

Syllabus: Fundamentals of turbulente; Characterization of turbulence; statistical description of the turbulent flow; Time average equations: asymptotic methods; Differential and algebraic models; Large Eddy simulation; numerical methods applied to turbulence

Bibliography: Bibliography: Turbulence, O.J. Hinze, McGraw Hill, 1959; A first course in turbulence, H. Tennekes, J.L. Lumley, The MIT Press, 1972; Turbulence models and their application in hydraulics, W. Rodi, Institut für Hydromechanik, University of Karlsrushe, 1984; Turbulent Flows, S.B. Pope, Cambridge University Press, 2000

Syllabus: Engine Types. Design and operating characteristics. Thermodynamics of air-fuel mixtures. Properties of working fluids. Ideal thermodynamic cycles. Fuel injection systems. Exhausting systems. Spark ignition engines. Compression ignition engines. Pollutant formation and control. Special Topics

Bibliography: Internal Combustion Engine Fundamentals, John B. Heywood, McGraw-Hill International Editions, 1988

Syllabus: Position and speed control. Vibration Control. Vehicles guidance. Force and deformation control. Transportation lag. Temperature Control. Pressure and flow control. Control of structures

Bibliography: Control Systems Principles and Design, E.O. Doebelin, John Wiley & Sons, 1985; Vibration with Control Measurement and Stability, D.J. Inman,., Prentice-Hall International, 1989; Engenharia de Controle Moderno, K. Ogata, Prentice-Hall do Brasil, 2a. Edição, 1990; Introduction to Dynamic System Analysis, T.D. Burton, McGraw-Hill, 1994

Syllabus: Vehicle as a Dynamic System: Sub-systems Interaction, Analysis and Experimental Tests, Analysis and Simulation Tools. Longitudinal Dynamics: Transmission System, Brake System. Vertical Dynamics: Suspensions, Rolling. Lateral Dynamics: Steering System, Handling and Stability, Human Influence on the System. Tire-Ground Interaction. Interaction of Vertical and Lateral Dynamics. Vehicles Collision: Accident Reconstruction

Bibliography: Fundamentals of Vehicle Dynamics, T.D. Gillespie, SAE, 1992; Car Suspension and Handling, D. Bastow,. & G. Howard, 3rd Ed., SAE, 1997; Tires Suspension and Handling, , J.C. Dixon, 2nd Ed., SAE, 1996; The Automotive Chassis: Engineering Principles, J. Reimpell, & H. Stoll, SAE, 1996; Race Car Vehicle Dynamics, , W.F Milliken. & D.L Milliken, SAE, 1997

Syllabus: Basic electronics/electric systems. Sensors and transducers: resistive, inductive, piezoelectric and strain-gauge sensors; position, speed, inertial, pressure flow and thermal transducers. Electro-mechanic actuators: DC, AC and step motors. Application examples. Laboratory practice. Class project

Bibliography: Industrial Electronics and Robotics, C. Schuler and McNamee, McGraw-Hill, 1986;., Robotics and Automated Systems, R.L, Hoekstsa, South Western Publishing Co., 1986; Brushless DC Motors, T. Sokira,. and W. Jaffe, TAB Books Inc., 1990

Syllabus: Introduction. 2D Objects Generation: straight lines, circles and curves (Splines and Bezier). Geometric Transformations: translation, rotation, scaling and projection. Clipping Algorithms: Sutherland-Hodgman, Cyrus-Beck. Hidden-surface Removal Algorithms: area subdivision, depth-sort, z-buffer, scan-line, ray-tracing. Illumination Models: Phong Shading, Gouraud Shading, Radiosity. Textures: noise function, solid texture

Bibliography: Computer Graphics, Principles and Practice, Foley, Van Dam, Hughes & Feigner Addison-Wesley, 1992; 3D Computer Graphics, A. Watt Addison-Wesley, 3rd Edition, 2000

Syllabus: Introduction. Characteristics of Solid Modelers . Solid Modelers Classification: Exaustive Enumeration, Cell Decomposition, Octree. Constructive Models: Half-Space Model, Constructive Solid Geometry (CSG). Boundary Representation (B-Rep): Winged-Edge, Half-Edge. Data-structure for planar and spatial subdivision

Bibliography: An Introduction to Solid Modeling, Martii Mäntylä, Computer Sciece Press, 1988; Solid Modeling With DesignBase: Theory and Implementation, Hiroaki Chiyokura, Addison-Wesley, 1988; The Design and Analysis of Spatial Data Structures, H. Samet, Addison-Wesley, 1989

Syllabus: The dynamics of systems. Dynamic systems modeling and simulation. Power interaction and load effect. Transmission, storage and energy dissipation. Transmission and actuation systems. Coupling systems. Instrumentation systems and control. Analysis of mechanisms and machine components. Hydraulic and pneumatic components. Specification of motors and actuators. Load choice. Effort determination. Dimensional project

Bibliography: Introduction to Dynamic System Analysis, T.D. Burton, McGraw-Hill, 1994; Modelling of Dynamic Systems, L. Ljung, and T. Glad, Prentice Hall, 1994; Introduction to Physical System Modelling, P.E. Wellstead, Academic Press, 1979; Introduction to Physical System Dynamics, R.C. Rosenberg and D.C. Karnopp, McGraw-Hill, 1983

Syllabus: Rotation and Translation of Bodies in Space. Orientation matrices and its equivalents: matrix of direction cosines, matrix of coordinate transformation,  Euler-Rodrigues parameters and Quaternions. Elementary sequential rotations:  Euler angles, Cardan angles. Angular velocity in space defined using the  time variation of the orientation matrix. Solution of the inverse problem: Obtaining the position given the angular velocity. Angular acceleration of bodies. Kinematics of motion including translation and rotation. Inertia Tensor. Linear and angular momentum. Kinetic and Potential Energy, work due to non-conservative forces.  Newton and Euler’s Law of motion. Lagrangean formulation. General motion of a body in space. Stability and Instability. Motion beyond the stability borders. Properties of the motion around an equilibrium position

Bibliography: H.I. Weber: Reasoning with Rotational dynamics – PUC-Rio – version 2011; S.T. Thornton & J.B. Marion: Classical Dynamics of Particles and Systems, Brooks/Cole – Thomson Learning 2004; A.V. Rao: Dynamics of Particles and Rigid Bodies – A Systematic Approach – Cambridge Univ. Press 2006

Syllabus: Total and Updated Lagrangian Formulations. Linearization of  the Principle of Virtual Work, with respect to finite element state variables. Incremental solution techniques -iterative methods: Newton-Raphson and Modified Newton-Raphson, Gauss-Seidel, Pre-condition Conjugate Gradient and BFGS

Bibliography: Introduction to the Mechanics of Continuous Medium, L. Malvern, Prentice Hall, 1969; Finite Element Procedures, K. J Bathe,., Prentice Hall, 1996; Nonlinear Finite Elements for Continua and Structures, T. Belytschko, W. K. Liu, B. Moran, J., Wiley, 2000.

Syllabus: Introduction to Structural Integrity: Technical and Management Views. Damage Mechanisms: Fatigue, Creep, Corrosion, SCC. Failure Modes and its Prevention including Fracture Mechanics. Health Monitoring of Structures. Remaining Life of Structures. Risk Analysis. Case Studies: Bridges, Cranes, diesel Engines, Pipelines, Pressure Vessels

Bibliography: “Fitness-for-Purpose”, API 579-1/ASME FFS-1, American Petroleum Institute, 2007; “Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures”, BS 7910, British Standards, 2005

Syllabus: Basic concepts of fluid mechanics. Basic equations for the fluid flow. Fluid statics. Viscous flow in pipelines (laminar and turbulent flow). Friction losses. Compressible flow in pipelines. Design of gas pipelines. Transient flow in pipelines. Systems for pumping liquids. Introduction to heat transfer. Heat transfer in pipelines. Applied design in pipelines

Bibliography: Fluid Mechanics, Streeter, V.L., Wylie, E.B. and Bedford, K.W., 1998, Hydraulics for Pipelines Vol. 1: Fundamentals, 2nd ed., Gulf Professional Publishing, Houston, Lester, C.B., 1994; Pipeline Design and Construction: A Practical Approach, Mohitpour, M., Golshan, H., Murray, A., ASME Press, N.Y, 2007

Syllabus: Life Cycle of a Pipeline. Pipeline Grade Steel. Production of Pipeline API 5L Grade Steel Tubes. Stress Analysis. Desing of On-shore Pipelines.Design of Off-shore Pipelines. Internal and External Protection Coatings

Bibliography: Engenharia de Dutos, Editor: J.L.F. Freire, ABCM – Associação Brasileira de Engenharia e Ciências Mecânicas, Rio de Janeiro, 2009; Pipeline Design & Construction – A Practical Approach, 3a ed., M. Mohitpour, H. Golshan, A. Murray, ASME-Press, The American Society for Mechanical Engineers-ASME, Three Park Avenue, New York, NY 10016, 2007; Pipeline Operation & Maintenance – A Practical Approach, 1a ed., M. Mohitpour, J. Szabo, T. Van Hardeveld, ASME-Press, The American Society for Mechanical Engineers -ASME, Three Park Avenue, New York, NY 10016, 2005; Marine Pipelines – Design and Installation, M.W. Braestrup, J.B. Anderson, L.W. Anderson, M.B. Bryndum, C.J. Christensen, Niels Rishøj, ASME – Blackwell Publishing, 2005; Subsea Pipeline Engineering, A. Palmer, R.A. King, PennWell Corporation, 2a ed., 2008; Mechanics of Offshore Pipelines vol. 1: Buckling and Collapse, S. Kyriakides, E. Corona, Elsevier, 2007; Subsea Pipelines and Risers, Yong Bai, Elsevier, 2a Ed., 2005

Syllabus: Fluid mechanics review. Introduction to rheology. The Generalized Newtonian Fluid model. Flow of non-Newtonian fluids in petroleum industry processes: drilling, completion, cementing and fracturing. Flow in reservoirs (porous media). Transport and recovery. Rheometry. Rheology of fluids found in the petroleum industry (drilling fluids, petroleum, polymers). Introduction to heat transfer in the petroleum industry processes

Bibliography: Dynamics of Polymeric Liquids, vol. 1, R.B. Bird, R.C. Armstrong e O. Hassager, John Wiley & Sons, 1987; Engineering Rheology, Roger I. Tanner, Clarendon Press, 1985; An Introduction to Rheology, H.A. Barnes, J.F. Hutton e K. Walters , Elsevier, 1989; Fluid Mechanics Measurements in Non-Newtonian Fluids, C.W. Macosko, P.R. Souza Mendes; Fluid Mechanics Measurements, R. J. Goldstein, ed., Taylor & Francis Publishers, Washington, DC, p. 509-574, 1996

Syllabus: Directional drilling: – Introduction to directional drilling; – Directional well planning; – Bottom hole assembly to directional drilling; – Directional surveying; – Complementary topics. – Offshore drilling: – Types of platforms; – Typical configuration of offshore wells; – Mud line suspension systems; – Subsea wellhead systems; – Spud in from floating rigs; – Drilling with guidelines; – Drilling without guidelines; – Jetting; – Drilling with BOP and riser connected; – Subsea well abandoning; – Operational sequence of typical offshore well; – Slender well; – Cementing job in floating rig; – Extended reach wells in deep water; – Safety margin of riser; – Well control in floating rig

Bibliography: Luiz Alberto Santos Rocha et al: “Perfuração Direcional”, Editora Interciência, 2006; Plácido, J.C.R., “Perfuração Offshore”, apresentação Powerpoint. Bourgoyne, A.T. et al: “Applied Drilling Engineering”, SPE Textbook Series, Vol. Richardson, Texas, USA, 1991; Thomas, J.E. et al: “Fundamentos de Engenharia de Petróleo”, Editora Interciência, 2001; Luiz Alberto Santos Rocha e Cecília Toledo de Azevedo: “Projetos de Poços de Petróleo”, Editora Interciência, 2007; Luiz Alberto Santos Rocha e Cecília Toledo de Azevedo: “Buscando o estado-da-arte nas estimativas de geopressões”, Boletim técnico da Produção de Petróleo, Rio de Janeiro – Volume 1, n° 1, p. 67-93, 2006; Machado: Reologia e Hidráulica Avançada, Editora Interciência, 2002

Syllabus: Classification fo the different fluids in the oil reservoir. Mass balance. Advanced/Enhanced oil recovery. Formation tests. Introduction to the simulation of oil reservoirs

Bibliography: Fundamentos da Engenharia de Petróleo (Thomas, J.E. et al., Ed. Interciência, 2001); Engenharia de Reservatórios de Petróleo (Rosa et al., Ed. Interciência – RJ – 2006); Introduction to Petroleum Reservoir Analysis (Koederitz,L.F., Harvey, A.H. e Honarpour, M., Contributions in Petroleum Geology and Engineering, n. 6, Gulf Publishing Company, 1989); Principles of Reservoir Engineering (Amyx, J.W., Bass Jr., D.M. e Whiting, R.L.), McGraw Hill Book Company, 1960

Syllabus: Fundamentals: energy, units, work and power, heat, renewable and conventional energy sources. Fundamentals of Thermodynamics: First Law of Thermodynamics, Second Law of Thermodynamics, entropy, Carnot cycle, Otto cycle, Diesel cycle, Rankine cycle, gas turbine (Brayton cycle), combined cycle, cogeneration, fuel cell. Nuclear Energy, nuclear power plants, fuel cycle and generation costs. Solar Energy: solar constant, water heating, photovoltaic cells, Rankine Cycle Solar Power Plant. Hydropower: Brazilian potential, forms of exploitation, generation costs. Wind energy: Brazilian potential, forms of exploitation, generation costs. Introduction to Environmental Impact Analysis. Introduction to Energy Savings. Brazilian Energy Matrix. World Energy (crises, consumption, use, environment)

Bibliography: Fundamentals of Thermodynamics (Collection Van Wylen), Borgnakke, C. and Sonntag, RE, 2009, Ed Edgard Blucher Ltda, SP; Nuclear Heat Transport, El Wakil, 1971, Renewable Energy, Sorensen, B., 2002, Analysis and Design of Energy Systems, Hodge, BK and Taylor, RP, 1999, National Energy Balance, EPE, 2011

Syllabus: Oil and gas offshore production concepts. A short history of oil and gas offshore production.  Critical aspects on the definition of the offshore production system. Phases of the development of oil and gas offshore fields. Types of production units. Mooring systems. Subsea equipment. Oil and gas recovery. Artificial lift, boosting and flow assurance.  Offshore oil and gas processing. Subsea boosting and processing systems. Offshore oil and gas export systems
Syllabus: Combustion thermochemistry. Introduction to mass transfer. Combustion chemical kinetics. Combustion chemistry mechanisms. Reactive system analysis involving coupling chemistry and thermodynamics. Laminar premixed flames. Laminar diffusion flames

Bibliography: Turns, S. R., An introduction to combustion: concepts and applications, 2nd ed. Boston: McGraw-Hill, 2000, 676 p.; Borghi, R., Champion, Michel, Modélisation et théorie des flammes, Paris: Editions Technip, 2000, 402 p.; Williams, F. A., Combustion theory: the fundamental theory of chemically reacting flow systems, 2nd ed. Cambridge: Perseus books, 1985. 680 p

Syllabus: Robot classification. Planar and spatial kinematics. Homogeneous transformations. Denavit-Hartenberg notation. Differential movement analysis. Jacobian matrices. Singularity and redundancy. Inverse kinematics. Trajectory synthesis. Optimal kinematic control of redundant robots. Free body diagram. Duality between static and kinematics. Servo-stiffness. Newton-Euler dynamic formulation. Physical interpretation of manipulator dynamics (gravity, inertial and coupling terms). Lagrange formulation. Inertia matrix of a robotic manipulator. Generalized forçes. Inverse dynamics. Luh-Walker-Paul algorithm. Introduction to trajectory control: PID, Computed Torque Control. Cartesian control. Introduction to force control: Hybrid Position/Force Control and its architecture. Natural and artificial constraints. Modeling and stability of robot-environment interaction

Bibliography: Robot Analysis and Control, Asada, H., Slotine, J.J., Wiley, 1986; Robot Dynamics and Control, Spong, W., Vidyasagar, M., Wiley, 1989; Introduction to Robotics: Mechanics and Control, Craig, J.J., Addison-Wesley, 1986; Methods of Analytical Dynamics, Meirovitch, L., Mc.Graw-Hill; Engenharia de Controle Moderno, Ogata, K., Prentice-Hall, 1990

Syllabus: Elementary components of mechatronics systems. Kinematics, static and dynamics of manipulators. Trajectory control: PID, Computed Torque Control, Lyapunov stability, Adaptive Control, Learning Control. Force Control – Hybrid Position/Force Control, Friction compensation in manipulators, assembly/insertion tasks, coordination of multiple manipulators. Tele-robotics. Compliant robots. Manipulator calibration. Servo-visual control of robots. Advanced control techniques

Bibliography: Robot Analysis and Control, Asada, H., Slotine, J.J, Wiley, 1986; Robot Dynamics and Control, Spong, W., Vidyasagar, M., , Wiley, 1989. Applied Nonlinear Control, Slotine, J.J., Li, W., Prentice Hall, 1991; Introduction to Robotics: Mechanics and Control, Craig, J.J., Addison-Wesley, 1986; Methods of Analytical Dynamics, Meirovitch, L., McGraw-Hill; Engenharia de Controle Moderno, Ogata, K., Prentice-Hall, 1990

Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Individual study of topics that are not covered in regular graduate courses of the mechanical engineering department
Syllabus: Oral and written presentation of the master thesis theme
Syllabus: Oral exam of the fundamentals of mechanical engineering, and proposal for the doctorate thesis
Syllabus: Assist a professor with academic and instructional responsibilities
Syllabus: Assist a professor with academic and instructional responsibilities
Syllabus: Assist a professor with academic and instructional responsibilities


The Department of Physics of PUC-Rio, ever since its foundation, has occupied an outstanding position in the Brazilian scientific arena, as can be seen from the number of publications of its faculty and their regular attendance at national and international conferences.

The M.Sc. program began in 1965, while the Ph.D. program was implemented in 1968. The research activities developed in the Department of Physics cover a broad spectrum of subjects including Atomic and Materials Physics, Applied Physics, Solid State Physics, Optics, Particles Physics and Field Theory and Phenomenology. The program aims to prepare scientists capable of developing ground-breaking technology.

Additional information can be found at the Department’s site  and, in Portuguese, here:



Syllabus: Operators, Dirac notation, Hilbert space. Experimental background of Quantum Mechanics: blackbody radiation, photoelectric effect, wave-particle duality. Bohr-Rutherford atom. Franck-Hertz experiment. Postulates of Quantum Mechanics, Schrödinger’s equation. One-dimension problems. The classical limit – Ehrenfest’s theorem. Harmonic Oscillator. The Uncertainty Principle. Symmetries. Angular momentum. The Hydrogen atom

Bibliography: R. Shankar – Principles of Quantum Mechanics – Plenum Press

Syllabus: Analytic Functions, Hilbert Transforms, Complex Integration, Cauchy Principle Value, Power Series, Analytical Continuation, Theory of Distributions, Residue Theory, Special Functions and Integral Representations, Laplace Transform and Gamma Function, Saddle Point Approximation, Fourier Transformation, Green’s Function, Causality and Analyticity, Dispersion Relations

Bibliography: Mathematics of Classical and Quantum Physics, Byron Fuller –Vol. II, Addison-Wesley

Syllabus: Lagrangian Formulation. Kinematics and Equations of Rigid Bodies. Small Oscillations. Hamiltonian Formulations. Canonical Transformations. Hamilton-Jacobi Theory. Relativistic Mechanics
Syllabus: Scattering. Scattering cross section. Born-Oppenheimer approximation. Phase shifts method. S matrix. Time Dependent Phenomena. Time dependent perturbation theory. Fermi golden rule. Adiabatic and sudden approximation. Second Quantization. Identical particles. Bosons and fermions. One-body and many- body operators. Equation of motion method in the occupation number formalism. Interaction of Radiation with Matter. Quantization of the radiation field and their interactions. Spontaneous and stimulated emission. Electrical and magnetic multi-polar approximation. Selection rules
Syllabus: Dirac equation and its solutions. Hydrogen Atom. Hole theory. Theory of propagators. Quantum electrodynamic processes: Coulomb scattering of electrons. Compton scattering. Bremsstralung. Pair annhilations. Vacuum polarization

Bibliography: Relativistic Quantum Mechanics, J. D. Bjorken and S. D. Drell, McGraw Hill; Quantum Electrodynamics, W. Greiner, Springer, Quantum Field Theory, Cambridge University Press, S. Weinberg

Syllabus: Maxwell Equations. Electromagnetic Waves. Wave guides. Electromagnetic Potentials and Gauge Transformations. Electromagnetic Fields in Matter. Electromagnetic Fields from Arbitrary Source Distributions. Electromagnetic Radiation and Radiating Systems. Relativistic Electrodynamics

Bibliography: J.D. Jackson, Classical Electrodynamics, Wiley & Sons)

Syllabus: Total and differential cross sections; Coulomb Potential; Asymptotic behavior: Rutherford scattering; Bare-Ion Collisions; Born approximation: elastic and inelastic collisions; High-velocity behavior: Bethe approximation; Ionization: low- and high-velocity collisions; correspondence with the classical case; Internal and external screening; Atom-atom collision: Bates-Griffing formulation; Closure approximation; Screening and Antiscreening; Sum-rule and Antiscreening; Time-dependent Perturbation theory; Semi-classical approximation; Current-vector formalism; Equivalence between the PWBA and the Semi-classical approximation; Antiscreening probability for hydrogenic atoms; Free-collision Model; Equivalence between the Antiscreening e electron-impact ionization; Independent Particle Model and the Independent Event Model

Bibliography: Physics of Atoms and Molecules, B. H. Bransden e C. J. Joachain, 2a ed., 2003; Intermediate Quantum Mechanics, H. A. Bethe e R. Jackiw, 2a ed., 1973; Introduction to the Theory of Ion-Atom Colisions, M.R.C. MacDowell and J.P. Coleman, North-Holland

Syllabus: Surface crystallography. Surface energy, surface relaxation, surface reconstruction and defects. Surface scattering. Physical and Chemical adsorption. Catalysis. Dessorption. Photon and ion induced desorption. Surface erosion induced by ion bombardment. Secondary electrons emission: mechanism

Bibliography: Modern Techniques of Surface Science, Woodruff and Delchar, Cambridge Science Series; Physics at Surfaces, A. Zangwill, Cambridge Univ. Press; Surfaces and Interfaces of Solids, H. Lüth, Springer-Verlag

Syllabus: Vacuum Technology. Physical Vapor Deposition. Chemical Vapor Deposition. Mechanism of thin films formation. Epitaxy. Interdiffusion and reaction. Mechanical Properties. Tribological Properties. Optical properties. Electronic properties. Thin films applications

Bibliography: The Material Science of Thin Film, M. Ohring, Academic Press; Film Deposition by Plasma Techniques, M. Konuma, Springer-Verlag, Cold Plasma in Materials Fabrication, A. Grill, IEEE Press

Syllabus: Interaction of radiation with matter. X-ray diffraction, Electron diffraction. Scanning and transmission electron. Mass spectrometry. Nuclear techniques: RBS, PIXE e nuclear reactions. Methods of surface analysis: LEED, ISS, SIMS, PDMS, XPS, AES, AFM e STM

Bibliography: Methods of Surface Analysis (Methods and Phenomena: their application in Science and Technology), A.W. Czanderna, Elsevier; Physical Methods for Materials Characterization, P.E.J. Flewitt and R.K. Wild, Institute of Physics, Publishing Ltd.; Handbook of Modern Ion Beam Analysis, J.R. Tesmer and M. Nastasi, Materials Research Society

Syllabus: Superconducting Materials. Thermodynamics of the Superconducting States. Superconductors in Magnetic Fields. Critical Currents. Type I and Type II Superconductors. High Temperature Superconductors. Josephson Effect. Technology and Applications

Bibliography: Superconductivity, W. Buckel, VCH; Introduction to Superconductivity and High-Tc Materials, M. Cyrot e D. Pavuna, World Scientific

Syllabus: Crystal Lattices. Periodic Structures. Symmetries. The translation symmetry group. Reciprocal lattices. Bloch Theorem. Band Structures. The Free electron model. Tight binding, kxp and pseudopotential band structure calculation. The effective mass theory. Transport Properties: Quantum theory of the harmonic crystal. Phonons. Donor and acceptor impurity doping. Disordered systems. Localized states. Electron-phonon interaction. Conductivity of doped semiconductor. Low Dimensional Systems: Bi-dimensional free electron gas. Magnetic Field effects. Landau levels. Bohm-Aharonov effect. Hall effect. Double well and superlattices heterostructures. Resonant tunneling. Nanoscopic systems. Quantum dots, wires and quantum wells. Electrical transport. Electronic correlation. Coulomb blockade

Bibliography: Electronic Structure and the Properties of Solids, W. A. Harrison; Handbook on Semiconductor, vol. I; Physics of Heterostructures, G. Bastard, Solid State Physics, N. Ashcroft, N.Mermin, The Theory of Brillouin Zones and Electronic States in Crystals, H Jones

Syllabus: Phase transitions. Mean-field theory. Numerical simulations. Ising model: exact and approximate results. Scaling theories and renormalization group

Bibliography: Introdução à Física Estatística, S. Salinas, EdUsp; The Theory of Critical Phenomena, J. Binney et al., Oxford; M. Kardar, Statistical Physics of Fields, Cambridge

Syllabus: Sensors and transducers – physics principles and applications. Signal conditioning – instrumentation amplifiers and signal filtering. The lock-in amplifier and the spectrum analyzer. Digital signal acquisition – AD/DA converters. Using instruments via the GPIB interface

Bibliography: The Art of Electronics, Paul Horowitz and Winfield Hill, Ed. Cambridge University Press, 2a edition

Syllabus: The molecular logic of life. The cell, viruses. Biomolecules. Water, ionization equilibrium. Proteins: amino acids, peptides, structure and function of proteins, enzymes and catalysis, molecular modeling. Biomembranes and membrane models: structure, active and passive transport. Nucleotides and nucleic acids: structure, genetic code, protein synthesis, genetic engineering. Absorption spectroscopy and fluorescence. Electron spin resonance. Nuclear magnetic resonance. Mass spectrometry
Syllabus: Fiber optics: fundamentals and characteristics. Laser: Fundamentals and characteristics. Mechanism for generation of short pulses (pulse duration: ps and fs). Active mode-locking. Passive mode-locking: saturable absorbers. Electro-optics modulator. Acousto-optic modulator. Basics of non-linear optics: non-linear Schroedinger equation. Non-linear optics in fibers: second order effects, third order effects, solitons. Bragg gratings

Bibliography: Lasers, Siegman; Nonlinear Optics, Boyd; Nonlinear Fiber Optics, Agrawal

Syllabus: Ensembles: Microcanonical, Canonical and Grand Canonical; Quantum statistics and applications at finite temperature. Non-ideal systems: methods of approximation. Thermodynamics of phase transitions

Bibliography: Introdução à Física Estatística, S. Salinas, EdUsp; Statistical Mechanics, K. Huang, 2a edição, John Wiley; M. Kardar, Statistical Physics of Particles, Cambridge

Syllabus: Many-body Formalism: Second Quantization. Many-body operators. Green functions. Analytical properties. Equation of motion method. Time evolution operators. Causal Green functions. Wick theorem. Feynman diagrams. Dyson equation. Finite temperature formalism. Free electron gas. Keldysh formalism for out of equilibrium systems. Model Hamiltonians. Electron-phonon interaction. Superconductivity. Hubbard Hamiltonian. Metal-nonmetal transition. Itinerant magnetism. Impurity Anderson Hamiltonian. Kondo effect. Heavy fermion physics

Bibliography: Many Particle Physics – 2a edição, G. Mahan, Plenum Press,Methods of Quantum Field Theory in Statistical Physics A. Abrikosov, L. Gorkov e I Dzyaloshinski,Electron Correlations in Molecules and Solids, P Fulde, A Guide to Feyman Diagrams in the Many Body Problem, R Mattuck

Syllabus: Special Relativity: experimental basis; Einstein postulates; Lorentz transformations; Relativistic kinematics; Minkowsky space; Relativistic mechanics; Relativistic electrodynamics. General Relativity: the principle of equivalence; the principle of general covariance; General coordinate transformations; Geodesics; Covariant derivatives; Energy-Momentum tensor; Einstein equations; the Newtonian correspondence; Experimental tests of General Relativity. Relativistic Cosmology: Cosmological principles. Models of the Universe


The graduate program in Computer Science at the Department of Informatics (DI) is the oldest of its kind in the country and was the first to obtain the highest score awarded by CAPES, the agency of the Ministry of Education in charge of evaluating all national graduate programs.

The program comprises 9 areas: Data Bases, Computer Graphics, Software Engineering, Hypertext and Multimedia, Human-Computer Interaction, Programming Languages, Optimization and Automatic Reasoning, Computer Networks, Distributed Systems, Theory of Computing.

The department also hosts the Institute of Software Technology (ITS), which congregates 13 thematic laboratories and serves as a center for projects developed with the industry and funding agencies.

Additional information can be found, in Portuguese, here.


The Mathematics Department was created in 1966. Its undergraduate program began in 1968, the M.Sc program started in 1969 and the Ph.D. program in 1973. The graduate programs specialize both on Pure and Applied Mathematics. So far, more than 292 Master of Science degrees and 105 Doctor of Philosophy degrees have been awarded by the Department.

The department is a structural unit of PUC-Rio which concentrates all the academic, scientific and administrative activities related to the teaching, study and research of Mathematics. The department is responsible for all of the Math-related disciplines that are offered in the varied university curricula, both at the undergraduate and graduate level. By integrating the different fields of study, the department’s course offerings is constituted of different disciplines in Mathematics which make up not only the Basic Core courses for students in the Science and Technology Center (Electrical Engineering, Mechanical Engineering, Civil Engineering, Materials and Metallurgy Sciences, Mathematics, Chemistry, Physics and Informatics) but also those for students in the Center of Social Sciences majoring in Business Administration, Economics and Actuary.

An interesting aspect of the graduate program in Mathematics is the close contact established between pure and applied mathematicians with researchers of other fields – an integration that is encouraged by the University, especially due to the fact that PUC-Rio is strong in technological and economic research and in the interaction with the private sector. The Mathematics program is also directly involved with the business world, mainly with companies in the petroleum, insurance and healthcare industries.

The academic staff of the program is made up of nationally and internationally renowned researchers whose scientific publications appear in journals published worldwide. Of its 16 faculty members, 15 professors have been awarded important research grants and two of them are members of the Brazilian Academy of Sciences. The Department’s involvement in exchange programs with other universities in Brazil and abroad is intense and the quality of its graduate program in Mathematics is recognized by the scientific community. .

Additional information can be found at the Department’s site, in Portuguese, here.


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Syllabus: Fields, vector spaces, bases, dimension, matrix algebra, linear operators. n-dimensional real and complex vector spaces as normed spaces. Gaussian elimination, determinants. Invertible matrices. Eigenvalues, eigenvectors, invariant subspaces. Characteristic polynomial. Diagonalization of operators. Real and complex Jordan forms. Inner product. Orthogonal bases. Singular value decomposition. Self-adjoint operators, symmetric matrices. Spectral theorem
Syllabus: Rings, polynomial rings, Ideals. Quotient rings. Homomorphisms. Field of fractions of an integral domain. Euclidian domains. Irreducibility of polynomials. Groups. Permutation groups. Matrix groups. Abelian groups. Homomorphisms and quotient groups. Group actions
Syllabus: Fields and Field extensions. Algebraic number fields. Finite fields. Characteristic of a field. Constructions by ruler and compass. Galois Theory. Examples of low degree. Resolution of polynomials equations of degree 3 and 4 in one variable. Solvable groups, resolution by radicals. Examples of equations that cannot be solved by radicals
Syllabus: Ideals in commutative rings. Spectrum of a ring. Zariski topology. Radicals. Modules. Tensor product. Localization. Noetherian and Artinian rings. Primary decomposition. Support. Algebraic extensions, Noether’s normalization theorem and Hilbert Nullstellensatz. Integral extensions, “going-up” and “going down” theorems. Discrete valutation rings. Invertible Ideals. Completion, Artin-Rees’ lemma, Krull’s theorem, Hensel’s theorem. Dimension theory
Syllabus: Vector and matrix norms, orthogonal projections. Matrix algebra algorithms with rounding error analysis. System of linear equations: LU decomposition, positive definite systems, band symmetric, bloc and sparse matrices. QR and SVD decompositions with applications. Iterative methods, Krylov subspace methods, conjugate gradient and related methods. Algorithms for eigenvalue decomposition
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Syllabus: Affine space. Closed algebraic subsets. Zariski topology. Regular functions. Sheaves. Algebraic Varieties. Morphisms. Projective Varieties. Properness theorem. Irreducible components. Rational functions. Finite morphisms. Dimension: Krull dimension, transcendence degree, Zariski tangent space. Krull’s lemma. Local properties. Smooth points. Rational maps. Blow-up. Normalization. Dimension of the fibers. Bertini’s theorem. Vector bundles. Canonical line bundle. Adjunction formula. Divisors, inversible sheaves, canonical divisor. Linear systems. Ample line bundles, immersions in the projective space. Coherent sheaves. Riemann-Roch for curves. Applications. Intersection numbers. Hodge index theorem. Birational maps of surfaces
Syllabus: Holomorphic functions in several variables. Complex varieties. Kähler metrics. Blow-up. Complex vector bundles, connections, curvature, Chern classes. Sheaves and cohomology. Harmonic forms, Hodge theorem and applications. Kähler identities, Hodge decomposition. Serre-Kodaira duality. Lefschetz decomposition. Divisors and line bundles. Bertini theorem. Adjunction formula. Kodaira’s vanishing theorem. Lefschetz’s theorem on hyperplane sections. Lefschetz’s theorem on (1,1) classes. Algebraic varieties. Chow’s theorem. Kodaira’s immersion theorem. Picard and Albanese varieties. Applications
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Syllabus: Kolmogorov’s axioms of probability. Discrete random variables. Counting problems and probability as the relative frequency of events. Continuous random variables. Mean and variance. Conditional mean and variance. Generating functions and characteristic functions. The deMoivre-Laplace limit theorem. The Poisson limit theorem. The law of large numbers. The basic central limit theorem. Introduction to random walks, markov chains and probability on graphs. The Monte Carlo method
Syllabus: Probability spaces, basic properties. Construction of probability measures in R and Rn. Random variables and vectors. Distributions of probability and distribution functions in Rn. Independence and product measures. Expectation of random variables: basic properties and inequalities. Types of convergence of random variables. Law of large numbers: weak convergence and Borel-Cantelli lemmas. Strong law of large numbers. Kolmogorov’s three-series Theorem. Characteristic functions and convergence in distribution in Rn. The Theorem of Lindeberg-Feller. Applications. Further topics: Kolmogorov’s extension theorem (existence of sequences of i.i.d. random variables)
Syllabus: Stable laws and infinitely divisible laws. Expectation and conditional probability; properties, existence theorems and regularizations. Discrete time Martingales: Doob’s decomposition theorem, Doob’s inequalities, stopping times, optional stopping theorem, crossing number inequality, Martingale convergence theorem. Markov chains; random walks in countable spaces, transient and recurrent behavior. Birkhoff’s ergodic theorem
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Syllabus: Initial value problems: simple and multiple pass method, polynomial interpolation, stability and stiffness, linear and non-linear systems. Boundary value problems: finite difference method for linear problem and discretization. Methods for non-linear problems: shooting, projection, collocation, Garlekin and spline approximations. Explicit and implicit methods for elliptic, parabolic and hyperbolic equations. Fourier transforms. Discretization from integral form. Semi-discrete methods. Error and stability analysis
strong>Syllabus: Fourier analysis and wavelets for discrete PDE’s. Approximation spaces, finite elements. Viscosity solutions for PDE’s. Variational formulations. Invariant approximations. Physical invariants and discrete exterior calculus. Simulation with reduced sampling and particle methods
Syllabus: Geometric transformations; 3d interface; arcball and quaternions; curve drawing; sampling; basis of geometric data structure; rendering and shading; graphs of 2d and 3d functions; programming notions in C/C++ or python; openGL basics
Syllabus: Splines; geometric interpolation; Delaunay triangulations; mesh data structure; parametric and implicit surfaces; boolean operations
Syllabus: Image models, discrete convolution, smoothing, linear filters, scale spaces, colour histograms manipulations; gaussian mixture models and edition, statistical learning, colorization, snakes, watershed, distance transform, image foresting transform, min cut segmentation, mathematical morphology, features, SIFT, tracking, openCV
Syllabus: Revision of cell complexes and their topological properties, definition of discrete topological invariants as Euler characteristic, Betti numbers, fundamental homology cycles. Morse, Morse-Smale, Witten-Morse theories and their discretization through piecewise-linear, finite elements and Forman approaches with applications to Computer Graphics. Applications of those techniques to geometry processing and shape edition
Syllabus: Triangulations and simplicial complexes, Voronoï and Laguerre diagrams, Delaunay and regular triangulations, interpolations with paraboloids, medial axes and alpha-shapes, sampling on surfaces, geodesic and discrete curvature computation, discrete Laplace operators and minimal surfaces, Laplacian surface deformation
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Syllabus: Complex derivative; Cauchy-Riemann equations. Power series; analytic functions. Complex line integrals. Index of a curve, homotopy. Cauchy’s theorem; Cauchy’s integral formula. Homologous curves. Morera and Goursat’s theorems. Poles. Laurent series. Residuals. Riemann sphere; meromorphic functions. Maximum modulus theorem. Schwartz lemma. Möbius mappings; cross-ratio. Normal families, Montel’s theorem. Riemann mapping theorem. Additional topics
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Syllabus: Measure spaces. Exterior measure; Carathéodory extension theorem. Completion. Examples: Lebesgue measure. Measurable functions. Integral. Convergence theorems. Borel measures; regularity. Riesz representation theorem in the space of continuous functions. L^p spaces. Product measures; Fubini-Tonelli Theorem. Signed measures. Hahn decomposition theorem, absolute continuity, Radon-Nikodym theorem, Lebesgue decomposition. Differentiation of monotonic functions, functions of bounded variation, differentiation of an indefinite integral, Lebesgue points of density, absolute continuity
Syllabus: Normed vector spaces and Banach spaces. Dual spaces. Zorn’s lemma and the Hahn-Banach theorem – analytic and geometric forms. Baire’s theorem and the Banach-Steinhaus theorem. Open mapping and closed graph theorems. Weak topologies, reflexive spaces. Separable spaces. Hilbert spaces. The Lax-Milgram and Stampacchia´s theorems. Spectral theory in Hilbert spaces. Lebesgue-measurable functions and L^p spaces. Sobolev spaces. Applications to boundary value problems for partial differential equations
Syllabus: Topology of N-dimensional euclidean spaces: metric structures, topological structures and the notion of completeness. Scalar fields, continuity, and the notion of derivative of a scalar valued function in R^N. The contraction principle, the Inverse Function Theorem and the Implicit Function theorem. The rank theorem and normal forms for mappings between euclidean spaces. Taylor’s formula for the approximant. Jordan measurable sets. The integral in the sense of Riemann, and the notion of integrable function. Fubini’s theorem and the change of variable formula for N-dimensional domains
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Syllabus: Simplicial and singular homology. Excision. Mayer-Vietoris sequence. Singular and De Rham cohomology. Orientation and duality in manifolds
Syllabus: Higher order homotopy groups. Fibrations and fiber bundles; homotopy exact sequence. Universal fibrations. Elementary calculation of some homotopy groups of the classical groups
Syllabus: Metric spaces, Topological spaces. Continuity. Connected and compact spaces. Fundamental group. Covering spaces. Classification of surfaces
Syllabus: Sard Theorem. Transversality. Intersection theory mod 2: intersection number, degree, winding number. Oriented intersection theory. Lefschetz fixed point theorem. Euler characteristic. Vector fields; Poincaré-Hopf Theorem. Introduction to Morse theory. Classification of compact surfaces
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Syllabus: Planar and spatial curves. Frenet frame and applications. Euclidean space. Calculus on surfaces: areas, isometries, conformal mappings. Orientation. Gauss normal map, curvatures, special lines (curvature lines, asymptotic lines, geodesics). Gauss egregium theorem. Gauss-Bonnet theorem and applications
Syllabus: Definition of Riemann surface. Holomorphic maps and their properties. Isothermal parameters. Construction of Riemann surfaces. Riemann surface of an algebraic equation. Conformal structures. Branched coverings. Hurwitz formula. Riemann relation. Analytic continuation. Uniformization theorem, proof and examples: the unit disc as the universal covering of the sphere minus three points. Riemann surfaces as quotient of its universal covering surface, Koebe-Poincaré theorem. Conformal structures on the tori. Weierstrass P function and other elliptic functions. Conformal structures on the annuli. Great Picard theorem
Syllabus: Sheaves. Algebraic Functions. Fundamental group and singular (co)homology of compact Riemann surfaces. Monodromy. Algebraic Curves. Divisors, line bundles, canonical line bundle. Linear systems, maps to the projective space. Sheaves cohomology, finiteness theorems. Dolbeault’s theorem. Serre duality. Riemann-Roch theorem. Harmonic forms. Vanishing of the cohomology, ample line bundles, immersion into the projective space. Hyperellitpic curves. Picard group. Jacobian. Abel’s theorem. Jacobi’s theorem. Applications to algebraic curves and their jacobians
Syllabus: Representations of finite groups. Schur’s lemma. Characters. Class functions, irreducible representations and conjugacy classes. The regular representation. Induced and restricted representations. Frobenius reciprocity. Group Algebra. Applications. Elements of Lie Groups and Lie algebras. Lie theorems. Killing form. Semi-simple Lie algebras. Cartan subalgebras. Maximal tori. Roots, weight spaces. Weyl group. Unitary trick for compact Lie groups. Representations of compact Lie groups. Applications. Irreducible representations of SL(n,C) and GL(n,C)
Syllabus: Differentiable manifolds. Examples. Submanifolds. Tangent space. Differentiable maps. Embeddings and immersions. Partitions of unity. Orientations. Manifolds with boundary. Differential forms. Exterior derivative. Frobenius theorem. Integration of forms. Stokes Theorem. Applications
Syllabus: Topological groups, the classical groups, Lie groups, homomorphisms of Lie groups, subgroups, coverings, Lie algebra associated to a Lie group, simply connected Lie groups, exponential mapping, closed subgroups, elementary representation theory, adjoint representation, maximal tori, group actions, orbits and orbit spaces. Homogeneous spaces, fixed points, actions on coverings
Syllabus: Riemannian metrics. Riemannian connection. Geodesics. Curvatures. Jacobi fields. Complete Riemannian manifolds. Isometric immersions. Spaces of constant curvature. Variations of energy. Rauch comparison theorem. Morse index theorem. Homogeneous spaces
Syllabus: Several equivalent definitions of minimal surfaces in Euclidean space. Classic examples and their geometric characterizations. The Weierstrass representation. Curvature estimates and Bernstein’s theorem. Schwarz reflection principle. Conjugate and associate minimal surfaces. Complete minimal surfaces of finite total curvature. The maximum principle, Rado theorem and the half-space theorem. Douglas-Rado solution to the Plateau problem
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Syllabus: Differential equations of first order. Reduction of high order equations to first order systems. Existence and uniqueness of solutions. Dependence on the initial conditions. Extension of solutions. Linear systems with constant coefficients. Non-homogeneous linear equations and non-autonomous linear equations. Poincaré-Bendixson theorem
Syllabus: Introduction. Classic methods for solving PDE. First order equations. Cauchy problem. Caucky-Kowalevskaya theorem. Classical second-order PDEs and boundary value problems. Well-posed problems. Generalizations to systems of PDE and higher order equations
Syllabus: Maximum principles for second order linear elliptic equations. Schauder a priori estimates. Compactness principles for sequences of solutions of elliptic PDE. Existence theorem for the classical Dirichlet problem for second-order linear elliptic PDE – Perron’s method (sub- and super-solutions method). Alexandrov-Bakelman-Pucci maximum principle. Applications to the theory of solvablity and regularity of solutions of general PDEs – Krylov-Safonov theory. First eigenvalue of an elliptic operator, maximum principle. Applications to the qualitative theory – Alexandrov’s moving planes method, symmetry of positive solutions of elliptic PDE
Syllabus: Sobolev spaces. Weak solutions in Sobolev spaces of elliptic PDE in divergence form. Solvability of linear elliptic equations in divergence form and regularity of the weak solutions. “Bootstrap” methods for regularity of the weak solutions of nonlinear equations. Variational characterization of the eigenvalues of a self-adjoint elliptic operator of second order. Variational formulation of solutions of divergence-form PDE. Methods for searching critical points – direct minimization, “mountain-pass” and “linking” type theorems. Notion of weak viscosity solution of an elliptic PDE. Existence and regularity of the viscosity solutions of general nonlinear elliptic PDE
Syllabus: Schauder’s fixed point theorem for compact maps. Nonlinear Leray-Schauder alternative. Leray-Schauder fixed point theorem. Existence of solutions of quasilinear elliptic equations following from a priori estimates for the solutions and their gradient. Maximum principles for nonlinear elliptic equations of second order. A priori estimates in the C^1-norm for solutions of constant mean curvature equations in various settings. Applications to the Dirichlet problem in bounded domains with smooth boundary data. Perron’s method, applications to Dirichlet problems in unbounded domains with continuous boundary data
Syllabus: Basic notions of dynamics: periodicity, recurrence, transitivity, minimality. Fundamental examples: contractions, linear maps, rotations, gradient flows, Morse-Smale functions. Circle dynamics: rotation number, Denjoy example and theorem, Poincaré´s classification. Expanding maps, Symbolic dynamics, topological mixing, shifts of finite type, Smale horseshoe, toral automorphisms, geodesic and horocyclic flows on surfaces, kneeding theory
Syllabus: Local stability theory for hyperbolic periodic points of diffeomorphisms and closed orbits of flows. Hartman-Grobman Theorem, and existence of invariant submanifolds. Morse-Smale diffeomorphisms, Hyperbolic sets, examples: Anosov linear systems, Plykin atractor, solenoid. Lambda-Lemma, transversal homoclinic points and horseshoes, symbolic dynamics. Stable manifold theorem for Anosov systems, expansiveness and shadowing property, Anosov closing lemma and stability of hyperbolic sets. Structural stability of Morse-Smale systems, cycles and filtrations, omega stability for Axiom A systems without cycles, omega explosions
Syllabus: Invariant measures; the weak topology and existence of invariant probabilities for continuous maps. Examples. Recurrence and ergodicity: Poincaré recurrence theorem, topological and metric versions. Birkhoff theorem. Ergodicity, unique ergodicity, mixing. Examples: shifts, rotations, expanding maps of the circle, toral automorphisms, Furstenberg example, geodesic and horocyclic flows on surfaces. Ergodic decomposition. Topological and metric entropies: generating partitions, Kolmogorov-Sinai theorem
Syllabus: Linear symplectic spaces and their geometry. Darboux’s theorem for symplectic forms and contact forms. The nonlinear theory of symplectic spaces and basic notions of symplectic topology. Lagrangean geometry. Weinstein’s Lagrangean neighborhood theorem. The theorem of Givental on germs of Lagrangean varieties. Weinstein’s trick of the Lagrangian graph. Momentum maps and reduction theory. An introduction to one dimensional variational calculus. The geometry of Hamiltonian and Lagrangian systems. Applications to classical mechanics, geometric optics and integrable systems
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Metrology for Quality and Innovation

The Postgraduate Program in Metrology of Pontifical Catholic University of Rio de Janeiro (PósMQI) was implemented in 1996 in response to the Brazilian Government’s Human Resources Metrology Program (RH-Metrologia), aimed at promoting Metrology and the development of qualified human resources to meet the country’s demands in areas related to the Science of Measurements. Consistent with the essentially interdisciplinary nature of Metrology, the Program benefits from the combination of existing laboratory skills and infrastructure in various Departments and Units of the University’s Center for Science and Technology.

Over the years, in addition to graduate education in topics of interest to metrology and its related areas, the Program has evolved to new areas of interest and competence, meeting the guidelines of the Country’s Industrial Policy and its National Strategy for Science, Technology and Innovation. In addition to focusing on education and research in Metrology and Quality, also prioritizes its innovation pillar, aiming at meeting the new demands of the different industry and services sectors of the Brazilian economy. It also seeks to cooperate with other Science and Technology Institutions around the world, which are dedicated to the scientific and technological interface with measurement techniques and measurement standards.

Within this context (i) PósMQI meets the critical demands of industrial competitiveness, corporate sustainability and the Metrology segments in Energy, Chemistry and Biosciences, among others; (ii) promotes quality in its broadest sense, focusing on quality systems, environment, product and people certification, social responsibility, labor relations and the environment; and (iii) monitors and evaluates local, regional and national innovation programs and systems, contributing to the development of practices, routines and metrics for their effective management. It investigates the interfaces between Science and Technology and those of measurement, as well as exploring new frontiers in an emerging, knowledge-based society driven by entrepreneurship, creativity and innovative capacity.

Acting with the focus on its unique Area of Concentration (Metrology for Quality and Innovation), the Program offers the following three complementary lines of research in metrology:

  • Instrumentation and Measurement;
  • Strategic Management of Innovation and
  • Sustainability; and Smart Grid.

The Postgraduate Program in Metrology of Pontifical Catholic University of Rio de Janeiro currently holds the highest evaluation score (5) in the four-year periodic evaluation carried out by the Ministry of Education (CAPES/MEC) of Brazil, reflecting the excellence of its performance, maturity and credibility. By 2018, the Program graduated 236 Masters in Metrology.

Additional information can be found at the Program’s site and in Portuguese, here.


Syllabus: The course aims to guide M.Sc. students (1) to be acquainted with the research lines of the program and research projects in development, (2) to disseminate among the students and faculty the experience and knowledge of external experts working in Metrology and its related areas; (3) to facilitate interaction and exchange of knowledge among students, professors and external experts in order to stimulate the debate on special topics that reflect the state of the art in metrology and its applications in different areas of knowledge

Bibliography: International Journals in Metrology

Syllabus: Introduction and History of the Science of Measurement. National, Regional and International Organizations of Metrology. International Vocabulary of Metrology; International Vocabulary of Legal Metrology; Guide to the Expression of Uncertainty in Measurement; International System of Units. Metrological Reliability of Measurement Systems. Laboratory Infrastructure for Calibration and Testing; International Organization for Accreditation and Mutual Recognition Agreements
Syllabus: The course fulfills two complementary purposes: (i) to leverage basic knowledge about the functions of industrial technology (especially those that comprise the national quality infrastructure and impact on mutual recognition of measurement results, calibration certificates and test reports), and (ii) to enable graduate students to access international literature on key issues related to international trade and technical barriers to trade. Among the topics studied are: Basic fundaments of S&T; of industrial technology (metrology, standards, technical regulations, accreditation, conformity assessment, intellectual and industrial property and technology management); organizational structure of S&T in Brazil and functions of international organizations active in metrology and related fields. The discipline also discusses the voluntary nature of standards and the compulsory approach for technical regulations (mandatory standards); conformity assessment (certification, testing, labeling) in regulated fields (compulsory) and voluntary and fundamentals of technology transfer, technology assessment at the company and intellectual property (trademarks and patents)

Bibliography: FROTA, M.N., OHAYON, P. & MAGUELLONE Chambon. Padroes e Unidades de Medida: Referências Metrológicas da Franca e do Brasil, (BNM/Franca), editado na França e impresso no Brasil por editora Qualitymark, 1999. ARMANDO Albertazzi G.Jr e ANDRÉ R. de Sousa, Fundamentos de Metrologia Científica e Industrial –editora Manole-2008 3. COSTA MONTEIRO E. Notas de Aula da Disciplina MQI 2001 – Fundamentos da Metrologia. VIM – International Vocabulary of Metrology – Basic and general concepts and associated terms – JCGM 200:2008 , BIPM, The International System of Units (SI), 8th edition, 2006, Guide to the expression of uncertainty in measurement (1993, amended 1995) (published by ISO in the name of BIPM, IEC, IFCC, IUPAC, IUPAP and OIML. OIML V1:2000, International Vocabulary of Terms in Legal Metrology (VIML)

Syllabus: Descriptive statistics, location and dispersion parameters, Random Variable; discrete and continuous, Bayes Theorem, Probability concepts and probability function and probability density function, Examples of discrete and continuous models, independence, correlation, transformation of variables, Random sample, Point and interval parameter estimation, regression models and basic concepts of hypothesis tests
Syllabus: Fundamentals of scientific methodology. Classification of research methodologies by type. Overview and of electronic databases for scientific research and practical applications. Comprehension of research contexts and approaches to delimitate the research. Formulation of research questions and definition of general and specific aims. Preparation of the presentation for research project seminar at the end of period. Research methods focusing on specific needs identified by students

Bibliography: LAKATOS, Eva Maria, MARCONI, Marina de Andrade. Fundamentos de metodologia científica. 3ª ed. São Paulo: Atlas, 1991. OLIVEIRA, Silvio Luiz. Tratado de metodologia científica. São Paulo: Pioneira, 2001. SALOMON, Délcio. Como fazer uma dissertação. São Paulo: Martins Fontes, 1994. GIL, Antonio Carlos. Como elaborar projetos de pesquisa. 3ª ed. São Paulo: Atlas, 1991. VERGARA, Sylvia Constant. Projetos e relatórios de pesquisa em administração. 6ª edição. Rio de Janeiro: Atlas, 2005. PUC- Rio. Normas para apresentação de teses e dissertações. Rio de Janeiro: PUC-Rio, Vice-Diretoria para Assuntos Acadêmicos, 2001

Syllabus: Scientific Writing – Reports, Dissertations, Theses, Original articles, Review Articles, etc. Publishing Process (author, editor, reviewer, etc.); Quality Criteria (QUALIS, Impact Factor, etc. ); Good Practices for Scientific Presentation (Oral and Poster); Scientific Visualization with Matlab; Intellectual Property and Patents; Ethics in Scientific Research and Publication
Syllabus: Basic concepts of measurement and fundamental terms of metrology (VIM). Concept of error and uncertainty. Modeling of the experiment: construction of the histogram, continuous distributions, chi-square statistical criteria for elimination of erroneous points. Analysis of uncertainty and its propagation. Applications of the theory and principles of ISO-GUM to the expression of uncertainty in measurements in different fields of science and technology. Planning of experiments and choice of gauges. Calibration of instruments: number of measurements and testing of hypotheses. Adjust data and interpolation by the least squares method. Measuring physico-chemical properties and their uncertainty. Propagation of uncertainty in complex experimental and analytical functions. Analysis of metrological reliability
Syllabus: Instruments and measurement systems: basic concepts; components; classifications; quantities, units, standards and calibration; static and dynamic characterization. Conditioning of the electrical signal: basic electricity and electronics; amplification, attenuation, offset and protection; signal transmission; signal digitizing (multiplexing, sampling, A/D conversion); practical aspects (types of analog signals, acquisition modes); Nyquist Theorem, filtering. Noise: sources and reduction techniques; bridge circuits and electrical parameters measurement; sensors and transducers: applications in specific measurements. Introduction to LABVIEW: data acquisition; instrumentation control. Introduction to MATLAB: signal processing
Syllabus: Introduction to MATLAB: data structures; MATLAB programming. Digital signal analysis: analog, sampled and digital signals; Series. Scientific visualization: unidimensional and multidimensional graphics. Digital signal processing: interpolation; Regression; Frequency domain x time domain; Fourier Transform; Digital filtering
Syllabus: Basic concepts and models of innovation. Open innovation model. Innovation and sustainability. Key factors in managing innovation. Innovation as a management process. Developing a model of innovation strategy. National innovation systems. Exploring paradigms and technological trajectories. Clusters of innovation and integration for strategic learning. Sources of innovation and functions of Basic Industrial Technology (TIB). Case studies of innovation in an integrated vision with TIB
Syllabus: The course is structured in three parts. Part 1: Our origins: cosmology; anthropic principle and the formation of biodiversity; concepts in anthropology; concepts in epistemology of science; Gaia theory revisited. (Part 2) Sustainable Development: the meaning of the sustainability; consumerism and society for consumers; conscious consumption; waste recovery; renewable energy and energy efficiency; indicators, indices and sustainability assessment and (Part 3) The new capitalism: business and sustainable development; corporate social responsibility; economics of sustainability; valuation of biodiversity; corporate carbon strategies and the Kyoto Protocol

Bibliography: MAY, Peter H. (Org.). Economia do meio ambiente: teoria e prática. Rio de Janeiro; Editora Elsevier, 2010. LOMBARDI, Antonio. Créditos de carbono e sustentabilidade: os caminhos do novo capitalismo. Editora Lazuli, São Paulo, 2008. Su-Yol Lee, Corporate carbon strategies in responding to climate change, Business Strategy and the Environment, 22-48, 21, 2012. Donella Meadows, Jorgen Randers and Dennis Meadows, Limits to Growth: The 30-Year Update, Chelsea Green Publishing Company, United States, 2004

Syllabus: Theories and models of organizational learning. Formal and informal processes of learning in organizations. Learning levels: individual, groupS, organizational and inter-organizational. Factors influencing organizational learning: structure, strategy, information systems and incentives, culture, environment and organizational change. Relationship between culture and learning in organizations. Conceptual approaches and typologies of organizational culture. Factors influencing the formation of culture. Organizational subcultures. Taxonomies of organizational cultures. Metrics and tools for analyzing organizational cultures. Influence of organizational culture in managing metrological function and measurement systems. Major elements and profiles of metrological culture

Bibliography: EASTERBY-SMITH, M.; BURGOYNE, J. ARAUJO, L. (Orgs.) Aprendizagem organizacional e organização de aprendizagem: desenvolvimento na teoria e na prática. São Paulo: Atlas, 2001. ARGYRIS, C.; SCHÖN, D. A. Organizational learning II: theory, method, and pratice. Addison-Wesley, 1996. SCHEIN, Edgar H. Organizational culture and leadership. San Francisco: Jossey Bass, 1985/1992. TRICE, Harrison M.; BEYER, Janice M. The cultures of work organizations. Prentice Hall, 1993. HOFSTEDE, Geert. Culturas e organizações: compreender a nossa programação mental. Lisboa: Sílabo, 1997

Syllabus: Introduction to Electrophysiology; Cardiac Electrophysiology; Instrumentation for Measurement of Bioelectric Phenomena: Bioelectrods; Fluorescence Measurement for Optical Mapping of Bioelectric Activity; Surface Potential Measurement; Biomagnetic Measurement; Simulations and Signal Processing
Syllabus: Introduction to biometrology; Metrology in Basic Biomedical Sciences; Development of advanced Instrumentation and Techniques for Biomeasurements; Metrological Traceability in Laboratory Medicine and Quality Control for Medical Devices
Syllabus: What is the color. The three key factors: lighting, object, observer. Visual aspects of color. Systems ordination: Munsell, Ostwald, NCS. Industrial Collections: Pantone, Scotdic. The physics of color in lighting: Combination of colored lights, color admixtures. Sources and illuminating pattern. The measurement of irradiation, the spectral distribution of light. The Physics of Color: transmittance, reflectance and photoluminescence. Reasons why materials modify the light. Absorption, scattering and reflectance. Measurement of transmittance and reflectance: work with spectrophotometer. Interpretation of reflectance curves. Instrumentation: Industrial spectrophotometers. Parameters measured reflectance. Fluorescence and photoluminescence. The measurement of transmittance and reflectance of fluorescent materials. The psychophysics of color: The CIE colorimetry; illuminants and standard observers. Measurement of XYZ, xy. Metamerism. Psychometrics of colors: The CIELAB space. Formulas of different colors. Measurement differences (the practice). Control of instrumental colors: Tolerances: pass/fail. Formulas tolerance: CMC and CIEDE2000. Separation nuances. Determination of tolerance and separation nuances (the practice). Formulation and optimization of revenue: Mixtures of subtractive color – combination of dyes. Mixtures simple: the law of Lambert-Beer. Complex mixtures: the law of Kubelka and Munk. Calculation of transmittance and reflectance of combinations of colorants. Preparation of the database (the practice). Formulation of revenue. The colorimetry as a tool for industrial process control
Syllabus: Light and radiation: Physical quantities in photometric and radiometric (flow, power, intensity, luminance, radiance, irradiance). Detectors (selection and specification of the detector, detecting elements, filters, diffusers). Photometric standards and measurement techniques (equipment, uncertainty, calibration). Spectroradiometric (comparison of photometry and spectroradiometric techniques, standards, instrumentation, errors and measurement uncertainty)
Syllabus: Temperature: Temperature range of thermodynamic temperature and circulation. ITS-90. Transducers for measuring temperature: description and measurement uncertainties. Resistance thermometer. Thermometer in liquid glass. Thermocouples. Analysis of the temperature and transient error indication. Calibration. National Infrastructure of National Metrology Laboratories. Pressure: complementary ranges of pressure standards. Primary and secondary standards. Pressure balance. Column of liquid. Measurement of atmospheric pressure: Barometer. Pressure transducers: Bourdon, capacitive, resistive, diaphragm, heat. Gauge resolution with little pressure. Hysteresis and linearity. Measurement of pressure fluid flow. Pitot tubes. Pressure measurement at high speeds. High pressures: transducers. Flow: Standards for primary and transfer liquids and gases. Rate of flow meters: positive displacement, drag, variable area, mass. Venturi-type meters, calibrated orifice, nozzle sonic and subsonic, rotameter, turbine, gears, vanes, lobes, ultrasonic. Meters for high and low flow. Speed ??measurement: Pitot tube, hot wire anemometer and laser. Integration of the velocity field for flow measurement: uncertainty. Use of tracers. Heat Meters
Syllabus: Importance of agribusiness to the Brazilian and global socioeconomic dynamics. Overview of major agribusiness production chains in Brazil. Competitiveness and sustainability of the national agribusiness and its insertion in the international market. Importance of metrology, standardization and regulatory frameworks in agribusiness chains. Safety and quality of food production chains of animal and plant origin. International regulation on food safety. Codex Alimentarius. Systems HACCP (Hazard Analysis and Critical Control Points). ISO 22005: general principles for traceability in the feed and food chain. Typology and conformity assessment agroindustrial traceability. Agricultural certification. Models for assessing agricultural sustainability and its application
Syllabus: To familiarize students with criteria for design of production systems for electrical and thermal energy. Economic assessment of energy production systems. Commissioning of production systems of electrical and thermal energy. Fuel and energy. Fundamentals systems and equipment for thermal power generation and electricity. Cogeneration. Air conditioning. Boilers. Heating solar thermal and photovoltaic. Wind Energy. Standards for performance evaluation and its uncertainty. Design criteria. Economic analysis of the production of thermal and electric energy. Principles of commissioning
Syllabus: Alternative energy sources; Energy and environment; Certification of avoided emissions and Market of Carbon; Pricing of electricity, energy demand in industry, commerce and services, Conservation of thermal and hydraulic systems; The role of PROCEL and CONPET; Energy diagnosis; Energy Planning, Management from the demand point of view; Efficiency in Lighting and thermal comfort; Efficiency in Buildings; PPHs (Research on Possessions and Usage Habits of Electrical Appliance) for the low income class; MV Protocols (Measurement and Verification) for projects of Energy Efficiency; Performance Contracts and the Role of ESCOs
Syllabus: Procedures for Assessment of Vehicles Performance in Laboratory and on the Road; ABNT, ISO and SAE Standards; Embedded Instrumentation and BenchTests; Acquisition and Data Processing; Measurements of Longitudinal and Lateral Acceleration, Velocity, Distance Braking; Power, Torque and Fuel Consumption; Employment of Dedicated Equipment: CorreVit and G-Analyst. LabView for Integration of Instrumentation System and Signals Monitoring. Tests in Special Environments: Motion Simulator, Chassis Dynamometer, Impact Testing, Emissions Testing, Vibration & Sound level Testing
Syllabus: Regulation, and standardization. General principles of good regulatory practice. Choosing conformity assessment procedures. Regulatory Impact Assessment (RIA) and main analytical tools. Relationship between the principles, structure and process of risk management according to ISO 31000:2009 Standard. Supervisory practices and other market monitoring. Guide for implementing the policies developed on the basis of the New Approach and the Global Approach of the European Commission. Scope of Directives “New Approach”. responsibilities. compliance. procedure of conformity assessment. Notified bodies. CE marking. External aspects

Bibliography: 1.CONMETRO. Guia de boas práticas de regulamentação técnica. Brasília: CONMETRO, 2007. 2.INMETRO. Diferenças entre regulamentação e normalização. Rio de Janeiro: Publicações do Inmetro, 2009. 3.COMISSÃO EUROPÉIA. Guia para Aplicação das Diretivas elaboradas com Base nas Disposições da Nova Abordagem e da Abordagem Global. Bruxelas, setembro de 1999. 4.ABNT. ISO NBR 31000:2009. Gestão de riscos. Princípios e diretrizes. Novembro de 2009. 5.ABNT. ISO Guia 73. Gestão de riscos. Vocabulário. Novembro de 2009

Syllabus: Concepts, principles and objectives of standardization and its impacts. Fundamentals of management systems. Motivators and benefits of management systems standardization. Quality management system. Quality management system according to ISO 9001 Standard. Environmental standards. The environmental management system according to ISO 14001. Occupational health and safety management system. The occupational and health management system according to PAS OHSAS 18001 Specification. Standardization in social responsibility. Social responsibility in accordance with ISO 26000 Standard . Integrated management systems. Reasons and benefits of integration. Elements common to management systems: PAS 99. The role of management systems auditing. Concepts and principles related auditing. Methodology for management and auditing according to ISO 19011 Standard. Guidelines to perform audits according to SA 8000. Certification of management systems. Accreditation process for certification bodies

Bibliography: 1.Guasch, J. L. et al. Quality systems and standards for a competitive edge. Washington: The World Bank Publication. ISBN-10: 0-8213-6895-8 (electronic), 2007. 2. ABNT NBR ISO/IEC. Guia 2. Normalização e atividades relacionadas – Vocabulário geral. 2ª edição. 2006. 3. Associação Brasileira de Normas Técnicas. Objetivos e princípios da normalização. Rio de Janeiro: ABNT, 1984. 4. Ribeiro Neto, J.B.M.; Tavares, J.C.; Hoffman, S.C. Sistemas de gestão integrados: qualidade, meio ambiente, responsabilidade social e segurança e saúde no trabalho. 5.British Standards Institution. BSI. PAS 99:2006. Specification of common management system requirements as a framework for integration, London: British Standards Institution, 2006. 6.Centro da Qualidade, Segurança e Produtividade. QSP SIG – Sistemas integrados de gestão: da teoria à prática. São Paulo: Coleção Risk Tecnologia, 2003. 102 p. 7.Cerqueira, J. P. Sistemas de gestão integrados: ISO 9001, OHSAS 18001, SA 8000, NBR 16001. Conceitos e aplicações. Rio de Janeiro: Qualitymark, 2006

Syllabus: Dimensions of sustainable development and its synergies. Sustainability measurement systems: concepts, functions and features. ‘Pressure-state-response’ models. Capital valuation and accounting models. Models that connect the human wellbeing and ecosystem. Models based on themes, sectors or specific issues related to sustainability. Key elements for selecting sustainability measurement systems in different socioproductive and organizational contexts. Sustainability Assessment and Measurement Principles (STAMP). Sustainability from the business perspective: Triple Bottom Line approach. Corporate Social Responsibility (CSR), Dow Jones Sustainability Index and the Global Reporting Initiative. Sustainability measurement systems in Brazil. Future prospects for measuring sustainability

Bibliography: BRUNDTLAND, G. H. Nosso futuro comum, 2. ed. Rio de Janeiro: FGV. 1991. ELKINGTON, J. Cannibals with forks: the triple bottom line of 21st Century Business. Oxford, U.K.Capstone Publishing Limited. 1998. IISD. Compendium of sustainable development indicator initiatives. Disponível em: . BELLEN, H. M. Indicadores de sustentabilidade: uma análise comparativa, Editora FGV, 2005. LABUSCHAGNE, C. et al. Assessing the sustainability performance of industries. Journal of Cleaner Production, v. 13, n. 4, p. 373–385, march 2005. PINTÉR, L.; HARDI, P.; BARTELMUS, P. Indicators of sustainable development: proposals for a way forward. IISD. 2005. BOHRINGER, C.; JOCHEM, P. Measuring the immeasurable: a survey of sustainability indices. Ecological Economics, v. 63, n. 1, p.1-8, 2007

Syllabus: Study of the Guide to the Expression of Uncertainty in Measurement. The Gaussian distribution, Statistical inference, Maximum likelihood estimation of parametric models, Non-parametric hypothesis tests, Outliers analysis; Grubbs and Chauvenet procedure to remove measurements discontinuities, Measurements distribution, fitting distribution to random sample; Qui-Square and Kolmogorv & Smirnov fitting tests, ANOVA with one and two factors, evaluating measurements uncertainties, Goodness of fitting tests for measurements errors


The aim of the Graduate Programs in Chemistry is to provide the students with all necessary tools to become successful as academic professionals and leading scientists or highly prepared professionals to innovate in the industry. The student has a wide option of complementary disciplines, in such the field as didactics, informatics and administration, as well as the opportunity of doing experimental work with the most advanced instrumental techniques.

The lines of research developed at the Department focus on 4 major areas:

Energy, Environment and Sea Science
Nanosciences, interfaces and colloids
Drugs and Chemical-Biological Interactions
Analytical Methods and metrological quality

Additional information can be found at the Department’s site and, in Portuguese, here.


Syllabus: Variable Content.
Syllabus: Variable Content.
Syllabus: Ionic solutions: concept of equilibrium, non-ideal effects, activity coefficient, ionic strength, ion-ion interactions, ion-solvent, pair formation, influences on equilibrium constants. Mass, proton, charge and electronic balances. Acid-base reactions: reactivation of equilibrium concepts and calculations, tamponade capacity. Precipitation/dissolution: kinetic and equilibrium conditions for solid phase formation and dissolution, contamination, colloids formation, concepts of solubility, effects on solubility, equilibrium calculations and diagrams, titration and indication. Complexation reactions: concepts on complex formation, types of ligands and their applications, chelates, kinetics and equilibrium in complexation reactions, equilibrium and speciation calculations, Titration and indication. Redox reactions: concepts on equilibrium and kinetics, effects of the medium, electrodes, equilibrium calculations, titration and indication
Syllabus: Molecular symmetry and group theory, vibrational spectroscopy, molecular orbital theory applied to Inorganic Chemistry; coordination complexes; Chemical bonding in coordination complexes, Introduction to Organometallic Chemistry; Reactivity and mechanisms
Syllabus: Syllabus: Properties of ideal and real gases; Thermodynamics Postulates: 1st law of thermodynamics, work, heat, and power; Intensive and extensive Parameters; Thermodynamics Postulates and equilibrium conditions: 2nd law of thermodynamics, entropy, Gibbs and Helmholtz energy; formal Relationship: Euler’s Equation, Gibbs-Duhem and Maxwell Relationship; Reversible Processes. Maximum work Theorem; Principle of minimum energy; Alternative Formulations: Legendre Transformations, Thermodynamic Potentials and Massieu Functions; Extreme Principle in Legendre transformed transformations; Stability of Thermodynamic Systems, Phase Transitions of the 1st order. Physical Transformations of pure substances; Surface Tension; Curvilinear Surfaces; Capillarity; Simple Mixtures; Colligative Properties; Activities; Chemical Equilibrium
Syllabus: Introduction and definitions. Adsorption. Kinetics of heterogeneous reactions. Preparation, characterization and evaluation of catalysts. Laboratory Reactors. Deactivation of catalyzers. Catalytic Processes
Syllabus: Chemical Metrology: identification of key variables of an analytical system aiming their optimization, experimental design and data processing, analytical chemistry, ionic chemistry: characterization of an ionic system in aqueous equilibrium; precipitation and co-precipitation, analytical chemistry, separations: solvent and ion exchange extractions; samples opening; inorganic chemistry: synthesis and characterization of a complex, synthesis and characterization of a zeolite; physico-chemistry: cathode rays, the hydrogen spectrum
Syllabus: Electrochemical cells, interfacial region, fundamentals of kinetics and electrode reactions mechanisms, mass transport, kinetics and transport in electrode reactions. Introduction to electrochemical methods of analysis. Potentiometry, coulometry, voltammetry, electrochemical reactions mechanisms, ultramicroelectrodes, preconcentration techniques. Chronopotentiometry, Electrochemical Impedance Spectroscopy, Sensors and Biosensors. Seminars on some topics of the literature
Syllabus: Nature and interaction of light with matter, Introduction to quantum mechanics, atomic spectroscopy, Molecular Spectroscopy
Syllabus: The atomic spectrum. The phenomena of fluorescence and atomic absorption. Atomic Absorption: Basic instrumentation. Line width and sensitivity. Beer’s law. Radiation sources and detectors. Atomization techniques: flame, hydride generation, cold vapor and graphite furnace. Spectral and non-spectral interferences. Figures of merit. Atomic fluorescence: basic instrumentation, technical interference. Continuous Source Atomic Absorption. Automation: coupling with flow injection systems; online preconcentration systems. Hyphenated techniques for speciation analysis
Syllabus: Atomic emission spectrometry: atomic spectra, excitation sources (arc, spark, GDL, DCP, ICP); sequential optical and multichannel systems, detectors, sample introduction systems for ICP OES and ICPMS, spectral and non-spectral interferences; calibration techniques; OES applications in environmental, new materials and biomedical issues, etc. Inductively coupled plasma mass spectrometry (ICPMS): Theoretical principles; instrumentation (Q-ICPMS, HR-ICPMS, MC-ICPMS, TOF-ICPMS); interferences in ICPMS; types of calibration; special techniques for liquids and solid sample introduction in ICPMS: micro-sampling and introduction of discrete samples, flow injection analysis (FIA), laser ablation, electrothermal vaporisation (ETV); hyphenated techniques for speciation analysis (ion chromatography, capillary electrophoresis); figures of merit of the ICPMS technique; examples of applications in elemental and isotopic analysis in different matrices
Syllabus: Introduction: The mass spectrum, The mass spectrometer, History, Basic terminology: Ìons, peaks, resolution
Syllabus: Stability of atomic nuclei, types of radioactive decay, interaction of radiation with matter, detecting radiation, nuclear Reactions, neutron activation analysis, natural radioactive series and applications in environmental studies
Syllabus: Study of the atmosphere, hydrosphere and lithosphere focusing on chemical and related phenomena, and their importance in biogeochemical cycles
Syllabus: The atmosphere, chemical and photochemical reactions of the Atmosphere, chemistry of the stratosphere: Ozone, greenhouse, Aerosols. Atmospheric chemistry of the aqueous phase. Air samplers: collection, chemical analyses, emission patterns and legislation. Chemistry of the indoors. Air pollution: effects on climate and health
Syllabus: Forms of scientific communication. Components of scientific texts. Tables and figures. Scientific literature, databases and bibliographic tools. The publishing process. Arbitration. Some features of scientific language. Impact factors. Understanding the development of scientific projects and seeking funding. How to present scientific work.
Syllabus: Introduction; Chemical composition of organic matter; analytical techniques in organic geochemistry; Organi matter global cycle; Diagenesis; geochemical indicators, applications and case studies
Syllabus: Introduction to Thermal Analyses, Instrumentation, Applications in Inorganic Chemistry; characterization techniques of coordination complexes; basic experiments on TG/DTG (lab)
Syllabus: Types of energy sources. Fossil fuels. Renewable fuels. Green Chemistry. Economic evaluation. Future prospects
Syllabus: Introduction to Nanotechnology, Nanomaterials, Nanodevices; nanoscale microscopy techniques; Synthesis of nanomaterials; Molecular Self-Assembly; molecular simulation, molecular nanotechnology
Syllabus: Thin layer chromatography (TLC): principle (lecture). TLC: preparation and activation of the plates (Lab). TLC: sample preparation (one or more kinds of environmental samples) and separation by TLC (Lab). Open column chromatography (OCC) principle (lecture). OCC: column preparation (lab). OCC: application to environmental samples (Lab). SPME: fundamentals (lecture). SPME: applications (Lab). Separation and quantification of compounds of environmental concern using HPLC, GC/MS, GC/FIC, GC/ECD
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Chemical reactions in gas phases, transition state theory, unimolecular reactions; calculations of molecular reactions, kinetics of reactions in Surfaces; Chemical reactions in solution; Solvation; transition state theory in solution; models for diffusion, Kramer Theory of solvent viscosity in chemical reactions, electron transfer reactions in solution. Applications: Atmospheric Chemistry, Environmental Catalysis, Combustion and reactions of inorganic compounds
strong>Syllabus: Advanced Topics not included in other courses in the area
strong>Syllabus: Advanced Topics not included in other courses in the area
strong>Syllabus: Advanced Topics not included in other courses in the area
strong>Syllabus: Advanced Topics not included in other courses in the area
strong>Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Chemical bonding and Molecular Structure, Stereochemistry, Conformation and stereoselectivity; Acids and Bases; Structural Effects on Reactivity and Stability; Nucleophilic Substitution, Addition and Elimination Reactions; Carbanions and other Carbon Nucleophiles; Substitution Reactions, Condensation and Addition to Carbonilic Compounds; Aromaticity and Aromatic Substitution reactions, Introduction to Environmental Organic Chemistry, Clean Chemistry
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Regulation of the chemical composition of natural waters. Dissolved carbon dioxide and the carbonate system. Dissolution and precipitation of hydroxides, oxides, carbonates, sulfates and phosphates. Redox balance and microbial mediation. Photochemical processes. The solid-solution interface and sorption of organic and inorganic substances in natural and anthropogenic particles. Interactions between particles and colloidal systems. Cycling, regulation and biological role of trace metals. Natural and synthetic organic chemicals in aquatic systems. Use of stable isotope markers in aquatic chemistry
Syllabus: Introduction, Classification and partitioning of aquatic environments; Chemical composition of seawater; Biogeochemical cycles, primary production, sediment chemistry, biogeochemical processes in estuaries; natural variability and human disturbances
Syllabus: Introduction to Quantum Mechanics, Schˆdinger Equation, Atomic Structure, Molecular Structure, Hartree-Fock and post-Hartree-Fock Method, Density Functional Theory, Semi-empirical Method, Molecular Mechanics and Dynamics. Applications of computational tools to chemical problems
Syllabus: Chemical elements in biology. General functions of biological elements. Eletrochemical functions, osmotic control, messaging. Formation of structures. Metal-activated enzymes. Metallo-enzymes. Oxygen in biology. Nitrogen fixation. Storage and transport of iron. Deficiency and toxicity of elements. Applications in medicine
Syllabus: Laboratory course to be given in accordance with the contents of QUI 2526
Syllabus: Considerations on signal to noise ratio; Introduction to molecular spectroscopy; Optical properties of materials and their relationship regarding the use of spectrophotometric techniques; Photo-physics of molecular absorption (absorption, Beer’s law, deviations from Beer’s law); Absorption spectrophotometry in liquid media and solid phase; Instrumentation and strategies to increase sensitivity; Photo-physics bases of luminescence; Instrumentation for photoluminescence spectroscopy; Fluorimetry; Phosphorimetry on solid substrates, directly in solution and in cryogenic conditions; Upper derived and synchronization techniques; Time-Resolved Techniques; Coupling of absorption and luminescence spectrophotometric techniques with separation techniques
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Advanced Topics not included in other courses in the area
Syllabus: Experimental evaluation of different systems for the introduction of aqueous and organic solutions and solids. Optimization of conditions for OES measurements with different excitation sources (GDL, PCI) and ICPMS. Study and correction of spectral and non-spectral interferences. Calibration techniques for OES and ICPMS and determination of performance characteristics. Typical applications of both techniques in the determination of trace elements in different matrices. Hyphenated techniques for speciation analysis
Syllabus: Presentations by the students of the postgraduate program regarding advances in the fields of analytical and inorganic chemistry
Syllabus: Presentations by the students of the postgraduate program regarding advances in the fields of analytical and inorganic chemistry
Syllabus: Presentations by the students of the postgraduate program regarding advances in the fields of analytical and inorganic chemistry
Syllabus: Presentations by the students of the postgraduate program regarding advances in the fields of analytical and inorganic chemistry
Syllabus: The national and international cenario of Chemical Metrology (MQ), the international system of units (SI) and vocabulary in MQ. Statistical techniques for the evaluation of analytical results. Chemical analysis as a measurement system: from sampling to the final result. Characteristic performance parameters of analytical methods: accuracy, precision (repeatability, reproducibility), dynamic range, robustness, limit of detection and quantification, etc. Primary and standard methods of analysis. Uncertainty evaluation and presentation of analytical results. Control and quality assurance in analytical laboratories. Certified reference materials and traceability in analytical chemistry. Proficiency exercises and interlaboratory comparisons. The organization of testing laboratories according to the NBR ISO/IEC 17025 and accreditation
Syllabus: Internship under the supervision of the advisor in an individual laboratory or research center
Syllabus: Internship under the supervision of the advisor in an individual laboratory or research center
Syllabus: Variable Content.
Syllabus: This internship includes charges related to academic assignments, participating in supervised teaching in only 01 undergraduate course per semester
Syllabus: This internship includes charges related to academic assignments, participating in supervised teaching in only 01 undergraduate course per semester
Syllabus: This internship includes charges related to academic assignments, participating in supervised teaching in only 01 undergraduate course per semester