The Master's program is designed to be completed within up to 02 years (24 months). According to the current regulations, among the requirements for obtaining the degree is the completion of courses, both required and elective, totaling 24 credits.

Of these, 09 credits are from required courses (Algorithms and Programs, Interdisciplinary Activities, Computational Linear Algebra). We suggest that 02 of them be taken in semester 1 and the other one in semester 2.

Another 09 credits are from elective courses, which may also be taken in other graduate programs (PPGs) at any educational institution. We suggest that 01 of them be taken in semester 1 and the others in semester 2.

In the third semester, if the student has already completed all credits, they must enroll in the Dissertation Project course, only so as not to lose their ties to the program. A section of this course is offered every semester, under the responsibility of the Coordinator.

Finally, in the fourth and last semester, the student must enroll in the required course Dissertation Writing, specifically in the section under the responsibility of their advisor. Every semester, one section of this course is offered by each of the advisors.

Students awarded a scholarship must take the Undergraduate Teaching Internship course, which is worth 02 credits. These may be counted toward the total of 18 credits.

Most courses have 03 credits, but there are also courses with 02 and 04 credits. In these cases, the schedule must be adjusted.

The elective courses offered each semester vary.

The PhD program is designed to be completed within up to 04 years (48 months). According to the current regulations, among the requirements for obtaining the degree is the completion of required and elective courses, totaling 48 credits.

For students who completed their Master's in this PPG, 18 credits can be recognized. Of the remaining 30, 03 correspond to the required courses Seminars I, Seminars II and Seminars III, and 12 correspond to the required course Thesis Writing. Enrollment in the latter course should take place only in the semester in which the thesis defense is expected.

Elective courses may be taken in other PPGs at any educational institution, as long as the maximum limit is respected, and it is also possible to earn credits through publications in journals. See Normative Instruction NI 02/2023 - RULES FOR THE RECOGNITION OF CREDITS. We suggest that all courses be taken by the second semester.

The sequence of Seminars courses (I, II and III) should begin in the second semester and be completed in the fourth semester. However, since they follow the development of the project, and it is expected that certain stages of its progress will be completed with each course, this may be changed at the advisor's direction. If it is convenient to postpone taking them and the student has already completed the credits, they may enroll in one of the Thesis Project courses.

In the fifth, sixth and seventh semesters, all credits are expected to have been completed, with enrollment in a Thesis Project section. These courses exist so that the student does not lose their ties to the program. Every semester, sections of Thesis Project 1, Thesis Project 2, Thesis Project 3, Thesis Project 4, Thesis Project 5 and Thesis Project 6 are offered, under the responsibility of the Coordinator.

Finally, in the eighth and last semester, the student must enroll in the required course Thesis Writing, specifically in the section under the responsibility of their advisor. Every semester, one section of this course is offered by each of the advisors.

Students awarded a scholarship must take the courses Teaching Internship I and Teaching Internship II, which are worth 02 credits each. These may be counted toward the total credits. Students without a scholarship may also take them.

Most courses have 03 credits, but there are also courses with 02 and 04 credits. In these cases, the schedule must be adjusted. The elective courses offered each semester vary.

If the student comes from a Master's completed in another PPG, they must take the courses Algorithms and Programs, Interdisciplinary Activities and Computational Linear Algebra, and the recognition of Master's credits must be analyzed individually.

Code: 01205P
Required: Yes
Workload (hours): 45
Credits: 3

Course topics: Solving systems of linear algebraic equations: Gaussian elimination. LU decomposition. Cholesky decomposition. Triangular systems. Banded systems. Block tridiagonal systems. Sparse systems; Orthogonalization of systems of equations: Householder and Gram-Schmidt methods; Eigenvalue problem: properties and decomposition. QR algorithm.

Core Bibliography:

GOLUB, G.H.; VAN LOAN, C.F. Matrix Computations. 4th ed. Baltimore: Johns Hopkins University Press, 2013.

STRANG, G. Linear Algebra and its Applications. 4th ed. Canada: Brooks/Cole, 2006.

MEYER, C.D. Matrix Analysis and Applied Linear Algebra. 2nd ed. Philadelphia: SIAM, 2023.

Supplementary Bibliography:
Gene H. Golub, Charles F. Van Loan, Matrix Computations, 4th Edition, SIAM, 2013
Carl D. Meyer Matrix Analysis and Applied Linear Algebra, Second Edition, SIAM, 2023
STRANG, G. Linear algebra and its applications, 4th edition, Brooks/Cole, 2006.
Anton, H. and Busby, R. C. Contemporary Linear Algebra, Wiley, 2002.
J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
CALDER, J., and OLVER, P. J. Linear Algebra, Data Science, and Machine Learning, Springer, 2025

Code: 03043P
Required: Yes
Workload (hours): 45
Credits: 3

Course topics: Algorithm construction; data structures. Algorithm complexity. Programming with C/C++ and FORTRAN.

Core Bibliography:

GUIMARAES, A.M., LAGES, N.A.C.L., Algoritmos e estruturas de dados, Rio de Janeiro : LTC, 1985.
BHARGAVA, A. Entendendo Algoritmos, 2017.
MANZANO, José Augusto N. G., de OLIVEIRA, Jayr Figueiredo. Algoritmos - Lógica para Desenvolvimento de Programação Imperativa de Computadores. 2025.

Supplementary Bibliography:
CORMEN, Thomas H.; LEISERSON, Charles E.; RIVEST, Ronald L.; STEIN, Clifford. Introduction to Algorithms. 4th ed. Cambridge: MIT Press, 2022.
BACKES, André Ricardo. Algoritmos e estruturas de dados em linguagem C. 1. ed. Rio de Janeiro: LTC, 2023.
MATTHES, Eric. Curso Intensivo de Python: uma introdução prática e baseada em projetos à programação. 3. ed. São Paulo: Novatec Editora, 2023.
WIGGINS, Chris; JONES, Matthew. Como os dados aconteceram: da era da razão à era dos algoritmos. 1. ed. Rio de Janeiro: Alta Books, 2025. ISBN 9788521638315.
CAETANO, Marco Antonio Leonel. Pandas e o demônio dos dados: algoritmos em python para sistemas de informação. 1. ed. São Paulo: Blucher, 2025. ISBN 9788521225140.

Code: 23033P
Required: Yes
Workload (hours): 45
Credits: 3

Course topics: Development by students, under the guidance of a multidisciplinary faculty committee, of academic projects with interdisciplinary solutions, including small and medium-sized applications, in principle in teams. Projects must have requirements defined within criteria of academic and chronological feasibility. The themes will be associated with the research lines currently existing in the Program, involving the faculty, aiming to level perceptions and to integrate knowledge and methodologies from an interdisciplinary perspective. Prescription of content remediation for any coverage gaps in topics identified as essential.

Core Bibliography:

NETO, A.J.S., Interdisciplinaridade em ciência, tecnologia & inovação / Editores Arlindo Philippi Jr. São Paulo : Manole, 2011.
BROWN, T., Design thinking : uma metodologia poderosa para decretar o fim das velhas ideias, Rio de Janeiro : Elsevier, 2010.

Supplementary Bibliography:
PROJECT MANAGEMENT INSTITUTE. A guide to the Project Management Body of Knowledge — PMBOK® Guide: eighth edition and The Standard for Project Management. Newtown Square: Project Management Institute, 2025. ISBN 9781628258295.
REPKO, Allen F.; SZOSTAK, Rick. Interdisciplinary research: process and theory. 5. ed. Thousand Oaks: SAGE Publications, 2025. ISBN 9781071884256.
BOOTH, Wayne C.; COLOMB, Gregory G.; WILLIAMS, Joseph M.; BIZUP, Joseph; FITZGERALD, William T. The craft of research. 5. ed. Chicago: University of Chicago Press, 2024. ISBN 9780226826677.
BUCKINGHAM, Louisa; DONG, Jihua; JIANG, Feng Kevin (org.). Interdisciplinary practices in academia: writing, teaching and assessment. Abingdon: Routledge, 2023. ISBN 9781032202938.
PHILIPPI JR, Arlindo; FERNANDES, Valdir (Orgs.). Práticas da Interdisciplinaridade no Ensino e Pesquisa. Barueri: Manole, 2020.ISBN: 978-8520438930

Code: 21011P
Required: Yes (Master's only)
Workload (hours): 90
Credits: 6

Course topics: Writing of the Master's dissertation.

Code: 04156P
Required: Yes (PhD only)
Workload (hours): 180
Credits: 12

Course topics: Writing of the doctoral thesis.

Code: 04167P
Required: Yes (PhD only)
Workload (hours): 15
Credits: 1

Course topics: Monitoring of the progress of doctoral theses throughout the entire course period.

Code: 04168P
Required: Yes (PhD only)
Workload (hours): 15
Credits: 1

Course topics: Monitoring of the progress of doctoral theses throughout the entire course period.

Code: 04169P
Required: Yes (PhD only)
Workload (hours): 15
Credits: 1

Course topics: Monitoring of the progress of doctoral theses throughout the entire course period.

Code: 01237P
Required: No
Workload (hours): 60 hours
Credits: 4

Course topics: General properties of galaxies; Galaxies: structure and kinematics; Morphological classification; Hubble's law; Galactic content: gas, dust and stars; Stellar populations; Galactic nuclear activity; Supermassive black holes and accretion disks; Spatial distribution of galaxies; Galaxy clusters: structure, dynamics, galactic and gaseous content; Morphology-density relation: galaxy interactions and tidal effects; Galaxy luminosity function; Formation and evolution of galaxies and clusters; Cosmic microwave background radiation.

Core Bibliography:

- P. Schneider, Extragalactic Astronomy and Cosmology - An Introduction, 1a Edição, Editora Springer-Verlag, Berlim, 2006.
- SPARKE, L. S. & GALLAGHER III, J. S., Galaxies in The Universe: An Introduction, Cambridge University Press, 2nd edition, 2007.
- COMBES, F. et al. Galaxies and Cosmology, Springer, 2nd edition, 2010.
- BINNEY, J. e TREMAINE, S., Galatic Dynamics, Princeton Series in Astrophysics, 2nd Edition, 2008
- BINNEY, J., MERRFIELD, M., Galactic Astronomy, Princeton University Press, 1998
- OSTERBROCK, D. E. & FERLAND, G. J. Ferland, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei, University Science Books, 2nd edition

Supplementary Bibliography:

Code: 23048P
Required: No
Workload (hours): 45 hours
Credits: 3

Course topics: Fuzzy sets: definition and basic concepts of fuzzy sets; membership functions; operations; extension principle; fuzzy numbers; fuzzy relations; basic connectives of fuzzy logic; approximate reasoning; linguistic variables; fuzzy rule-based systems; fuzzy inference methods; defuzzification methods. Interval mathematics: basic definitions; operations; properties; function evaluation. Interval fuzzy sets: definition and basic concepts of interval fuzzy sets; membership functions; operations; extension principle; interval fuzzy numbers.

Core Bibliography:

Barros, Laécio Carvalho de.. Tópicos de lógica fuzzy e biomatemática / Laécio Carvalho de Barros, Rodney Carlos Bassanezi. - Campinas: Unicamp, 2010.
Klir, George J.. Fuzzy sets and Fuzzy logic : theory and applications / George J. Klir, Bo Yuan. - New Jersey : Prentice Hall, c1995.
Ross, Timothy J.. Fuzzy Logic with Engineering Applications / Timothy J. Ross. - São Paulo, SP : Érica, 2011.
Harris, J.. Fuzzy Logic applications in engineering science / J. Harris. - Netherlands : Springer, c2006.
Fundamentals of fuzzy sets / editado por Didier Dubois, Henri Prade ; prefácio de Lotfi A. Zadeh. - Boston : Kluwer Academic Publishers, 2000.
Buckley, James J.. An introduction to fuzzy logic and fuzzy sets / James J. Buckley, Esfandiar Eslami. - Heidelberg; New York : Physica-Verlag, 2002.

Supplementary Bibliography:

JAFELÍCE, Rosana Sueli da Motta; BARROS, Laécio Carvalho de; BASSANEZI, Rodney Carlos. Teoria dos Conjuntos Fuzzy com Aplicações. São Carlos: SBMAC, 2023. (Série: Notas em Matemática Aplicada, v. 43). ISBN: 978-65-86388-13-8.
KREINOVICH, Vladik; SERVIN, Christian. Decision Making Under Uncertainty: Interval and Fuzzy Techniques. Cham: Springer, 2023.
BARROS, Laécio Carvalho de; BASSANEZI, Rodney Carlos; LODWICK, Weldon Alexander. A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics: Theory and Applications. 2. ed. Cham: Springer, 2024. (Series: Studies in Fuzziness and Soft Computing). ISBN: 978-3-031-50491-4.
ROSS, Timothy J. Fuzzy Logic with Engineering Applications. 4. ed. Hoboken: John Wiley & Sons, 2016 (Reimpressões ativas). ISBN: 978-1-119-23586-6.
SIDDIQUE, Nazmul; ADELI, Hojjat. Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks and Evolutionary Computing. 2nd ed. Chichester: John Wiley & Sons, 2023.

Code: 01206P
Required: No
Workload (hours): 30
Credits: 2

Course topics: Definition and classification of ODEs. Initial value problems. Well-posedness results. Linear differential equations. Classical solutions. Sturm-Liouville problems. Spectral analysis. Qualitative theory. Phase space. Nonlinear equations, well-posedness, singularities, stability, bifurcation.

Core Bibliography:

Monteiro, Luiz Henrique Alves.. Sistemas dinâmicos / Luiz Henrique Alves Monteiro. - São Paulo : Livraria da fisica, 2002.
Boyce, William E.. Equações diferenciais elementares e problemas de valores de contorno / William E. Boyce, Richard C. DiPrima ; traduzido por Horácio Macedo. - Rio de Janeiro : LTC, 1994.
Boas, Mary L.. Mathematical methods in the physical sciences / Mary L. Boas. - New York : J. Wiley, c2006.
Machado, Kleber Daum. Equacoes diferenciais aplicadas a fisica / Kleber Daum Machado. - Ponta Grossa : Ed. da UEPG, 1999.
Zill, Dennis G.. Equações diferenciais com aplicações em modelagem / Dennis G. Zill ; tradução Heitor Honda Frederico. - São Paulo : Cengage Learning, c2011.
Kreyszig, Erwin.. Advanced engineering mathematics / Erwin Kreyszig. - New York : John-Wiley, c1962.

Supplementary Bibliography:
Strogatz, S.H., Nonlinear Dynamics and Chaos, Addison-Wesley, 1994.
Grimshaw, R., Nonlinear Ordinary Differential Equations, Oxford: Blackwell Scientific Publicatiosns, 1990.
Hirsch, M.W., Smale, S., Devaney, R.L., Differential Equations, Dynamical Systems and an Introduction to Chaos, Academic Press, 3rd. Edition, 2012.
Allen, L.J.S., An Introduction to Mathematical Biology, Prentice Hall, 1st. Edition, 2006.
Beltrami, E., Mathematics for Dynamic Modeling, Academic Press Inc., 1987.

Code: 01207P
Required: No
Workload (hours): 30
Credits: 2

Course topics: First-order PDEs: wave, diffusion, Laplace, Poisson and Schrödinger equations. General form of the solution. Characteristics and existence of solutions. Separation of variables method. Integral transform methods. Green's functions. Dirichlet and Neumann problems.

Core Bibliography:

Mathematical methods for physics and engineering : a comprehensive guide / K. F. Riley, M. P. Hobson and S. J. Bence. - Cambridge : cambridge University, c1997.
Machado, Kleber Daum. Equacoes diferenciais aplicadas a fisica / Kleber Daum Machado. - Ponta Grossa : Ed. da UEPG, 1999.
Zill, Dennis G.. Equações diferenciais com aplicações em modelagem / Dennis G. Zill ; tradução Heitor Honda Frederico. - São Paulo : Cengage Learning, c2011.
Kreyszig, Erwin.. Advanced engineering mathematics / Erwin Kreyszig ; in collaboration with Herbert Kreyszig, Edward J. Norminton. - Hoboken, NJ : John Wiley & Sons, 2011.
Boas, Mary L.. Mathematical methods in the physical sciences / Mary L. Boas. - New York : J. Wiley, c2006.

Supplementary Bibliography:
EVANS, L. C. Partial Differential Equations, 2nd edition, AMS, 2022.
Iório, V. M e Iório, R. Equações diferenciais Parciais: Uma Introdução. IMPA, 2018.
Logan, J. D, Applied Partial Differential Equations, 3th edition, Springer, 2020.
Figueiredo, D.G. Análise de Fourier e Equações Diferenciais Parciais, 5 ed, IMPA, 2018.
Zill, D. G.. Equações diferenciais com aplicações em modelagem, Cengage Learning, 2011.

Code: 04154P
Required: Yes (only for PhD students with a CAPES DS scholarship - optional for other PhD students)
Workload (hours): 30
Credits: 2

Course topics: Various activities involving undergraduate teaching in areas (courses) related to the research lines of PPGMC.

Code: 04165P
Required: Yes (only for PhD students with a CAPES DS scholarship - optional for other PhD students)
Workload (hours): 30
Credits: 2

Course topics: Teaching activities in undergraduate courses.

Code: 21010P
Required: Yes (only for Master's students with a CAPES DS scholarship - optional for other Master's students)
Workload (hours): 30
Credits: 2

Course topics: Program aimed at improving the student's graduate training, with a view to strengthening their pedagogical skills, preparing them for teaching activities and promoting integration between graduate and undergraduate education.

Code: 23043P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Types of sensors. Representation of uncertainty. Feature extraction. Modeling, recognition and interpretation of information. Mapping and localization.

Core Bibliography:

Supplementary Bibliography:

Code: 01052P
Required: No
Workload (hours): 30
Credits: 2

Course topics: Inference based on sampling design (classical) and model-based inference (likelihood theory). Estimation methods: moments, least squares, and maximum likelihood. Sampling distribution: concept and applications using simulations. Properties of estimators: bias, precision, accuracy and consistency. Properties of maximum likelihood estimators. Fisher information. Confidence intervals for maximum likelihood estimators: normal approximation and profile likelihood method. Confidence intervals by simulation: parametric and non-parametric bootstrap. Hypothesis tests: general procedure and applications. Type I and type II errors. Power of a test. Likelihood ratio test. Estimation by the least squares method. Tests of regression and correlation coefficients (parametric and non-parametric). Statistical quality control for variables.

Core Bibliography:

BUSSAB, W.O.; MORETTIN, P.A. (2002) Estatística Básica (5 a. Edição). Editora Saraiva.
HOEL, P.G. (1980) Estatística Matemática (4 a.Ed.) Editora Guanabara.
MOOD, A .M.; GRAYABILL, F., BOES, D.C. (1974) Introduction to the theory of statistics. McGraw-Hill
NOLAN, D.; SPEED, T. (2000) Stat Lab: Mathematical Statistics Through Applications. Springer Verlag.
SIEGEL, S. (1975) Estatística Não-Paramétrica. McGraw-Hill.
SOONG, T.T. (1986) Modelos probabilísticos em Engenharia e Ciências. LTC Editora S.A.
SOUZA, G.S. (1998) Introdução aos Modelos de Regressão Linear e Não-linear. EMBRAPA. 489p.
VENABLES, W.N.; SMITH, D.M. (2001) An Introduction to R.
ZAR (1984) Biostatistical analysis (2nd Ed.) - Prentice-Hall.

Supplementary Bibliography:

Code: 23100P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Trends, challenges, scope and opportunities in Intelligent Robotics. Introduction to Mobile and Manipulator Robotics and their scientific problems. Introduction to Robotic Perception and Robotic Vision. Introduction to Robotic Architectures: Reactive, Deliberative and Hybrid.

Core Bibliography:

Supplementary Bibliography:

Code: 04153P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Introduction to Computational Wave Mechanics; Wave climate; Ocean wave theories and theoretical aspects; Numerical simulation techniques for ocean waves in tanks; Post-processing techniques in numerical simulation of ocean waves; Numerical simulation of ocean waves; Numerical simulation of converters of ocean wave energy into electrical energy.

Core Bibliography:

Supplementary Bibliography:

DEAN, R. G.; DALRYMPLE, R. A. Water Wave Mechanics for Engineers and Scientists. Singapore: World Scientific, 1991. (Advanced Series on Ocean Engineering, v. 2).
HOLTHUIJSEN, L. H. Waves in Oceanic and Coastal Waters. Cambridge: Cambridge University Press, 2007.
MALISKA, C. R. Fundamentals of Computational Fluid Dynamics: The Finite Volume Method. Cham: Springer, 2023. (Fluid Mechanics and Its Applications, v. 135).
LIN, P. Numerical Modeling of Water Waves. Boca Raton: CRC Press, 2008.
FOLLEY, M. (ed.). Numerical Modelling of Wave Energy Converters: State-of-the-Art Techniques for Single Devices and Arrays. London: Academic Press, 2016.
FALNES, J.; KURNIAWAN, A. Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction. 2. ed. Cambridge: Cambridge University Press, 2020.

Code: 04155P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Fundamental thermophysical concepts and properties. Conservation equations of mass, momentum and energy for control volume and differential forms. Dimensional analysis. Internal flows. External flows.

Core Bibliography:

Supplementary Bibliography:

ÇENGEL, Y. A.; CIMBALA, J. M. Fluid mechanics: fundamentals and applications. Fourth edition ed. New York, NY: McGraw-Hill Education, 2017.
MUNSON, B. R. (ED.). Fundamentals of fluid mechanics. 6. ed ed. Hoboken, NJ: Wiley, 2009.
MITCHELL, J. W.; FOX, R. W.; MCDONALD, A. T. Fox and McDonald’s introduction to fluid mechanics. 10th edition, EMEA edition ed. Hoboken: Wiley, 2020.
WHITE, F. M.; XUE, H. Fluid mechanics. Ninth edition ed. New York, NY: McGraw-Hill, 2021.

Code: 04151P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Types of structures. Stresses: concept, equilibrium equations, stress transformation. Strains: strain components, strain-displacement relations, strain transformation. Mechanical properties of materials: elasticity, plasticity and failure theories. Normal force: stresses, strains and displacements. Torsion: stresses, strains and displacements in bars with circular and non-circular cross sections. Bending: stresses, strains, differential equation of the elastic line and its integration. Shear: elementary shear theory, thin-walled profiles, shear flow, shear center. Buckling of bars: axial and eccentric load. Thin plate theory: differential equation, Navier and Levy solutions. Plate buckling: fundamental equations, available analytical solutions. Post-buckling behavior of plates. Computational modeling applied to Solid Mechanics.

Core Bibliography:

Supplementary Bibliography:

BEER, F. P.; JOHNSTON, E. R.; DEWOLF, J. T.; MAZUREK, D. F. Mechanics of Materials. 8th ed. McGraw-Hill Education, 2020.
HIBBELER, R. C. Mechanics of Materials. 11th ed. Pearson, 2022.
JERATH, S. Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shells. John Wiley & Sons, 2021.
MADENCI, E.; GUVEN, I. The Finite Element Method and Applications in Engineering Using ANSYS. 2nd ed. Springer, 2015.
MOAVENI, S. Finite Element Analysis: Theory and Application with ANSYS. 5th ed. Pearson, 2020.
SADD, M. H. Elasticity: Theory, Applications, and Numerics. 5th ed. Elsevier, 2025.
SZILARD, R. Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods. John Wiley & Sons, 2004.

Code: 03046P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Numerical interpolation, approximation and differentiation of functions. Roots of algebraic and transcendental equations. Numerical computation of special functions (Bessel, elliptic integral functions). Systems of linear and nonlinear equations. Curve fitting. Numerical integration. Solutions of ordinary and partial differential equations. Simulation of dynamical systems. Eigenvalue and eigenvector problems. Fourier transforms: DFT and FFT.

Core Bibliography:

Supplementary Bibliography:

Iserles, A. A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press, 1996.
Uri Ascher and Chen Greif, A First Course in Numerical Methods, SIAM, 2011.
Uri Ascher, Numerical Methods for Evolutionary Differential Equations, SIAM, 2008.
Uri Ascher and Linda Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998.
Golub, G. H. and Ortega, J. M., Scientific Computing and Differential Equations: an Introduction to Numerical Methods. Academic Press, 1992.

Code: 01076P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Newtonian modeling formalism, Euler-Lagrange formalism, dynamic modeling of systems, examples, dynamic modeling of rigid manipulator robots, dynamic modeling of manipulator robots with flexible links, direct and inverse kinematic models, development of kinematic models of manipulator robots, kinematics of rigid bodies in spatial motion, kinematic models of mobile robots, dynamic models of mobile robots, applications to underwater robotics.

Core Bibliography:

FOSSEN, T. I., 1994. Guidance and Control of Ocean Vehicles. Chichester: John Wiley & Sons.
SPONG, M. W. and Vidyasagar, M., 1989. Robot dynamic and control. John Wiley and Sons.
MEIROVITCH, M., 1970. Methods of analytical dynamics. McGraw-Hill.
CRAIG, J. J., 1986. Introduction to robotics, mechanics and control. Addison Wesley.
FRANKLIN, G. F. and Powell, J. D., 1995. Feedback control of dynamic systems. 3ed, New York, Addison-Wesley.

Supplementary Bibliography:

Code: 03048P
Required: No (Master's only)
Workload (hours): 0
Credits: 0

Course topics: In this course, the student will develop the preparation of the defense and the execution of the dissertation project.

Core Bibliography:

Supplementary Bibliography:

Code: 04157P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 04158P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 04159P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 04160P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 04161P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 04162P
Required: No (PhD only)
Workload (hours): 0
Credits: 0

Course topics: Specific work related to the preparation of the doctoral thesis.

Code: 01209P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Introduction to thermal systems and optimization, Modeling of equipment and systems, Energy and exergy analysis, Computational tools.

Core Bibliography:

Supplementary Bibliography:

Code: 23003P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Simulation. Models. Social simulation. Dynamical systems. Micro and macro simulation. Agent-based simulation environments. Applications using cellular automata and multi-agent systems techniques.

Core Bibliography:

Supplementary Bibliography:

Christopher M Langan. The Reality Self-Simulation Principle: Reality is a Self-Simulation, 2022.
Hannah Rush. Social Sim Resource Guide: Mimic Social Simulation / Social Media Simulation, 2023.
Belinda Bradbury. Social Simulation: Computer Simulation of Societies, 2019.
Dylan Allman. The Simulation Holds: On Reality, the Self, and the Fictions That Run Us, 2026.

Code: 01137P
Required: No
Workload (hours): 60
Credits: 4

Course topics: Fundamental concepts for forecasting. Stochastic processes and time series. Graphical analysis of time series. Accuracy of a forecasting model. Simple forecasting methods. Regression models for time series. Time series decomposition. Exponential smoothing models. Box-Jenkins models.

Core Bibliography:

Supplementary Bibliography:

Code: 21108P
Required: No
Workload (hours): 15
Credits: 1

Course topics: Lectures by various professors.

Code: 03049P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Natural form, questions and theory; Mechanical structures; Thermal structures; Conductive trees; Trees in fluids; Rivers and ducts; Convective trees; Structures in power systems; Structures in time: rhythm; Structures in economics and transportation; Shapes with constant resistance.

Core Bibliography:

BEJAN, A (2000) Shape and Structure, from Engineering to Nature, Cambridge University Press.
BEJAN, A. (2003) Convection Heat Transfer, 2nd edition, Wiley.
BEJAN, A. (1999) Advanced Engineering Thermodynamic, 2nd edition, Wiley.
TSATSARONIS, G.; MORAN, M.; BEJAN A. (1996) Thermal Design and Optimization, Wiley.

Supplementary Bibliography:
A. Bejan, J.P. Zane, Design in nature: how the constructal law governs evolution in biology, physics, technology, and social organizations, Anchor 1 (2013) 1–296.
A. Bejan, Freedom and Evolution, Springer International Publishing, Cham, 2020, https://doi.org/10.1007/978-3-030-34009-4.
A. Bejan, S. Lorente, Design with Constructal Theory, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2008, https://doi.org/10.1002/9780470432709
E.D. dos Santos, L.A. Isoldi; M. N. Gomes ; L.A.O. Rocha. The Constructal Design Applied to Renewable Energy Systems. In: Eduardo Rincón-Mejía; Alejandro de las Heras. (Org.). (Org.). Sustainable Energy Technologies. 1ed.Boca Raton: CRC Press - Taylor & Francis Group, 2017, v. 1, p. 63-87.
L.A.O. Rocha, S. Lorente, A. Bejan. Constructal Theory in Heat Transfer. Handbook of Thermal Science and Engineering. 1a.ed.: Springer International Publishing, 2017, v. , p. 1-32.
G.D. Telli, C. Biserni, C. Naldi, L.A. Isoldi, E.D. dos Santos, L.A.O. Rocha. Evolution of the constructal design application on fins and cavities as a passive element for heat transfer problems. International Communications in Heat and Mass Transfer 178 (2026) 111933. https://doi.org/10.1016/j.icheatmasstransfer.2026.111933

Code: 03050P
Required: No
Workload (hours): 60
Credits: 4

Course topics: Special topics in modeling applied to Computing. The course will address topics specific to each advisor.

Core Bibliography:

Supplementary Bibliography:

Code: 01208P
Required: No
Workload (hours): 60
Credits: 4

Course topics: Special topics in computational modeling applied to the description of physical systems. The course will address specific topics in each edition.

Core Bibliography:

Supplementary Bibliography:

Code: 04166P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Special topics in computational modeling applied to thermofluid systems. The course will address topics specific to each advisor.

Core Bibliography:

Supplementary Bibliography:

Code: 03052P
Required: No
Workload (hours): 60
Credits: 4

Course topics: Special topics in computational modeling applied to thermofluid systems. The course will address topics specific to each advisor.

Core Bibliography:

Supplementary Bibliography:

Code: 03053P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Introduction; Conservation equations; Obtaining the approximate conservation equations; Interpolation functions; Solution of diffusion problems; Solution of convection problems.

Core Bibliography:

Supplementary Bibliography:

MALISKA, C. R. Fundamentals of Computational Fluid Dynamics: The Finite Volume Method. 1st ed. 2023 ed. Cham: Springer International Publishing, 2023.
VERSTEEG, H.; MALALASEKRA, M. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2. ed. [s.l.] Prentice Hall, 2007.
GREENSHIELDS, C. J.; WELLER, H. G. Notes on computational fluid dynamics: general principles. Reading, UK: CFD Direct Limited, 2022.
ÇENGEL, Y. A.; CIMBALA, J. M. Fluid mechanics: fundamentals and applications. Fourth edition ed. New York, NY: McGraw-Hill Education, 2017.
PATANKAR, S. Numerical Heat Transfer and Fluid Flow. [s.l.] Taylor & Francis, 1980.

Code: 04152P
Required: No
Workload (hours): 45
Credits: 3

Course topics: Fundamental principles of heat transfer; fundamental principles of heat convection; laminar boundary layer; laminar convection inside ducts; laminar convection over bodies; internal natural convection; transition to turbulent regime; turbulent flow in ducts; free turbulent flow.

Core Bibliography:

BEJAN, Convection Heat Transfer, Wyley Interscience.
BEJAN, Transferência de Calor, Edgard Blücher Ltda.
INCROPERA, F.P. e DE WITT, D. P., Fundamentos de Transferência de Calor e Massa, LTC.

Supplementary Bibliography:
A. Bejan, Heat Transfer: Evolution, Design and Performance, 1st Ed., Wiley, 2022.
A. Bejan, Convection Heat Transfer, 4th Ed., Wiley, 2013.
F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentos de Transferência de Calor e de Massa, 7ª Ed., LTC, 2014.
H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd Ed., Pearson, 2007