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Computational Mathematics

Computational Mathematics

Code	10356
Year	2
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	-
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.
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.