**Chemical Engineering**

The professionals of the mentioned area have a wide working field that comprises, among others, the oil, petrochemical, metallurgical, textile, agriculture, cement, food, pharmaceutical, glass, plastic and biofuel industries. The chemical engineer is responsible for the project, operation, accompaniment, optimization, control and automation processes, besides research and environmental managing. At PUC-Rio, Chemical Engineering is an interdepartmental course ministered by the Departments of Chemical and Materials Engineering and Chemistry. The possibility of dual eligibility in Chemistry and in Production, Oil and Environmental Engineering constitutes a differential in the University chemical engineer formation, which enlarges still its insertion opportunity in the labor market.

**Chemistry**

The Graduation, with technological attributions, is the course offered within this area. The adopted curricular structure allows the fast obtainment of a double Chemistry / Engineering eligibility, forming professionals with solid and updated knowledge, which attend properly the market necessities. The strict relation with the post-graduation offers to student the contact to the last generation equipment and techniques, thus contributing for a strong scientific and technological formation. The working in mentioned market includes the chemical industries, the oil sector, the pharmaceutical and cosmetic industries, the companies for water and industrial waste material treatment, as well as recycling, among others.

**Syllabuses:**

**Syllabus**: CHEMISTRY IN AQUEOUS SOLUTIONS. IONIC EQUILIBRIUM: ACID-BASE; PRECIPITATED FORMATION; COMPLEX FORMATION; MATHEMATICAL CALCULATIONS INVOLVING SIMPLE AND COMPLEX EQUILIBRIUM SYSTEMS. ELECTROCHEMISTRY: REDOX EQUILIBRIUM. STATISTICS: TYPES OF ERRORS IN ANALYTICAL CHEMISTRY; PRECISION; ACCURACY; CONFIDENCE LIMITS; DATA TREATMENT, GRAVIMETRIC METHODS

**Bibliography**: SKOOG, D.A.; WEST, D.M.; Holler, F.J.; Crouch, S.R. Fundamentals of analytical chemistry 7th Ed., New York, Sounders College Publishing, 1997, 870 p. BACCAN, N.; DE ANDRADE J.C.; GODINHO O.E.S.; BARONE J.S. Química analítica quantitativa elementar, 3º Edição, São Paulo, Editora Edgard Blucher LTDA, 2004, 308 p. HARRIS, D.; Explorando a química analítica, 4º edição, Rio de Janeiro, LTC- Livros Técnicos Científicos e Editora, 2011, 568 p

**Syllabus**: REDOX VOLUMETRY; MOLECULAR ABSORPTIOMETRY: ELECTROMAGNETIC RADIATION PROPERTIES; THE LIGHT ABSORPTION PROCESS; BEER-LAMBERT LAW AND ITS DEVIATIONS; INSTRUMENTATION AND APPLICATIONS. LUMINESCENCE SPECTROMETRY: PRINCIPLES, INSTRUMENTATION AND APPLICATIONS. ATOMICA ABSORPTION SPECTROMETRY; PROCESS OCCURRING IN FLAME: INSTRUMENTATION AND APPLICATIONS, ATOMIC EMISSION SPECTROMETRY: EXCITATION PROCESS: ATOMIC EMISSION IN FLAMES AND IN ARGON PLASMA: INSTRUMENTATION E APPLICATIONS. POTENTIOMETRY: REFERENCE AND WORKING ELECTRODES; DIRECT POTENTIOMETRY; POTENTIOMETRIC TITRATIONS. GAS CHROMATOGRAPHY AND LIQUID CHROMATOGRAPHY: BASIC PRINCIPLES, INSTRUMENTATION AND APPLICATIONS

**Bibliography**: SKOOG, D.A.; WEST, D.M.; Holler, F.J.; Crouch, S.R. Fundamentals of analytical chemistry 7th Ed., New York, Sounders College Publishing, 1997, 870 p. HARRIS, D.; Explorando a química analítica, 4º edição, Rio de Janeiro, LTC- Livros Técnicos Científicos e Editora, 2011, 568 p. HAGE, D.S.; CARR, J.D. Química analítica e análise quantitativa. 1º Edição, São Paulo, Editora Pearson, 2011, 705 p

**Civil Engineering**

The civil construction industry development, the investment in big constructions, as well as the high productivity of the oil sector has consolidated the insertion of the civil engineer within the labor market. The graduation program of PUC-Rio, highly appraised internationally, establishes a strong basis in mathematics and basic sciences, in engineering, project management and production tools, as well as in the application of Civil Engineering technologies. The course still offers an ample formation and emphasis possibilities in the Structural, Geotechnical and Environmental areas. The Structure studies enable the project and construction of buildings, bridges and large structures using armed concrete, protended concrete, steel and new materials. The Geotechnics acts on the behavior of soils, rocks and new geotechnical materials for project implementation, as well as on the solution of works associated with landslide prevention, foundations, tunnels, excavations, dams, highways and landfills, among others. The Environmental area approaches environmental, sanitation, water captivation and treatment and sewage system projects, as well as techniques for the prevention and recuperation of environmental degradation.

**Syllabuses:**

**Syllabus**: The biosphere and its equilibrium. Biodiversity. Effects of human presence and technology on the environment. Control of the various forms of pollution. Preservation of natural resources. Main environmental problems

**Bibliography**: BRAGA, B.; HESPANHOL, I. Introdução à Engenharia Ambiental; São Paulo: Prentice Hall Brasil, 2005. MASTERS, G. M. Introduction to environmental engineering and science; Englewood Cliffs, NJ: Prentice Hall, 1991

**Syllabus**: Developing an engineering design or a research paper of theoretical or experimental character under the supervision and supervision of a teacher. The project or research work can be carried out individually or in groups and shall be submitted in writing within the norms established by the course

**Syllabus**: At least 160 hours of training in engineering, preferably company getting its acceptance at the discretion of course Coordination

**Syllabus**: Review of vector analyis. Force vectors. Position vectors. Equilibrium of a particle. Free body diagram. Coplanar force systems. Three-dimensional force systems. Moment of a force. Moment of a force about an axis. Moment of a couple. Equivalent systems. Reduction of a force and couple system. Distributed loading. Equilibrium of a rigid body (2D and 3D). Support reactions. Equations of equilibrium. Simple trusses: the method of joints, the method of sections. Beams: shear and moment equations and diagrams. Flexible cables: parabolic cable and catenary. Dry friction. Equilibrium and frictional equations. Center of gravity and centroid. Fluid pressure. Equilibrium of submerged bodies. Moments of inertia. Paralleled axis theorem. Product of inertia. Moments of inertia for an area about inclined axes. Mohr’s circle

**Bibliography**: HIBBELER, R. C.. Estática: Mecânica para Engenharia, 10a. Edição. Upper Saddle, N.J.: Prentice-Hall, 2004. HIBBELER, R. C.. Dinâmica: Mecânica para Engenharia, 10a. Edição. Upper Saddle, N.J.: Prentice-Hall, 2004. MERIAM, J.L. (James L.).; KROIGE, L.G. . Mecânica: Estática. 5ª ed. RJ: Editora LTC -Livros Técnicos e Científicos, 2004. MERIAM, J.L. (James L.).; KROIGE, L.G. . Mecânica: Dinâmica. 5ª ed. RJ: Editora LTC -Livros Técnicos e Científicos, 2004

**Syllabus**: Internal structure of the Earth and plate tectonics, volcanism and Seismicity, minerals, igneous rocks: intrusive and extrusive, sedimentary rocks, metamorphic rocks, rocks structures and folding, weathering and soil formation, pedogenetic and erosion processes, action of underground and surface waters, mass movements, oceanic and physiography of the seabed, mineral and energy resources, geological outline of Brazil, Earth’s relief modelling

**Bibliography**: POPP, José Henrique. Geologia geral. 5. ed. Rio de Janeiro: LTC, 1998. 376 p. ISBN 8521611374, LEINZ, V. & AMARAL, S.E. Geologia Geral. Cia. Editora Nacional, 397p., 1989

**Syllabus**: Characterization of geological and technological properties of soil and rock materials; Minerals and rocks (sedimentary, igneous and metamorphic rocks): recognition practices, macroscopic and microscopic identification, description of properties; Technical field visits to description of the materials studied in the laboratory, geological research, identification of structural problems and description of geological accidents

**Bibliography**: TEIXEIRA, Wilson. Decifrando a terra. São Paulo: Oficina de textos, 2000. 557 p. ISBN 8586238147

**Syllabus**: Structural systems and elements. Structures morphology. Stable and unstable structures. Determinate and indeterminate structures. Geometric stability. Structural design loads. Internal loads and reactions. Differential equilibrium equations. Analysis of statically determinate beams, trusses and rigid frames. Deflection of beams: equation of elastic curve. Determinate spatial structures. Deflections of beams, trusses, and rigid frames by virtual-work

**Bibliography**: H. L. Soriano, – Estática das Estruturas, Editora Ciência Moderna. Rio de Janeiro. 2007. SUSSEKIND, Jose Carlos,. Curso de analise estrutural /. Porto Alegre : Globo, 1975- 3v. CAMPANARI, Flavio Antonio. Teoria das estruturas /. Rio de Janeiro : Guanabara Dois, 1985. 4v. : ISBN 8570300468 : (broch.)

**Syllabus**: Basic concepts of structural analysis: structural model, equilibrium and compatibility. Principle of superposition and linear behavior. Principle of virtual works. Evaluation of structure displacements. Force method: trusses, plane frames and grillages. Displacement method: trusses, plane frames with inextensible members, and grillages. Displacement method: plane frame with extensible members. Displacement methods: formalization of the direct stiffness method. Usage of plane frame structural analysis programs. Simplifications for symmetric structures. Method of moment distribution for beams and plane frames with inextensible members. Effect of live loads and movable (bridge) live loads in statically determinate and statically indeterminate structures: influence lines and envelop of internal forces

**Bibliography**: MARTHA, L. F. Métodos Básicos da Análise de Estruturas Rio de Janeiro, 2005 / Available at URL: http://www.tecgraf.puc-rio.br/~lfm. SUSEKIND, Jose Carlos,. Curso de analise estrutural. Vol 2 e 3. Porto Alegre : Globo, 1977. SORIANO, Humberto Lima e Lima, SOUZA, Silvio de. Análise de Estruturas, v.1. Métodos das Forças e Métodos dos deslocamentos. Editora: Ciência Moderna

**Syllabus**: History of the strength of materials. Simplifying hypotheses. Objectives of the strength of materials. Material behavior in structural engineering. Tension, compression and shear. Members under axial load. Torsion of bars: circular and rectangular sections and thin walled sections. Stresses in beams. Deflections in beams. Stress and strain analysis, Mohr’s circle. Work and deformation energy. Dynamic load and impact. Introduction to column stability: critical load

**Bibliography**: HIBBELER, R. C., Resistência dos Materiais – 5ª edição / São Paulo: Editora LTC, 2000 IBSN 8521612281. POPOV, E.P. (Egor Paul),. Introdução à Mecânica dos Sólidos / SP: Edgard Blücher, 1978. NASH, William A. (William Arthur), 1922 – Resistência dos Materiais: resumo da teoria, problemas resolvidos, problemas propostos. Rio de Janeiro: McGraw-Hill do Brasil, c 1970

**Syllabus**: Statically indeterminate beams. Beams on elastic foundation. Stability of straight columns with different boundary conditions, beam-column equation, large displacements, effect of initial displacements and eccentric load. Bending and twisting of beams. Warping of sections. Bending and twisting of beams with thin-walled cross section. Rectangular cross sections. Membrane analogy. Temperature effects. Physical and geometrical nonlinearities. Plastic analysis of trusses, beams and frames. Inelastic buckling. Yield conditions in biaxial and triaxial stress states. Dynamic effects. Impact. Energy theorems and methods: Castigliano, Crotti-Engesser, Menabrea.. minimum potential energy principle, Rayleigh-Ritz method. Displacements in inelastic beams. Residual stresses in bending. Moment-curvature relations for nonlinear materials. Application of energy methods to linear and nonlinear analysis of trusses and beams

**Bibliography**: TIMOSHENKO, Stephen, Resistência dos Materiais. Rio de Janeiro: Ao Livro Técnico, 1966. 2v. TIMOSHENKO, Stephen; GERE, James M. Mecânica dos Sólidos. Rio de Janeiro: Livros Técnicos e Científicos, 1983.POPOV, E. P. (Egor Paul),. Introdução a mecânica dos solidos /. São Paulo : Edgard Blücher 1978. 534p. SUSSEKIND, Jose Carlos,. Curso de analise estrutural – vol.2, cap. III /. Porto Alegre : Globo, 1976

**Syllabus**: Applications of basic principles of fluid mechanics to problems of hydraulic engineering; flow in penstocks and channels. Hydrometry. Flow through porous media. Dimensional analysis and its applications to physical models

**Bibliography**: AZEVEDO NETTO, José M. de. Manual de hidráulica. São Paulo: Edgard Blücher, 2003. ISBN8521202776. QUINTELA, Antonio de Carvalho. Hidráulica. 3. ed. Lisboa: Fundação Calouste Gulbenkian, 1991. 539 p. ISBN 972310167X (broch.). NEVES, E.T. Curso de Hidráulica Geral. Porto Alegre, Globo, 1960. SILVESTRE, A. Hidráulica Geral. Rio, Livros Técnicos e Científicos, 1979. MELO PORTO. Hidráulica Básica. São Carlos, EESC-USP, 1998

**Syllabus**: Shape and dimensions of the Earth. Study of the relief. Measurements of angles and distances. Surveyor’s instruments. Planimetry and altimetry. Survey methods of low, medium and high precision. Geometric, trigonometric leveling and taqueométrico. Magnetic and true orientation of topographic cards. Calculating areas and volumes. Fundamentals of Photogrammetry

**Bibliography**: ESPARTEL, L. Curso de Topografia. Rio de Janeiro: Editora Globo, 2005. ESPARTEL, Lelis,; LUDERITZ, João. Caderneta de campo /. 10.ed. – Porto Alegre : Globo, 1977. RAMOS, Djacir – Geodésia na Prática – Teoria e exercícios. GOMES, E.; PESSOA, L.M. da Cunha; SILVA JUNIIOR, L. B. – Medindo Impoveis Rurais com GPS, L K Editora & Comunicação Ltda

**Syllabus**: Main geotechnical problems. Origin and formation of soils. Geological-geotechnical profiles: direct and indirect surveys; sampling undeformed configuration and dented. Soil characterization: granulometric distribution, physical indexes, consistency limits, geotechnical classification systems. Soil structures; Mineralogy of clays; compacted soils. Strains in soil mass: geostatic stress, induced voltages. Effective stress and pressure dissipations; capillarity. Percolation in soils: concept of massive loads, permanent flow, permeability coefficient. General flow equation, solutions of the equation of permanent flux

**Bibliography**: BRAJA, M. Das; Fundamentos da Engenharia Geotécnica. Editora: Thomson Learning (Pioneira)2006. ISBN-10: 8522105480. PINTO, Carlos de Sousa. Curso básico de macânica dos solos: em 16 aulas. São Paulo: Oficina de textos, 2000. 247 p. ISBN 8586238120. T. William Lambe, Robert V. Whitman . Soil Mechanics. Paperback, 576 pages. January 1991 ISBN: 978-0-471-51192-2

**Syllabus**: Soil characterization Tests: particle size distribution, moisture content, Atterberg limits, specific gravity, specific grain mass, organic matter content; Permeability; Reduced models of percolation in soils; Compression Testing: Proctor normal and modified Proctor

**Bibliography**: K.H.Head, Manual of Soil Laboratory Testing vol.1 e 2; Publication Date: 2008 Publisher: Whittles Publishing ISBN 10: 1904445365/ ISBN 13: 9781904445364. Normas técnicas da ABNT

**Syllabus**: Compressibility: confined and unconfined compression, compressibility parameters, one-dimensional consolidation. Drained and undrained requests. One-dimensional Consolidation theory: primary and secondary densification, radial density; solutions. Total and effective stress paths. Shear strength: mechanisms and rupture criteria. Triaxial and direct shear tests. Parameters of pressure dissipations, deformability and resistance. Behavior of sandy and clay soils. Behavior of unsaturated soil and compressed

**Bibliography**: CRAIG, R. F., Mecânica dos Solos, Editora: LTC, Ano: 2007 Edição: 7, Número de páginas: 380, ISBN: 9788521615446. PINTO, Carlos de Sousa. Curso básico de mecânica dos solos: em 16 aulas. São Paulo: Oficina de textos, 2002. ISBN 8586238185. LAMBE, T. William.; WHITMAN, Robert V.,. Soil mechanics, SI version. New York : Wiley c1979. ISBN 0471024910

**Syllabus**: One-dimensional consolidation test; Direct shear test; Triaxial drained and undrained tests; Special tests

**Bibliography**: K.H.Head, Manual of Soil Laboratory Testing vol.1 e 2 – Publication Date: 2008 Publisher: Whittles Publishing ISBN 10: 1904445365/ ISBN 13: 9781904445364. Normas técnicas da ABNT

**Syllabus**: Fundamental of engineering projects. Basic properties of solid materials. Related sciences to construction materials. Constitutive relations of solid materials. Principal materials used in civil construction. Production and properties of quick lime.Production and properties of materials made of soil. Production and properties of the constituents of concretes. Properties of fresh concrete. Properties of solid concrete.Dosage and technological control of concrete. Introduction to the non-conventional materials such as bamboo and natural fibres in civil engineering.Topic to be studied by students:Production and properties of metals in civil engineering

**Bibliography**: BAUER, L. A. Falcão (Luiz Alfredo Falcão). Materiais de construção. Vol. 1 e 2. 5ª ed. . Rio de Janeiro: Livros Técnicos e Científicos. ISBN 8521605609 (obra completa). GHAVAMI, K.; PITANGUEIRA, R.. Fundamentos e propriedades dos Materiais Sólidos. Rio de Janeiro: DEC-PUC Rio, 1995. PETRUCCI, Eladio Geraldo Requião,. Materiais de construção /. 6a ed. – Porto Alegre : Globo, 1982. 435p. : ((Enciclopedia tecnica universal Globo). PETRUCCI, Eladio Geraldo Requião,; PAULON, Vladimir Antonio,. Concreto de cimento Portland /. 10a ed. / Porto Alegre : Globo, 1983. 307p. : ((Enciclopédia técnica universal Globo)

**Syllabus**: Introduction. The Design Process. Material Properties. Durability. Ultimate and Serviceability Limit States. Design Actions. Design Strengths. Design of Structural Members. Design of Connections

**Bibliography**: PFEIL, Walter; PFEIL, Michele. Estruturas de madeira: dimensionamento segundo as normas brasileiras NBR 7190/97 e critérios das Normas Norte-Americana NDS e Européia EUROCODE: Ed. LTC, 2003. ALVES DIAS, A.; CALIL JÚNIOR, Carlito; LAHR, F. A. R. Dimensionamento de Elementos Estruturais de Madeira. 2002. Editora: Manole ISBN-10: 8520415156. ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 7190/97: projeto de estruturas de madeira. Rio de Janeiro, 1997. CALIL JR., C.; LAHR, F.A.R.; DIAS, A.A. Dimensionamento de elementos estruturais de madeira. Barueri, SP: Manole, 2003

**Syllabus**: Hydrometeors. Hydrological cycle. Watershed. Runoff. The atmosphere. Precipitation. Infiltration. Evaporation. Analysis of flow data. Regularization of rivers: floods and droughts. Statistics applied to forecast floods

**Bibliography**: PINTO, N. de S.. Hidrologia basica /. São Paulo : E. Blucher, 2003 ISBN8521201540. RÉMÉNIÉRAS, G.. L’Hydologie de I’Ingénieur – Colletion de La Diretion des etudes et Recherches D’Electicite de France. Eyrolles. Paris. ROCHE, M. ; Hidrologie. Orstom, Paris, 1975

**Syllabus**: Mechanical properties of concrete and steel. Principles for structural safety: serviceability and ultimate limit states. Bond between concrete and steel bars. Ultimate limit state design of sections under combined axial load and bending. Flexure: rectangular, T and box sections. Shear: behavior of beams failing in shear, truss model for beams. Reinforcement details for for beams. Verification of serviceability limit states of cracking and deflections of beams. Design of short and slender columns. Basic concepts on torsion

**Bibliography**: MEHTA, P. K. (Povindar K.).; MONTEIRO, Paulo J. M. Concreto : estrutura, propriedades e materiais /. São Paulo : Pini, 1994

**Syllabus**: Philosophy of structural design. The Design Process. Ultimate and Serviceability Limit States. Design Actions. Types of Slabs. Elastic Design of Slabs. Yield Line Theory for Slabs. Design of: Continuous Slabs; Ribbed Slabs; Deep Beams; Water Tanks; Swimming Pools; Stairways. Reinforcement Details

**Bibliography**: TEATINI CLÍMACO, J. C.. Estrutura de Concreto Armado: Fundamentos de Projeto, Dimensionamento e Verificação. Brasília: UNB, 2005. CARVALHO, R.C.; FIGUEIREDO FILHO, J.R. Cálculo e detalhamento de estruturas usuais de concreto armado. São Carlos: EdUFSCar, 2001. MAC GREGOR, J.G.; WIGHT, J.K. Reinforced concrete: mechanic and design. 4 ed. New-York: Prentice-Hall, 2005

**Syllabus**: Limit states design concepts. Structural steel properties. Building structural systems. Connections. Tension members. Local buckling of plates. Axially loaded compression members. Beams: Flange local buckling, web buckling, Laterally unbraced beams, The effect of shear on beam strength. Beam splices. Beam-columns. Overall stability and second-order effects. Building design

**Bibliography**: BELLEI, I. H.; PINHO, Fernando O.; PINHO, M.. Edifícios de Múltiplos Andares em Aço. São Paulo: PINI Ltda, 2004. SIMÕES, Rui A. D.. Manual de Dimensionamento de Estruturas Metálicas. Coimbra – Portugal: Associação Portuguesa da construção Metálica e Mista, 2005 ISBN9729837661. KULAK, G. L.; ADAMS, P. F.; GILMOR, M.I. – LIMIT STATES DESIGN IN STEEL STRUCTURESpublicado pelo CANADIAN INSTITUTE OF STEEL CONSTRUCTION, 1990, ISBN 08881 10693

**Syllabus**: Objectives, characteristics, politic, economic, localization, design and operation of transportation systems. Design and construction of highways and railways: recognition, prior design, geotechnical and geo-hydrological studies, final design, maps of explored areas, conformation and selection of road axle, horizontal and vertical curves, overwide and overlayer, visibility, cross sections, areas embankments, volumes, transportation and distribution of earth, budgeting and engineering reports. Comparisons of lines and traffic characteristics. Lease. Railway superstructure: design elements, design, complementary services, geometric design, budget. Use of softwares and graphic computation in road design. Project works

**Bibliography**: BERNUCCI, Liedi Bariani. Pavimentação asfáltica: formação básica para engenheiros. Rio de Janeiro: PETROBRAS, 2006. PONTES FILHO, Glauco. Estradas de Rodagem – Projeto Geométrico.. São Carlos, SP: GP Engenharia Bidim, ano 1998. Especificações Técnicas do DNIT. Manual de Pavimentação. DNIT, 1996. Manual de Reabilitação de pavimentos. DNIT, 1998

**Syllabus**: Technology of construction of buildings and other constructions. Preparatory work and installation of works. Location of the work. Implementation of the foundations. Constructive systems. Structures in masonry, concrete, steel and wood: materials, equipment and construction processes. Execution of shapes. Implementation of building facilities. Covers; waterproofing. Coverings; painting. Thermal and acoustic insulation. Frames, hardware and glass making. Planning and control of the buildings. Quality control techniques. Heavy construction. Prefabrication

**Bibliography**: YAZIGI, Walid. A Técnica de edificar. São Paulo: SindusCon – SP: Pini, 1998. 628 p. ISBN 8572660941. THOMAZ, Ercio.: Tecnologia, Gerenciamento e Qualidade na Construção; Ed. Pini, 2001. SOUZA, Roberto de et al.: Qualidade na Aquisição de Materiais e execução de Obra; Ed. Pini, 1996

**Syllabus**: The constructive process. New trends in construction: industrial, structural masonry construction systems, structures, tensioned. Pathologies and therapies of the constructions: foundations; thermal effects; cladding and facades; waterproofing; seal; drainage systems. New materials: chemicals; special concrete (reinforced concrete with fiber, high-strength concrete). Reporting and technical advice

**Syllabus**: Plumbing procedures for iced, cold, and hot water, sewer, stormwater, and fire fighting installations in residential and commercial buildings. Gas plumbing. Electrical installations. Telephone facilities. Building waste disposal and sanitation. Technical standards, legislation and specific documentation. Design of building installations

**Bibliography**: NISKIER, Julio.; MACINTYRE, Archibald Joseph. Instalações eletricas. Rio de Janeiro : Guanabara Dois, 1985. 556p. : ISBN 8570300670 (broch.). MACINTYRE, Archibald Joseph. Instalações Hidráulicas /. Rio de Janeiro : Guanabara Dois, 1982. 770p. MACINTYRE, Archibald Joseph. Instalações Hidráulicas-Prediais e Industriais. CREDER, Helio. Instalações Hidraúlicas e Sanitárias – LTC

**Syllabus**: Calculation of areas: Brazilian standards. Documents for approval at the General registry of real estate and housing finance system. Construction contracts and sub-contracting. Budget and cost forecast. Cash flows and resource aggregation curves. Housing system. Financing. Planning: timeline, time and cost. Planning techniques; PERT-CPM. Quality control systems of construction. Total quality. Productivity. Use of computers in the budget and planning; software for planning and construction management. Management information systems. Notions of Legal, Engineering surveys, appraisals, reports. Social and labor legislation. Notions of hygiene and occupational safety; Prevention and control of risks; the environment and occupational diseases; specific legislation and technical standards

**Bibliography**: LIMMER, C. V. – Planejamento, Orçamentação e Controle de Projetos e Obras – Ed. LTC, RJ, 1997. SOUZA, Roberto – Qualidade na Aquisição de Materiais e Execução de Obras. São Paulo: Ed. Pini Ltda., 1996. PARGA, Pedro. Calculo do Preço de Venda na Construção Civil – São Paulo:Ed. Pini Ltda., 2003 – SBN: 8572661433 ISBN-13: 9788572661430

**Syllabus**: Geotechnical works; geological-geotechnical factors; project constraints. Field trials: piezocone, reed and pressiometer. Ruptures limit equilibrium problems. Slope stability. Stresses of Earth and containment structures. Embankments on soft soil. Earth and rockfill dams. Open-air and underground excavations. Geosynthetics

**Bibliography**: Faiçal Massad. Obras De Terra, Editora: Oficina De Textos. ISBN: 8586238244

**Syllabus**: Shallow and deep foundations. Geotechnical and structure of pile caps, spread footing, single, associated and continuous. Equilibrium beams and raft foundation. Bearing capacity theories. Dynamic analysis. Settlement prediction. Pilegroup effect. Negative skin friction. Laterally loaded piles-ultimateload and deflection curves. Pile-raft foundation. Load tests. Retaining structures. Gravity walls and anchors. Foundation design for difficulty site condition

**Bibliography**: Braja M. Das, Principles of Foundation Engineering Editor: Thomson Learning College – 2005 ISBN: 9780534551445

**Syllabus**: Introduction to Architectural Design and Theory. Plans, sections and facades. Houses and Apartments Buildings. Commercial buildings and “shopping centers”. Buildings for specific purposes. Sustainable Architecture and Urbanism. Green Building Certification adopted in Brazil. Climate Design (e.g. building performance, acoustic and thermal comfort, daylight). CAD: Computer-aided design concepts. Urbanism and Urban Planning concepts. Building Codes

**Bibliography**: MINDLIN, Henrique,. Arquitetura moderna no Brasil. Rio de Janeiro: Aeroplano, 1999. 286 p. ISBN 858657905X. CHING, Francis. Dicionário Ilustrado de Arquitetura. 3a edição. São Paulo: Martins Fontes, 1998. ZEVI, Bruno. Saber Ver a Arquitetura. São Paulo: Martins Fontes, 1996. CHING, Francis D K. Arquitetura: forma, espaço e ordem. São Paulo: Martins Fontes. 1998. GREGOTTI, Vittorio. Território da Arquitetura. 3a edição. São Paulo: Perspectiva, 2001. CHING, Francis. Representação Gráfica em Arquitetura. 3a edição. Porto Alegre: Bookman, 2000

**Syllabus**: Water supply system: Capture, water supply, treatment, reservation, pumping, distribution. Raw water quality and treated water quality. Potability standards. Health and sanitation, waterborne diseases. Sewage sanitary systems. collection, transportation, treatment and disposal of sanitary sewage. Environment, quality criterion, pollution and preservation of water elements. Drainage systems for storm waters. Drainage collection system

**Bibliography**: TSUTIYA, Milton Tomoyuki; SOBRINHO, Pedro Além. Coleta e Transporte de Esgoto Sanitário. São Paulo: PHD/EPUSP, 1999. ISBN 8590082318. TSUTIYA, Milton Tomoyuki. Abastecimento de Água. São Paulo: PHD/EPUSP, 2004. ISBN 8590082369. JORDÃO, Eduardo Pacheco; PESSÔA, Constantino Arruda. Tratamento de Esgotos Domésticos. Rio de Janeiro: ABES/UFRJ, 2005. MONTGOMERY, JAMES M. Water Treatment Principles & Design. New York, 1985. John Wiley & Sons

**Syllabus**: The project, its methodology. Methodology for troubleshooting: formulation and analysis, specification and choice of solutions. Elementary examples of troubleshooting. Conceptual models, experimental, numerical and mathematical. Importance of simulation/computational modeling of engineering problems. Optimization concept and its relevance in the solution of engineering problems. Examples. Probabilistic aspects and decision-making, using Bayesian approach. Examples. Presentation of computational tools for troubleshooting (Mathcad, Excel, Finite Elements). Development of a complete project in Civil Engineering

**Bibliography**: G. Polya, A Arte de Resolver Problemas (“How to Solve It”), Ed. Interciência, 1977 (trad. Heitor Lisboa). M.F. Rubinstein e I.R. Firstenberg, Patterns of Problem Solving, 2nd. Edition, Prentice-Hall, 1995. R. Friedman, Problem Solving for Engineers and Scientists”, Van Nostrand, 1991. C.S. Revelle et al., Civil and Environmental Systems Engineering, Prentice Hall, 1996. J. Benjamin e C.A. Cornell, “Probability, Statistics and Decision for Civil Engineers”, McGraw-Hill, 1970. DAÍ, S. H. and WANG, O. M.. Reliability Analysis in Engineering Applications. New York: Van Nostrand Reinhold, 1992. FUSCO, Péricles B.. Fundamentos do Projeto Estrutural: Ed. USP, 1977. GRAZIANO, Francisco Paulo. Projeto e Execução de Estruturas de Concreto Armado. São Paulo: Ed. Nome da Rosa, 2005 ISBN -10: 8586872407

**Computer Engineering and Computer Science**

The undergraduate programs in Computing at PUC-Rio are repeatedly rated among the best in Brazil. Graduates are highly regarded by an ever-growing job market. Our programs do not emphasize technologies, which may disappear in two or three years, but focus instead on fundamental concepts and techniques, shaping professionals for a highly dynamic environment. Courses cover both traditional areas in Computing, such as software development and algorithms, and novel areas, such as entertainment, digital media, data science, and intelligent systems. Students have the opportunity to participate in internships and projects in innovating areas in the labs located in the University.

The Computer Engineering program provides a sold background in engineering and in computing, allowing its graduates to work both in software, in areas such as scientific computing, entertainment applications, or apps for mobile devices, as in areas that integrate software and hardware, such as embedded systems or computer networks.

The Computer Science graduates go on to leading positions either in the software industry or in research groups. They work not only using the appropriate existing technologies to create new software systems, but often on developing new technologies, like programming languages, game engines, or tools for big data visual.

**Control and Automation Engineering**

The Control and Automation curriculum focuses on the integration of several fields, especially those concerning Mechanical, Electrical and Computer Science areas. In this sense, the course has the objective to offer ample visions concerning the functioning of automatic systems, involving mechanical, electro-electronic and computational aspects, thus enabling the student to specialize in one of mentioned areas, later on. The control and automation engineer is capable to technically manage interdisciplinary projects, therefore able to work in wide variety areas, such as, the aeronautical, automotive, petrol and nuclear industries, as well as building automation, among others.

**Electrical Engineering**

The course offers specialization in Electronics and Computers, Electrical Energy or Telecommunication Systems. The course curriculum is continuously updated so as to follow the technological evolution. The disciplines offer a solid knowledge support in mathematics, physics, modeling and computing. They also emphasize the project and equipment development, the intensive use of labs and computational systems. The Electrical Engineering specific labor market embraces all companies of the mentioned area, especially state and private owned companies for electrical energy generation, transmission or distribution, companies for the supply of telecommunication services, companies for the installation or development of automated systems, research centers and industries for the manufacture of electrical equipment and systems, for telecommunication and computing, consulting companies and governmental agencies. The labor market in the service rendering area, as well as within the respective areas of large state and private owned companies, absorb a large number of engineers, due to their excellent mathematic basis, their knowledge in modeling and informatics and their high managerial capacity.

**Syllabuses:**

**Syllabus**: Introduction and basic definitions. Discrete-time signals and difference equations. Continuous-time signals and differential equations. Periodic signals. Z Transform. Laplace Transform. Fourier Series. Fourier Transforms

**Bibliography**: Alan V. Oppenheim and Alan S. Willsky, Signals & Systems, 2nd Edition, 1996, Prentice-Hall, USA. Alan V. Oppenheim e Alan S. Willsky, Sinais e Sistemas, 2a Edição, 2010, Pearson, Brasil

**Environmental Engineering**

The Environmental Engineering course is intrinsically interdisciplinary, offering a solid knowledge in technology, environmental management and legislation. The pedagogical project of the course has been conceived so as to graduate professionals capable of thinking globally and acting locally. The students are capable to apply the theoretical knowledge acquired to find solutions of environmental problems, including on a international level. The course offer the opportunity to study abroad, via double certification programs with prestigious European institutions, as well as in exchanges programs with other partners’ universities. The international programs count with the DAAD support of the German Government and with the grants from Branetec, a joint program between CAPES, from Brazil and NUFFIC, from the Netherlands.

**Syllabuses:**

**Syllabus**: Geotechnics and environmental damage: General aspects. Susceptibility and risk maps. Natural movements of solid masses: erosion, subsidence, slope instability. Mechanisms and control. Waste and tailings: characterization and classification. Landfills: Municipal and industrial landfills. Sludge disposal: sedimentation and thickening. Sandy tailings liquefaction. Transport of contaminants: physical and chemical aspects. Sampling and testing. Degraded areas: assessment, monitoring and remediation techniques

**Syllabus**: Sources of solid, liquid and gaseous pollutants in industrial processes. Assessment of environmental impacts. Basic aspects of environmental management in industry and pollution control. Case studies. Main operating processes on liquid effluent emissions, gases and solid residues

**Syllabus**: The world consumption. Conventional and alternative sources of energy. Non-renewable (fossil fuel) and renewable (array bioenergetics) sources. Solar energy (thermal and photovoltaic). Geomechanical energy (wind and tidal power) and geothermal energy. Fuel cell generator (hydrogen cells). Use & prospects for nuclear power: fission and fusion. Sustainability

**Syllabus**: Fundamental concepts. Types of the most common pollutants. Industrial ventilation. Equipment for removing particulate pollutants (cyclones, electrostatic precipitators, filters, washing towers). Equipment for removing gaseous pollutants. Legislation and trends in Brazil and in the world. ISO 14000. Design considerations and cost estimate. System sizing examples for removal of particulate and gaseous pollutants. Treatment of gaseous and particulates in vehicle emissions

**Syllabus**: Concepts and definitions. The environmental impact assessment process and its objectives. Planning and preparation of an environmental impact study. Identifying environmental impacts. Prediction of impacts. Assessment of the importance of environmental impacts. Technical analysis of environmental studies. Case studies

**Syllabus**: Concepts, definitions and processes of formation of degraded areas. Planning and conservation of soil and water for agricultural production and environmental remediation. Water and wind erosion. Characterization and diagnosis of degraded areas. Preparation of plans and executive design of remediation of degraded areas. Concept of Bioengineering. Vegetative and mechanical practices for erosion control and remediation of degraded areas. Tailings use in development and dissipation of runoff. Use of organic waste for the production of seedlings, fertilizing and for use as mulch. Ecological succession. Selection of plant species for revegetation of degraded areas. Planning for implementation of projects of recovery of degraded areas. Maintenance and monitoring of erosion control projects and the remediation of degraded areas

**Syllabus**: The proposal of this discipline is to apply the theoretical and practical concepts learned in the discipline ENG 1907 Analytical Chemistry for Environmental Engineers

**Syllabus**: Solid waste. Municipal waste. Characteristics and production of waste. Public cleaning. Street cleaning. Sweeping. Home waste collection. Packaging and transport of waste. Equipment. Transfer stations. Separate collection. Treatment and disposal of waste: reduction, recycling and materials recovery, composting, incineration, landfills. Hazardous waste: concept, characterization, control, handling, packaging, physical treatment, chemical, biological and thermal

**Syllabus**: Insertion of the topic in the context of Environmental Engineering; Public health situation in Brazil. Relationship with basic sanitation. Institutional Aspects. Basic concepts of epidemiology.Theory about the health-disease causal relationship. Environmental classification of infectious diseases. Basic sanitation actions and their effects on public health. Vector control. Biostatistics indicators. Aspects of analytic epidemiology. Methodology for assessing the impact of sanitation measures. Technology applied to basic sanitation.

**Syllabus**: Federal and State environmental legislation for the industry. Civilian organizations. Noise pollution. Licensing of waste disposal (minimization, recycling), liquid effluents, gaseous effluents and noise pollution. Environmental audits. Monitoring. Quality management. Risk management. Evaluation of environmental impacts. Legislation. Zoning. Practical cases

**Syllabus**: Study of safety risk analysis. Data survey. Database on environmental accidents. Formulating hypotheses. Frequencies estimation of probabilities. Mathematical models. Risk estimation. Mitigation of risks. Practical case studies. Major environmental accidents and their relationship to safety risk analysis. Typical cases: oil spill, industrial accidents and nuclear accidents

**Syllabus**: The course aims to teach to future environmental engineers the basic chemical analytical techniques so that they can, in the future, perform field tests, specify tests to commercial laboratories and to interpret the results obtained. The course covers analytical techniques such as gravimetric, volumetric, potentiometry and spectrophotometry in the visible region. Additionally, aiming a better learning, the course is complemented with laboratory testing activities, including the determination of total solids, alkalinity, hardness, chlorides, pH and dissolved oxygen

**Syllabus**: Introduction: classification, nomenclature and examples of environmental organic compounds (polycyclic aromatic hydrocarbons, pesticides, microcystins, among others). Total petroleum hydrocarbons (TPH). Polycyclic aromatic hydrocarbons (PAH’s). Pesticides (organochlorine, organophosphorus and carbamates). Partition equilibrium between solid, liquid and gaseous phases: vapour pressure, solubility in water and octanol-water partition coefficient. Sorption processes involving organic matter. Photochemistry of organic compounds in natural environments (water, soil, sediments): direct and indirect photolysis. The hydroxyl radical. Biodegradation and biological transformations. Bioaccumulation and bioaugmentation. Ecotoxicity aspects

**Syllabus**: Sampling, collection and preservation of environmental samples. Chain of custody. Choice of the methods for determination of organic compounds for analyses of environmental matrices: DL, QL, range, etc. Extraction processes, clean up, pre-merger, and analysis. Assessment of Total Petroleum Hydrocarbons (TPH) in soil samples and/or water. Assessment of polycyclic aromatic hydrocarbons (PAH’s) in soil samples and/or water and/or biota. Assessment of pesticides (organophosphates and carbamates) and samples of soil and/or water and/or biota and/or food. Photodegradation experiments: photolysis and photocatalysis. Toxicity tests

**Syllabus**: Geoprocessing: creation, evolution and interdisciplinary. Georeferenced data. Main GeoTechnologies. GPS. Remote sensing as a means of obtaining data. Geographical databases. Geographic information systems architecture. Spatial analysis. Numerical models of the terrain. GIS and environmental analysis

**Syllabus**: Historical evolution of the environmental issue. Historical cases. Environmental problems on a global scale. The concept of sustainable development and prospects for the future. Destruction of the ozone layer, acid rain, greenhouse effect. Biodiversity conservation. Desertification

**Syllabus**: Weather and climate. Factors and elements of climate. Object and method. Geographic impact of the shape and movements of the planet Earth. Differential heating of the Earth’s surface and the effect on the atmospheric parameters. Vertical composition of the atmosphere. General circulation of the atmosphere. Air masses and frontal development mechanisms. Climate change. Climate classification. Anthropogenic and climate actions

**Syllabus**: The concept of Ecology. Notions of communities and ecosystems. Definition and characteristics of communities. Development of communities. Mass and energy transfer in ecosystems. Ecology and dynamics of populations. Ecology and dynamics of communities. Applied ecology

**Materials and Nanotechnology Engineering**

Materials and Nanotechnology Engineering is the natural evolution for the Material Engineering, as it incorporates a knowingly important segment in the contemporaneous technological development, that is, the Nanotechnology. With its expanded scope after incorporating the atomic mechanisms that control the materials properties, this branch of the engineering allows the acquired knowledge to be managed, not only for the study of the conventional materials and their properties but also in the conception and implementation of new synthesis and transformation processes, which aim to obtain nanostructured materials with innovating characteristics and functionalities. So, it is up to the professional to get involved with the procedures of synthesis, processing and characterization of the materials, which should be conducted via a solid scientific knowledge, thus allowing the understanding and control of the crystalline structure, form and size of the materials, from the atomic and molecular scale up to the macroscopic system.

The Material and Nanotechnology Engineer shall stand out due to their solid base in Physics, Mathematics, Chemistry and Materials. Such scientific base enables this engineer to communicate and interact with any other engineering branch, as well as to perform in the most diverse areas of the productive sector. The strong fundamental basis also facilitates the multidisciplinary nature of such engineering and amplifies the acting field of its professionals, allowing them to adjust to the larger and diversified work in the base industries (mechanics, mining, oil, metallurgy, chemistry, etc.) and the consumer goods industries (electronics, cosmetics, biotechnology, medicines, dyes, polymers, etc.).

**Mathematics**

The Graduation in Mathematics conciliates a solid basis of the main mathematic fields (analysis, algebra, geometry, topology and applied mathematics) with a large curricular flexibility. The Graduation is known by its excellence, having always achieved the maximum concept in all submitted evaluations. It is also famous for the high academic level of the students being attracted: in the last ten years, half of the graduates entered into doctorate programs in several areas, in institutions such as Princeton, Harvard, New York University or MIT. The flexibility of the department curriculum allows that the students personalize their formation, cursing elective disciplines within the departments of their choice, whereas several students also study Engineering, Computing or Physics together with the Graduation. The professional insertion of the graduates is ample and comprehends segments such as academical institutions, the financial market, the oil sector and several public sector research agencies.

**Syllabuses:**

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**Syllabus**: Differential equations of the first order: geometric interpretation in terms of line fields, existence and uniqueness of solutions. Some resolution methods: Separable, exact and linear differential equations of the first order (homogeneous and nonhomogeneous). Linear difference equations of first order with constant coefficients. Linear differential and difference equations of the second order with constant coefficients. Linear systems in the plane. Power series resolution of differential equations.

**Syllabus**: Numbers, approximations of real numbers with sequences. Solution of equations and inequalities. Coordinate geometry, equations, lines, parabolas, equilateral hyperbola and circles. Functions and graphs. Affine function, quadratic function, polynomial and rational functions, roots. Algebra of functions. Trigonometry. Derivatives. Derivatives of Trigonometric Functions. Differentiation rules, including the chain rule. Applications: Derivatives and shape of a graph, optimization problems, related rates, approximation of a function using polynomials function, Newton’s method

**Syllabus**: Exponential and logarithm functions. Derivatives of inverse functions. L’Hôpital’s rule. Definite integrals, indefinite integrals. The Fundamental Theorem of Calculus. Applications of integration

**Syllabus**: Real numbers, decimal representation. Sequences. Functions and graphs. Continuity. Limit of a function, limits at infinity and asymptotes . Differentiability. Derivatives of elementary functions and their graphs. Higher-order derivatives. Optimization problems. Definite integral. The fundamental theorem of calculus, antiderivatives. Applications of integration

**Syllabus**: Vector functions and their derivatives: the Jacobian matrix. The general chain-rule and the inverse function theorem. Double and triple integrals: the change of variables formula. Parametric curves: velocity and tangent vectors. Path integrals, conservative fields and scalar potentials. Application: work and the kinetic energy theorem. Green´s theorem. Curl and divergence operators; the vector potential. Parametric surfaces: areas, tangent plane and graphs. The implicit function theorem. Surface integrals for scalar fields. Oriented surfaces and surface integrals for vector fields. Stokes and Gauss’ theorems

**Syllabus**: Real numbers, decimal representation. Sequences. Functions and graphs. Continuity. Limit of a function, limits at infinity and asymptotes . Differentiability. Derivatives of elementary functions and their graphs. Higher-order derivatives. Optimization problems. Definite integral. The fundamental theorem of calculus, antiderivatives. Applications of integration. Additional topics

**Syllabus**: Continuity and differentiability of functions of 2 and 3 variables: Graph, domain, image. Linear approximation. Critical points. The Weierstrass’s theorem. Lagrange multipliers. Double and triple integrals in Cartesian, polar, cylindrical and spherical coordinates. Additional topics

**Syllabus**: Systems of linear equations. Cartesian coordinates in two and three dimensions. Vectors, scalar product, determinants, vector product, triple product. Linear subspaces, basis. Linear maps, matrices. Eigenvalues and eigenvector

**Syllabus**: Invariant subspaces. Kernel, image and the rank–nullity theorem. LU decomposition. Least squares. The Gram–Schmidt process. QR decomposition. Eigenvalues and eigenvectors with numerical methods

**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**: 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

**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**: Set theory, functions and relations. Integers, mathematical induction. Combinatorics; counting problems, inclusion–exclusion principle. Discrete probability theory. Graph theory: trees, planar graphs, graph coloring, matching, Eulerian and Hamiltonian graphs. Flow networks.

**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

**Syllabus**: Fourier series. Partial differential equation, heat equation, wave Laplace’s equation. Fourier method for initial value problems and boundary value problems

**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**: Set and relation. Mathematical induction, proof by contradiction. Natural numbers. Cardinality and enumerability. Rational and real numbers. Limit, convergence of sequences and series. Topology of the real line: open, closed, compact, connected and dense sets. The Cantor ternary set. Continuous function: the Bolzano–Weierstrass theorem, the intermediate value theorem, uniform continuity

**Syllabus**: Review of topology and continuity of real functions. The derivative, the Mean Value Theorem, L’Hôpital’s rule, Taylor approximants. Integration in the sense of Riemann. The Fundamental Theorem of Calculus. Sequences of functions. Power series and analytic functions. The Stone-Weierstrass theorem. The Theorem of Arzela-Ascoli. Introduction to harmonic analysis and Fourier series

**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

**Syllabus**: Metric spaces, Topological spaces. Continuity. Connected and compact spaces. Fundamental group. Covering spaces. Classification of surfaces

**Syllabus**: Planar and spatial curves. Frenet frame and applications. Surfaces.in 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**: 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

**Mechanical Engineering**

The Mechanical Engineering constitutes one of the most ample engineering branches, comprising activities such as the energy generation, manufacture of machines and consumer goods, project and manufacture of airplanes, vessels and cars, automation of mechanical system, among many others. Incentivized by the investments performed within the aeronautical, automotive, naval, oil and energy areas, the labor market of the mechanical engineer is being steadily expanded. In order to attend it, the formation of this professional is based on solid mathematics, physics and chemical knowledge, being added hereto knowledge on materials, solid mechanics, dynamics and system control, thermodynamics and fluid mechanics. The knowledge of experimental and computational techniques is also decisive for the exercise of the profession.

**Syllabuses:**

**Syllabus:**Basic commands that allow the student to work through all the subjects presented on the theory. Introduce the key techniques and methods for computer aided design work. Program interface. Geometric objects. Importance of geometrical rational organization. Control of displayed information quantities. Basic geometrical transformations. Translation, rotation, scale changes and reflection. Manipulation of precision tools. Cilindrical projections. Orthogonal projection. Dihedral system. First-angle and third-angle projections. Frontal view definitions. Axonometric representation. Isometric, dimetric and trimetric concepts. Simple objects representations on isometric projections. Circumferences drawing on isometric projections. Arch intersection. Tangents. Four center method. Introduction to ABNT regulation for Technical Drawing. Different types of lines and its applications. Scale concept. Impression sheets

**Syllabus:**Hatch patterns. Symbols library. Composition of drawing. Technical writing. Reduction and ampliation scales. Technical A series ISO sheet patterns. Stamp use. Sheets marking and folding. Cavaleira perspective, reduction coefficient for 30º, 45º and 60º degrees. Solid construction from orthogonal projections. Cuts and sections. Visualization problems on strict geometric drawing. Use of conventional rules. Specific actions for section representation. Pipeline drawing. Pipeline elements. Pipes, connections and valves. Unifiar, bifilar and 3D drawing. Isometric and orthogonal projections. Organization of a basic symbol library. Definition of symbol classification.

**Syllabus:**Properties and definitions of fluids. Flow classification: permanent/transient, laminar / turbulent, viscous/inviscid, incompressible/compressible. Hydrostatic. Fluid flow. Fluid dynamics basic equations. Incompressible viscous fluid flow (external and internal). Localized and distributed pressure losses.

**Syllabus:**Fundamentals of thermodynamics. Introduction to transport phenomena. Heat transfer modes: conduction, convection, radiation. Mass transport

**Syllabus:**Definition of fluid properties. Methods of analysis. The continuum hypothesis . Velocity and stress fields. Mechanical behavior: Newtonian and Non-Newtonians fluids. Flow classification: steady/transient, laminar/turbulent, viscous/inviscid, incompressible/compressible. Dimensional analysis and similitude. Hydrostatics. Basic equations for a control volume: continuity, linear momentum, angular momentum, energy and 2nd law of thermodynamics. Energy considerations for the flow through tubes and ducts. Head losses in pipelines; local losses. Duct networks. Applications to pumps. Velocity and flow meters. Laboratory practice

**Syllabus:**Fourier’s law. Thermal properties. Heat diffusion equation. One dimensional, steady state conduction. Two dimensional, steady state conduction. Transient conduction. Convection. External flow. Internal flow. Free convection. Boiling and condensation. Heat exchangers. Radiation: processes and properties. Radiation exchange between surfaces.

**Syllabus:**Development of an engineering project or a research project under supervision of an advisor. The project can be developed by one student or a group of students, and should be presented in a written report that follows the guidelines established by the department

**Syllabus:**The student have to attend an internship program in an engineering company, with a maximum of 20 hours per week

**Syllabus:**Full time work experience, total of 600 hours, under supervision of a professor, at companies that have special agreement with the Department of Mechanical Engineering.

**Syllabus:**Review of vector algebra. Equilibrium of a system of forces. Internal and external forces. Equilibrium equations. Distributed forces. Statically equivalent forces and moments. Couples. Center of gravity. Concentrated forces and moments. Cables. Analysis of trusses. Introduction to the notion of stress field. Forces and moments transmitted in beams. Virtual Work. Moment of Inertia. Friction.

**Syllabus:**Introduction to heat engines. Concepts and definitions. Steam tables. Basic experiments: pressure, specific volume and temperature. Work and heat. First law of thermodynamics. Entropy. Second law of thermodynamics. Air tables. Irreversibilities. Energy.

**Syllabus:**Conventional draw of cuts and sections of mechanical elements. Dimensioning of mechanical parts: dimensioning the final product and dimensioning for production (manufacturing processes). Symbols to represent surface finishing Brazilian standards and ANSI. Surface roughness and uniformity. Introduction to the ISO system of tolerancies and fittings. Indication in mechanical drawings. Representing and dimensioning of power transmitting elements. Drawing and dimensioning of rolling and journal bearings. Couplings. Pulleys, sheaves and fly wheels. V belt drives and plane belts. Orientation for reading and interpretation of mechanical devices, sheet-metall-forming, complete mechanisms of metal-cutting machines and others. Conventional engineering designs and computer-aided design and automated drawing. Computer laboratory (CAD).

**Syllabus:**Stresses and strains: basic concepts. Beam under Uniaxial loadings: stresses and deformation. Torsion of solid circular, pipe and general thin walled section shafts: stresses and deformation. Plane state of stresses and strains. Principal stresses and corresponding directions. Mohr circle. Equilibrium equations. Strain-displacements compatibility relations. Constitutive laws. Ideal stress-strain relations. General 3D state of stresses and strains. Analysis of combined states of stress. Shear forces and bending moments in beams. Stresses in beams due to bending. Euler-Bernouille beam model.

**Syllabus:**Deflections of statically determinate and indeterminate beams under bending. Moment-curvature relations. Superposition. Buckling of slender columns. Stability conditions. Failure criteria under buckling. State of stresses beyond linear material behavior. Tresca and von Mises plasticity initiation criteria. Ciclic loading, histeresis, residual stresses. Stresses in thick wall cylinders under internal and external pressure. Rotating disks. Energy methods. Castigliano’s theorem. Principle of minimum work. Introduction to the finite element method. Straight beams under general bending loadings conditions. Shear center.

**Syllabus:**Kinematics of rigid bodies in space: angular velocities, transformation of vectors in different reference systems, angular acceleration, velocity and acceleration, relations between velocities and accelerations of two points fixed on a rigid body, velocity and acceleration of a point that moves in relation of a rigid body, rotation without slipping (gears, pulleys, belts, etc.), systems of rigid bodies: (constraints and restrictions). Planar motion, Laws of motion. Rotation of a dumbbell.Energy considerations. Impact situations. Planar mechanisms. Dynamics of rigid bodies: Inertia tensor, linear and angular momentum, conservation of energy and momentum, Newton-Euler equations, gyroscopic effects, free motion of a non-axisymmetric body in space.

**Syllabus:**Basic differential equations: continuity, momentum (Euler and Navier-Stokes). Rotational and irrotational flows. Internal and external incompressible viscous flow. Fully developed hydrodynamic flow. Boundary layer theory. Compressible flow. Sound speed. Reference conditions: stagnation and critic. Isoentropic flow. Flow through constant area ducts: Fanno and Rayleigh flows. Normal shock.

**Syllabus:**Techniques and control of manufacturing processes. Measurement errors. Instruments for direct and comparative measurements. Tolerance systems. ISSO standards. Tolerances. Basic hole and basic shaft systems. Fittings. Running, sliding and interference fits: measurement and control of conical elements. Threads. Thread systems. Control and measurement of threads. Thread tolerances. Gages. Calipers. Measurement and control of gears.

**Syllabus:**Static mechanical design under combined stresses. Strength criterion for several material classes. Fatigue: SN design method, Wöhler curve, Goodman diagram. Palmgreen-Miner rule. Fracture mechanics fundamentals. Stress intensity factor. Fracture toughness. Fatigue crack propagation. High temperature behavior. Norton-Arrhenius laws. Larson-Miller parameter. Damage mechanisms in high temperature. Mechanical tests laboratory.

**Syllabus:**Introduction to vibration and the fue response. Response to harmonic excitation. General forced response. Some motions about non-linear behavior – the pendulum. Introduction to Matlab. Multi-degree-of-freedom Systems. Conservative and non-conservative systems, Lagrange’s equation, frequency response function, nodal analysis. Distributed parameter systems. Vibration of a string. Vibration of rods and beams. Vibration testing and experimental modal analysis. Notions about the finite element method;

**Syllabus:**Manufacturing processes: machining processes, metal forming processes, non-conventional manufacturing processes. Machines for material-removal processes. Geometrical relationships and movements related to the machining processes. Cutting -Tool Materials and Cutting Fluids. Machinability. Cutting Forces and Power. Economics in machining processes. Selecting speeds for metal-cutting operations. Speed gearboxes in metal-cutting machines. Workshop works.

**Syllabus:**Introduction: definitions, standards, dimensions and units, technical report. Uncertainty analysis of experimental data. Pressure measurement. Flow and velocity measurement. Temperature measurement. Force, torque, starin, acceleration and velocity measurements. Sound measurements.

**Syllabus:**Ordinary differential equations. Initial-value problems. Numerical quadrature, stability, error analysis. Boundary value problems. Partial differential equations. Finite volume methods. Solution of equations. Systems of equations. Finite element methods. Mechanical engineering applications. Analytic and semi-analytic solutions.

**Syllabus:**Introduction to mechanical engineering design. Design of journal bearings; clutches and brakes; wire ropes; screws; mechanical springs; and gears.

**Syllabus:**Rankine power cycles. Steam turbines. Boilers. Condensers. Brayton, Otto and Diesel cycles for gas turbines and internal combustion engines. Refrigeration cycles and air conditioning systems. Compressors. Laboratory: testing of a Rankine cycle, and an internal combustion engine.

**Syllabus:**General characteristics and products of metal forming processes. Influence of stress states, strain-rates, temperature, friction and microstructures on cold and hot forming processes. Strain hardening. Fundamentals of plasticity. Forming force calculation: slab method, upper bound method. Processes, equipment, technology and calculation of force and power for cold and hot rolling, forging, forward and back extrusion and drawing. Sheet-metal forming. Formability of sheet metals. Processes, equipment, technology and design of dies for shearing, bending, deep drawing and stretch forming. Other sheet-forming methods: spinning rubber, explosive and superplastic forming.

**Syllabus:**Unified mathematical modeling of dynamic systems: mechanical, electrical, thermal, pneumatic and hydraulic systems. Coupled systems. Lumped parameters systems. Bond graphs technique. State space equations. Matricial methods and numerical analysis of the systems dynamic response. Stability. Simulation and analysis of dynamic systems.

**Syllabus:**Control basic concepts. Control systems design. Feedback and stability. Transfer functions. Poles and zeros. PID controllers. Root locus method. Frequency response method. State space linear systems description. Controllability and observability. State space control strategies. Optimal control notions.

**Syllabus:**General consideration on function, cost, environment, product liability, safety and use of codes and standards. I) Design of mechanical systems following codes. For example: design of pressure vessels following the ASME code. II) Structural design using numerical calculations. For example: design of a moving crane. III) Design of complex systems with the associated selection and specification of standard basic machine elements. IV) Dynamics considerations on design. For example: vehicle suspension.

**Syllabus:**Analysis of typical thermal engineering projects. Major steps of the project are covered: identification of system demands, plant conception, mass and energy balances, heat exchangers design, environmental impacts, economic analysis, use of standards.

**Syllabus:**Race cars science and technology. The evolution of the race cars from the 60´s till today: the empiricism to scientific treatment. Measurements, estimates and magnitude orders of the main variables: acceleration, speed, power, traction, braking, and tires lateral grip forces, and aerodynamic forces. Concepts of vehicle dynamics. Description of components: engine, gearbox, steering, suspension, brakes, aerofoils, instrumentation and control systems. Straight and in curves behavior. Simulation and performance evaluation. Scale and virtual prototypes.

**Syllabus:**Description of the topics of mechanics, electro-electronics and computing applied to the control and automation engineering. Short presentation of each discipline in the control and automation professional cycle and its correlation with the others. The need and importance of knowledge integration. The actuation areas of control and automation engineers.

**Syllabus:**Fluid-mechanical actuators: hydraulic and pneumatic systems components, circuits construction and interpretation. Electro-pneumatics and electro-hydraulics. Electro-mechanical actuators: motors and drives circuits. Application examples. Laboratory demonstrations.

**Syllabus:**Competitive strategy and operations strategy. Organizational Design: the “Production Function” and the “Engineering Function”. Work organisation work. Elements involved in products/services and processes design. Production planning and control. Characteristics of computer systems; Production control and quality control. Manufacture automation technology. Integrated management systems (SIGs, ERP), shop floor control (SFC) and integrated manufacturing systems (CIM); Evaluation methods of production performance.

**Syllabus:**Introduction to production systems; production control terminology; reliability in production systems; manufacture automation project; computer-integrated manufacturing environment; elements and techniques to support manufacturing integration and automation: CAD, CAM, CAE, CAPP, CNC programming, PCP, MRP, MRPII, ERP; materials manipulation and displacement technologies; integration technologies; integrated environments organization; softwares in support of modeling, design and computer simulation of manufacturing processes; numerical control machine tools. Flexible manufacturing cells CAD/CAM/CAE. Industrial robots and their applications. Robotic manufacturing-oriented project.

**Syllabus:**1 – Introduction. Basic Concepts. Classification of Optimization Problems. Basics of Calculus and Linear Algebra. 2 – Nonlinear Programming. Unconstrained Optimization. Optimality Conditions. Constrained Optimization. Lagrange Multipliers. Optimality Conditions. Indirect Optimization Methods. Exterior Penalty Function. Interior Penalty (Barrier) Function. Direct Optimization Methods. Random Search. Sequential Linear Programming. Sequential Quadratic Programming. 3 – Linear Programming. 4 – Introduction to Probabilistic Methods.

**Syllabus:**Robotics history. Plane Kinematics. Spatial Kinematics. Homogeneous transformations. Denavit-Hartenberg notation. Differential Motion Analysis. Jacobian matrices. Singularity and Redundancy. Inverse Kinematics. Trajectories summary. Optimal Control of Redundant Robots. Static: Free Body Diagram. Duality between kinematics and statics. Servo Stiffness. Dynamics: Newton-Euler formulation. Motion Equations. Physical Interpretation of the Manipulators Dynamics (Gravity, Inertial Forces, Dynamic Coupling). Lagrange formulation. Lagrange Motion Equation. Inertia matrix of a Robotic Manipulator. Physical Interpretation. Generalized Forces. Inverse Dynamics. Luh-Walker-Paul Recursive Algorithm.

**Syllabus:**Review of robots kinematics static and dynamics. Trajectories Control – PID, Computed Torque Control, Lyapunov Stability, Adaptive Control, Learning Control. Force Control – Hybrid Position / Force Control, Friction Compensation in Manipulators, Component Insertion, Multiple Manipulators Coordination. Telerobotics. Flexible robots. Manipulators Calibration. Visual Servo Control of Robots. Advanced Control Techniques.

**Syllabus:**Power Train. Engines. Brake Systems. Steering Systems. Suspension Systems. Chassis. Electro-Electronic Systems. Embedded Electronics. Control and Automation Systems

**Syllabus:**Vehicle type application and specification. Definition of key parameters. Determination of basic characteristics. Performance evaluation. Component specification.

**Syllabus:**Vehicle as a dynamic system. Tire-ground interaction. Longitudinal dynamics. Vertical dynamics. Lateral dynamics. Interaction of the longitudinal, vertical and lateral dynamics. Motorcycle dynamics. Structural dynamics. Vehicles collision and accident analysis and reconstruction.

**Syllabus:**Actuation and instrumentation systems. Ground vehicles modeling and parameter identification. Speed control. Vibration control. Attitude and trajectory control. Control of motorcycles. Engines control. Human control.

**Syllabus:**Standards and legislation for vehicles homologation. Basics of instrumentation for experiments applied to vehicle tests. Vehicle performance tests and instrumentation. Vehicle tests under controlled conditions in laboratory. Tests for development and evaluation of vehicles.

**Petrol Engineering**

The state monopoly end has initiated a new expansion cycle of the oil activity in the country. The significant increase in the Brazilian production allocates mentioned industry among the most dynamic segments of the national economy, ensuring the business and professional opportunity enlargement. In this context, the PUC Rio graduation program has the objective to capacitate the student and treat the problems relating to the oil and gas exploring, production and transport activities. The formation aggregates the basic engineering knowledge – especially in the Mechanics, Civil and Chemistry fields – to the knowledge applied to the oil exploration and production sector.

**Physics**

From the elementary particles to the Cosmos, the spectrum of the study topics in Physics is immense. The computers, laser, the genetic code deciphering, as well as the telecommunications constitute examples of the research results in the area, assigning a continuous larger importance to the physicist within the world scenery. The PUC-Rio graduation in Physics offers a wide scientific knowledge base, both theoretical and experimental. The course is highlighted by its requirements and excellence, corroborated by the excellent external evaluations. Our graduated physicists have easily entered in post-graduation programs in Brazil and abroad, and are becoming active professional in learning and research institutions. The graduation offered by PUC-Rio promotes the intellectual development, the thinking ability, the creative capacity and independence, which turn the students capable to solve new problems. Such qualities are more and more required by all professionals that opt for a fast insertion in the labor market. Thus, a wide spectrum of opportunities, from the technical areas up to the financial market, is turned available for the graduated students.

**Syllabuses:**

**Syllabus**: Unidimensional kinematics: position, position coordinates, observer, change of reference system, uniform motion and accelerated. Kinematics in the plan: Cartesian reference system bi-dimensional vectors, motion with constant acceleration, polar coordinates, circular motion

**Syllabus**: Forces and Newton’s Laws. Work. Work-Kinetic Energy Theorem. Conservative forces, potential energy and mechanical energy. Linear momentum. Conservation of linear momentum and collisions. Rotational kinematics. Moment of inertia of rigid bodies. Torque. Equilibrium of rigid bodies. Angular momentum and its conservation. Rolling motion of a rigid bodies

**Syllabus**: Force and Newton’s laws. Work-kinetic energy relation. Conservative forces, potential energy, mechanical energy. Linear momentum. Collisions and conservation of linear momentum. Rotational kinematics. Moment of inertia of rigid bodies. Torque. Equilibrium of rigid bodies. Angular momentum. Conservation of angular momentum. Rolling

**Syllabus**: Vectors. Kinematics vector. Forces and Newton’s Laws. Work. Work-Kinetic Energy Theorem. Conservative forces, potential energy and mechanical energy. Linear momentum. Conservation of linear momentum and collisions. Rotational kinematics. Moment of inertia of rigid bodies. Torque. Equilibrium of rigid bodies. Angular momentum and its conservation. Rolling motion of a rigid bodies

**Syllabus**: Vectors. Vector kinematics.Force and Newton’s laws. Work. Work-kinetic energy relation. Conservative forces, potential energy, mechanical energy. Linear momentum. Collisions and conservation of linear momentum. Rotational kinematics. Moment of inertia of rigid bodies. Torque. Equilibrium of rigid bodies. Angular momentum. Conservation of angular momentum. Rolling

**Syllabus**: Kinetic theory of gases. Microscopic definition of pressure, temperature and internal energy. Equations of state. Specific heat of gases. Classical statistics: Maxwell Boltzmann. Principles of thermodynamics: internal energy and entropy: reversibility and irreversibility. Macroscopic model of non-compressible fluids: statistical and fluid dynamics. Waves in material media in one dimension; rope differential equation under tension and the propagation of sound in air. Beat and interference. Stationary waves. Doppler Effect. Waves in two-dimension (wave tank): principles of Huygens and Fermat. Reflection, refraction, diffraction and interference

**Syllabus**: Kinetic theory of gases. Microscopic definition of pressure, temperature and internal energy. Equations of state. Specific heat of gases. Classical statistics: Maxwell Boltzmann. Principles of thermodynamics: internal energy and entropy: reversibility and irreversibility. Macroscopic model of non-compressible fluids: statistical and fluid dynamics. Waves in material media in one dimension; rope differential equation under tension and the propagation of sound in air. Beat and interference. Waves. Doppler Effect. Waves in two dimensions (wave tank): principles of Huygens and Fermat. Reflection, refraction, diffraction and interference

**Syllabus**: Electric charge, Coulomb’s Law and Electric field. Calculation fields distributions loads of Electric Field Lines. Movement of charged particles in an electric field. Electric flux and Gauss’s Law and electric field computation. Conductors in equilibrium. Field on the surface of a conductor. Atmospheric electric field. Electric potential, and calculation of potential fields, field calculation from the potential. Insulators in an electric field. Concept of capacitance. Combinations of capacitors, energy and dielectrics. Electric Current and Ohm’s law. Power. EFM Concept. RC circuits. Magnetic Field. Force on load. Movement of particles. Force on wire with current.Torque on a coil. Biot-Savart. Ampere’s law and calculation of magnetic fields. Magnetism in the art. Magnetic Flux and Faraday’s Law. EFM. motion. Lenz’s Law. Applications. Self Inductance and RL circuits. Energy stored in the inductor. Maxwell’s equations. LC circuit, oscillations. Concept of resonance. Alternating current circuits. Phasor concept. Power. Electromagnetic waves

**Syllabus**: Activities Laboratory on: Resistive Elements. Kirchhoff’s Laws. Equipotential lines. Measuring instruments. RC circuits. Magnetic field Ampere’s Law. Magnetic field detection. Lenz-Faraday’s Law. RLC circuits. Oscillations. Resonance

**Syllabus**: Electromagnetic Waves. Reflection and Refraction. Interference. Diffraction and Polarization. Notions of the Theory of Relativity. Origins of Quantum Theory: Behavior of light as a particle. Photoelectric and Compton effects. Atomic Models; notions of quantum mechanics, the uncertainty principle

**Syllabus**: Electromagnetic waves. Reflection and refraction of light. Interference and diffraction. Notions of Restricted Theory of Relativity. Origin of Quantum Physics: particle nature of light. Photoelectric and Compton effects. Models of Atomic Structure; notions of Quantum Mechanics; Uncertainty Principle; Atoms. Atomic Nucleus. Molecules and Solids; Elementary Particles; Cosmology

**Syllabus**: Elements of Newtonian mechanics. Motion of a particle in one dimension. Motion of a particle in two or three dimensions. Motion of a system of particles. Rigid bodies. Introduction to the mechanics of continuous media

**Syllabus**: Operators. Notions of Hilbert space, and of representation theory. Dirac notation. Historical origins. Wave-particle duality. Uncertainty principle. Wave functions. Probabilistic interpretation. Quantum Measurements. Schroedinger’s equation. Time evolution. Ehrenfest theorem. Stationary problems in one and three dimensions. Identical particles. Angular momentum. Spin

**Syllabus**: Sum of Angular Momenta. Variational and WKV Methods. Borh- Sommerfeld Quantization. Time Independent Perturbation Theory. Stark Effect. Time Dependent Perturbation Theory. Transitions induced by the Electromagnetic Field. Spontaneous Transitions and Selection Rules. Stationary Limit. Born Approximation

**Syllabus**: Electrostatics: field, potential, charge distributions. Multipole Expansion. Electrostatic field differential equations in vacuum. Laplace and Poisson equations solutions. Conductors and dielectrics. Electrostatic field differential equations in matter. Energy. Current: conductivity models. Continuity equation, stationary currents. Magnetic field in vacuum. Vector potential. Magnetostatic fields in matter. Faraday Law. Maxwell equations. Quasi-static magnetic field: Alternate current. Magnetic Energy

**Syllabus**: Maxwell’s Equations. Electromagnetic wave equation. Reflection and refraction of plane waves. Conservation Laws and Poynting’s Theorem. Electromagnetic waves in Matter, absorption and dispersion. Dipole radiation. Radiation by Point Charges. Electrodynamics and relativity

**Syllabus**: Black Body Radiation. Photoelectric and Compton effects. Wave-particle duality. Wave Mechanics. The Bohr Atom. Schroedinger equation. This statistical Quantum. Gas Electron. Energy Bands of Solids. Metals, Insulators, Semiconductors. P-N junction. Semiconductor heterostructures. Magnetism of Solids

**Syllabus**: Drude and Sommerfeld theories for metals. Crystal Structure. Reciprocal lattice. X-Ray Diffraction. Bloch theorem. Models of nearly free electron and electron strongly connected. Semi-classical dynamics of electrons. Cohesive energy. Crystal vibrations. Phonons. Experimental semiconductor solid: optical absorption, X-rays, low temperature superconductivity measurement, measurement of specific heat

**Syllabus**: Properties of nuclei: charge distribution, radius, mass and angular momentum. Natural and artificial radioactivity. Nuclear models. Nuclear reactions. Hadrons and Leptons. Weak interaction. Neutrinos. Standard Model. Nuclear Astrophysics

**Syllabus**: Experimental Practices: Michelson Interferometer (visible and microwave); Radiation (Stefan-Boltzmann Law); Measurement of Planck’s constant; Photoelectric effect; Rutherford Backscattering; Deposition of thin films; piezoelectric effect, thermal conductivity, liquid crystal, diffraction, Fourier optics

**Syllabus**: Experiences of research laboratories of the Physics Department in the areas of spectroscopy, physical grain, nonlinear optics and nano-photonics

**Syllabus**: Ordinary Differential Equations. Solutions by Series. Frobenius method. Partial Differential Equations. Problems of Boundary Conditions. Special Functions. Sturm-Liouville Problem. Method of Green’s functions

**Syllabus**: Introduction to statistical methods. Systems of several particles. Statistical thermodynamics. Macroscopic parameters. Ideal gases. Ensembles. Boltzmann, Bose-Einstein and Fermi-Dirac statistics

**Production Engineering**

Such engineering area counts on a dynamic labor market due to its ample actuation horizon, in the industrial, financial and service areas. It constitutes a link between the technology and administration of the organizations when handling the conception, the project and the management of basic engineering knowledge, especially in the Mechanics, Civil and Chemistry fields to the knowledge applied to the oil exploration and production sector. Additionally it deepens their knowledge in specific topics such as the production organization, evaluation of costs and projects, basic notions of financial management, transport and logistics, among other aspects.

**Syllabuses:**

**Syllabus**: Basic concepts. Systemic approach. The construction of an administrative theory, focused on maximum productivity. Managerial roles. Quality management in USA and the Toyota model. Humanistic and behavioral approach. Stiles of administration. Sociotechnical approach and semiautonomous work groups. Participative management, results oriented management. Management in the third millennium

**Syllabus**: Part I: Traditional capital budgeting – The economic role of the company; Value and Money general concepts; Cost function; Opportunity cost of capital; Time value of money; Mathematical Finance; Capital budgeting criteria under certainty. Part II – Investment analysis under uncertainty: Investment decision under uncertainty; risk measurement; The maximum expected return criterion; The meaning of utility; The meaning of certainty equivalent; The expected utility criterion; The value of information; Risk adjusted discount rates; Modern capital budgeting methods. Parte III: Microeconomics – Price and Demand; Production function; Market equilibrium; Macroeconomics overview; The regulatory function of the government

**Syllabus**: Random experiments, sample spaces and events. Definition and axioms of probability. Conditional probability, Bayes Theorem and independence. Random variables: probability distribution and cumulative distribution functions. Expected value, mean and variance. Moments and moment-generating function. The most important probability distributions. Function of random variables. Joint probability distributions. Expected values and moments. Linear combinations of random variables. Conditional probability distribution and independence. Central Limit Theorem. The Normal approximations to the Binomial and Poisson distributions. Practical applications

**Syllabus**: Population and sample. Single-sample statistics and sampling distributions. Parameter estimation: Methods of Moments and of Maximum Likelihood. Properties of estimators. Confidence intervals. Tests of hypotheses. Bayesian inference. Linear models, correlation and regression. Analysis of variance. 2-level factorial experiments. Robust methods. Use of data analysis softwares

**Syllabus**: Linear programming: Definition, formulation and models. Basic theorems, Simplex Method, Duality, Sensibility Analysis. Interpretation of results. Case studies. Integer programming: formulation, Branch & Bound Method. Use of mathematical programming software

**Syllabus**: Introduction to Stochastic Process. Markov Chain. Transition Matrix. Classification. Long-run properties of a Markov Chain. Steady-State. Absorbing Chains. Birth-and-Death Processes. Introduction to Queuing Theory. Markovian Queuing models. Queuing networks. Applications of Queuing Theory. Principles of Simulation. Modeling, verification and validation design of experiments and analysis of results

**Syllabus**: Methodology of job analysis. Steps of a project. Observing and recording the data. Job description, analysis and evaluation. Time study. Indirect labor standards and standard time. Work sampling studies. Methods-time measurement. Identification of bottlenecks in flow process charts. Motion studies. Therbligs. Fundamentals of product design, ergonomics and anthropology

**Syllabus**: Basic concepts: the economic problem, market system and prices, supply and demand, circular flow of income. Theory of consumer. Theory of production: cost and production functions, the short and the long run market classification. The firm supply and its demand for production factors. Theory of general equilibrium. Savings, consumption and investment. Economic growth

**Syllabus**: Demand Forecasting: Patterns of demand; forecasting and planning; forecasting process; methods of forecasting for constant, linear and seasonal models; variance and forecast bias control. Planning Framework in Organizations. Aggregate Planning: importance; strategies and mathematical models. Master Production Scheduling. Dependent Demand and the Master Production Schedule. Material Requirements Planning (MRP). BOM. Functional Interfaces. Development of the Master Production Schedule. Inventory Records. Key Factors in MRP. MRP Outputs. Just-in-Time: characteristics; Kanban system; Just-in-Time for services. Materials Management System. Production Sequencing and Scheduling

**Syllabus**: Introduction to integrated logistics systems. Logistics Strategies. Inventory management. Transportation and distribution systems management. Information Systems for logistics. International logistic. Central point Problem. Random spatial distribution. Pick and delivery Distribution. Design of Warehouses and Depots. Distribution Strategies considering transportation and inventory costs. Facility Location. Vehicle Routing

**Syllabus**: Model classification and criterion selection. Information gathering and analysis about the product, the production process and the scheduling. Systematic layout planning (SLP). Basic types of layout. Flow analysis. Space requirements and availability. Materials handling. Quantitative approaches to layout evaluation

**Syllabus**: Product life-cycle. Project Management. Design methodology: Product requirements, data collection, analysis and synthesis; generating alternatives, selection and presentation of a conceptual project; detailing of the executive project, technical drawings and prototypes. Group Technology. Implementation of CAD systems. Industrial property and patentable product

**Syllabus**: History, origin, development and current trends. The relationship of ergonomics with the strategic vision of business and competitiveness of the organization. The system model and ergonomic action. Development projects and the analysis method Ergonomic Work – AET. Man-machine system and anthropometry – definitions, objective, anthropometric variables, principles to use anthropometric data, applied statistics. Regulatory norm – NR17. Study and analysis of posture. Observable variables and observation methods. Ergonomics and the concept of a work accident. Cognitive Ergonomics. Technological factors and ergonomic diagnosis. Organizational ergonomics. The concept of accessibility within the ergonomic action. Reviews and limits of ergonomic intervention. Social and Environmental Responsibility, the mission of the Industrial Engineer and Ergonomics

**Syllabus**: Scientific, industrial and legal metrology. Primary, secondary and industrial standards. Metrological traceability and cross-check. Calibration services. Technical standards. Written standards as genetic code of industries. Sectoral, regional, national and international standards. Specification, test methods, terminology, symbology. Industrial quality. Quality certification. Conformity mark. Conformity for exports and imports. Technological innovation. Innovation loop. Social constructivism. Radical and incremental innovation. Patent and trade mark legislation and national offices. Intellectual property

**Syllabus**: Financial mathematics and the time value of money. Methods for projects selection. Economic rationality of discount cash-flow methods. Independent and mutually exclusive projects. Capital rationing. Equipment substitution. Inflation influence. Financial leasing. Risk and uncertainty: notions of the cost and structure of capital, capital asset pricing models, portfolio theory, valuation of intangibles and flexibilities of investment projects

**Syllabus**: Introduction to Accounting. Accounting records. Analysis of financial statements, ratios and tests. Flows of funds. Basis of cost accounting, appropriation and cost control. Business planning and budgeting. Emphasis on the managerial use of accounting

**Syllabus**: Manufacturing & Service Operations Management. Productivity and Competitiveness. Connection between Operations Management and other areas. Strategic Choices. Market Analysis. Competitive Priorities and Operations Management. Product Lifecycle. Positioning Strategy. Manufacturing Strategy. Choice of Production Processes. Vertical Integration, Flexibility, scale economy and Capital Intensity. Technology and Strategy

**Syllabus**: Introduction: What makes decisions difficult; types of decision problems; decision making under uncertainty and under risk; conflicting criteria; scale of the problem. Modeling decisions: elements of decision problems, structuring decisions; choice process; sensitivity analysis, creativity and structuring of decisions. Modeling uncertainty: subjective probability; probabilistic models for decision making; use of data; Monte Carlo method; value of information. Modeling preferences: attitudes towards risk; axioms of utility, resulting paradoxes and other implications; multiple and conflicting objectives: basic techniques; utility models for multiple attributes

**Syllabus**: Statistical basics of the control chart. Control Charts for Attributes. Control Charts for Variables: control charts for process mean and control charts for process variability. Special methods for process control: Cumulative-Sum control chart (CUSUM) and Exponentially Weighted Moving Average control chart (EWMA). Acceptance sampling: single-sampling plans for attributes

**Syllabus**: Marketing function in the managerial process and its interrelations with other areas. Consumer behavior. Market structure, product planning, pricing, promotion, channels, distribution. Marketing study, research and survey

**Syllabus**: Classification and types of Information Systems. Systems development, database Project, Entity-Relationship Model. Relational Model and Normalization. Computer-aided software engineering. Database management systems. Application to case studies

**Syllabus**: The organizational context of the XXI century and the main challenges for effective management. Relevant issues for discussion: sustainability, knowledge and innovation, some concepts on strategic planning and a few tools. Results oriented strategic management

**Syllabus**: Introduction: concepts of occupational safety and healthy. Accidents and illnesses: legal definitions, Brazilian and world situation. Occupational safety: protection against fire, explosion, electric shock, safety signs, individual and collective protective equipment. Healthy: physical, chemical and biological risks. CIPA’s Organization and SESMT’s. Brazilian law enforcement, worker participation in risk control. Project in a real situation

**Syllabus**: Decision making and the organizational context of planning and control of production (PCP). Fundamentals of economic analysis of decision making. Aggregate production planning and master production scheduling. Material requirements planning and capacity – (MRP II). Analysis and inventory control under independent demand. The economic lot sizing production problem – (ELSP). Lot sizing of purchase under dynamic demand over time horizon. Production sequencing

**Syllabus**: Definitions and basic concepts. Problems and challenges in projects. The Project Management Institute (PMI) and the Project Management Body of Knowledge (PMBOK). Planning: technical and managerial aspects. Typical project structures. Scope, time and quality. Planning tools (WBS, GANTT, PERT/CPM, PDM, S-Curve). Conflict management. The role of a project manager leader

**Syllabus**: Evolution of quality control, concept of control, and means of control. Quality assurance: concepts, criteria, operational procedures, prototype, conformity to standards, experiments and role of the inspector. Quality Management: concepts, japanese system. Total Quality Management. The 10 commandments of quality and quality certification. ISO 9000 series: concepts, elements, quality manuals and general procedure. Auditing: basic concepts, types, the auditor profile and the steps of auditing. Brazilian Certification System. Mandatory certification

**Syllabus**: Importance of services in the economy. Service operations. Strategic importance. Consumer behavior. Operations strategy. Design of service systems. Service systems planning, scheduling and control. Service quality and improvement. Customer relations. Performance and quality metrics

**Syllabus**: Accounting Statements Performance. Short-Term Finance and Planning. Credit Management. Cash Management. International Corporate Finance

**Syllabus**: Risk Analysis in Finance. Future and Forward Markets. Hedge Strategies with Futures. Interest Rate Futures. Exchange Rate Futures. Swaps. Duration. Fixed Income Bonds and Volatilities

**Syllabus**: Derivatives markets. Basic properties of options. Strategy of negotiations. Binomial Trees. Black and Scholes model. Options on currency, indexes and futures. Implied volatility. Greeks. Exotic options

**Syllabus**: Logistics historical evolution. Logistics basic concepts. Logistics in the organizational structure. Logistics strategies planning. Logistics quality and service level. Supply Chain. Transports role in logistics. Warehouses role in logistics. Logistics information system

**Syllabus**: Physical distribution systems. Distribution channels and the customer service. Information and control systems. Location. Distribution centers location. Division of regions in zones. The traveling salesman problem. Vehicles routing

**Syllabus**: Regional Blocks; International Trade Dynamics; International Marketing; International Certificates; Quality Systems; International Trade Logistics

**Syllabus**: Procurement Function. Supply Chain and Procurement. Transaction-Cost Economics. Governance Structures. Resource-Base View. Outsourcing. Strategic Sourcing. Purchasing Portfolio. Supply Strategies. Global Sourcing. Supplier Selection. Purchasing Negotiations. Supplier Development. Supplier Performance Evaluation. e-Marketplace. e-Procurement