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. This objective is realized by the transmission of the following competences: a) Analyse errors and determine error propogation, b) Calculate roots of a non-linear equation and extreme values of a real function, c) Solve systems of linear and non-linear equations, d) Approximate and interpolate random data sets by polynomial functions, e) Differentiate and integrate functions analytically and numerically, f) Solve differential equations and systems of differential equations numerically.
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Main Bibliography |
- Paulo Rebelo, 'Nota de aula' - R. L. Burden & J. D. Faires, " Numerical Analysis 9e", Brooks/Cole. Cengage Learning, 2011. - H. Pina, "Métodos Numéricos", Mc GrawHill, Alfragide, 1995. - M. R. Valença , "Métodos Numéricos", INIC, Braga, 1988. - A. Stanoyevitch, “Introduction to MATLAB with Numerical Preliminaries", John Wiley & Sons, 2005. - A. Quarteroni e F. Saleri, “Cálculo científico com MATLAB e Octave”, Springer-Verlag, 2007. - 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.
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