Numerical Analysis II

Code	14809
Year	3
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	NA
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) calculate numerically approximations for the eigenvalues and eigenvectors of a matrix; b) solve numerically systems of non-linear equations; c) use computational methods to solve nonlinear programming problems; d) approximate functions; e) obtain numerically solutions of ordinary differential equations with values at the boundary; f) solve differential equations with partial derivatives 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. Approximation of eigenvalues and eigenvectors 2. Numerical Solution of Nonlinear Systems of Equations 3. Nonlinear optimization 4. Approximation of functions 5. Boundary-Value Problems for Ordinary Differential Equations 6. Numerical Solutions to Partial Differential Equations
Main Bibliography	• H. Pina, "Métodos Numéricos", Mc GrawHill, Alfragide, 1995. • M.R. Valença, "Métodos Numéricos", INIC, Braga, 1988. • R.I. Burden & J.D. Faires & A.M. Burden, "Numerical Analysis 10e", PWSKent, Boston, 2015. • J.C. Butcher, "The Numerical Analysis of Ordinary Differential Equations 2e", John Wiley & Sons, Auckland, 2
Language	Portuguese. Tutorial support is available in English.