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Matemática Computacional

Código 10356
Ano 2
Semestre S2
Créditos ECTS 6
Carga Horária TP(60H)
Área Científica Matemática
Mode of delivery Face to face.
Work placements There isn't.
Learning outcomes The general objective of this course is the study of efficient and stable numerical methods for solving certain mathematical problems. The study of each numerical method includes the analytic deduction of the formulae used, the description in algorithmic language and the presentation of techniques to estimate the solution error.

Syllabus 1. Errors and respective propagation.
2. Roots and extreme values of functions.
3. Solution of systems of linear and non-linear equations.
4. Interpolation, curve adjustment and function approximation.
5. Numerical differentiation and integration.
6. Numerical methods for differential equations and systems of differential equations; consistency, stability and convergence.
Teaching Methodologies and Assessment Criteria The course is structured in theoretical-practical classes. The teacher introduces the concepts, states and proves the fundamental results, provides examples and applications. The combination of the theory with the practice in the classes allows the exercises to be performed immediately after each theoretical content, which improves the acquisition of knowledge and skills. In addition, the student is encouraged to participate in classes, to interact with the teacher and with colleagues, and to work autonomously, in the form of exercises, formulation and problem solving.
Main Bibliography I. Main references

• R.L. Burden & J.D. Faires , " Numerical Analysis 9e", 2011, Brooks/Cole, Cengage Learning.
• H. Pina, "Métodos Numéricos", Mc Graw-Hill, Alfragide, 1995.
• M.R. Valença , "Métodos Numéricos", INIC, Braga, 1988.

II. Secondary references

• J.C. Butcher , "The Numerical Analysis of Ordinary Differential Equations", John Wiley & Sons, Auckland, 1987.
• E. Hairer , S.P. Nørsett & G. Wanner , " Solving Ordinary Differential Equations I ", Springer Series in Comput. Mathematics, Vol. 8, Springer-Verlag, Heidelberg, 1987.
• E. Hairer & G. Wanner , " Solving Ordinary Differential Equations II ", Springer Series in Comput. Mathematics, Vol. 8, Springer-Verlag, Heidelberg, 1987.
Language Portuguese. Tutorial support is available in English.
Data da última atualização: 2025-03-24
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