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Computational Mathematics

Computational Mathematics

Code	15082
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	With this curricular unit it is intended that the student obtain numerical tools to solve the most varied mathematical problems. At the end of this curricular unit the student should be able to: a) analyze the errors and determine their propagation; b) determine numerically zeros of functions; c) solve numerically systems of linear equations; d) interpolate and approximate functions; e) derive and integrate functions numerically; f) solve equations and systems of differential equations by numerical methods; g) in face of a proposed problem, translate it mathematically, identify possible methods to solve it, choose the most appropriate, implement it and critically analyze the results.
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 Analysis10e", 2016, 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.
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.
Language	Portuguese. Tutorial support is available in English.