Code |
8363
|
Year |
1
|
Semester |
S2
|
ECTS Credits |
6
|
Workload |
TP(60H)
|
Scientific area |
Mathematics
|
Mode of delivery |
Face-to-face.
|
Work placements |
Not applicable.
|
Learning outcomes |
The course unit is an introduction to the concepts of Linear Algebra and Numerical Analysis.The main objective is that the student dominates the basic concepts of Linear Algebra in theory of matrices, linear equation systems, determinants, vector spaces,linear transformations, eigenvalues and eigenvectors and, in Numerical Analysis, that he dominates algorithms for solving math problems on the computer.We introduce experimental competencies to complement the traditional method of studying the contents (eg., using Maple TA software),helping in the understanding of learning facts, concepts and mathematical principles.Learning methods, processes and techniques for applying the comprehension are provided. At the end of course unit, students should be able to: solve practical problems and application exercises about the subjects given in the course; apply methods and algorithms to solve problems related to their area of training and which are used throughout their academic career.
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Syllabus |
LINEAR ALGEBRA: Vectors and matrices; characteristic; solution and classification of linear systems; invertible matrices; determinants; vector spaces; linear transformations; eigenvalues and eigenvectors. NUMERICAL ANALYSIS: Error definitions; Taylor polynomial; numerical methods for solving non-linear equations (bisection, regula-falsi, Newton-Raphson, secant); direct and iterative methods for solving linear systems (LU, Cholesky, Jacobi, Gauss-Seidel); polynomial interpolation (method of indeterminate coefficients, Lagrange, Newton, inverse interpolation); numerical differentiation; numerical integration (closed Newton-Cotes formulae: trapezoidal and composed trapezoidal rules, Simpson and composed Simpson rules, open Newton-Cotes formulae); numerical solution of ordinary differential equations (Picard method, methods based on Taylor series, Euler method, Runge-Kutta methods).
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Main Bibliography |
1) Cabral, I., Perdigão, C., Saiago, C., Álgebra Linear, Escolar Editora,2010. 2) Magalhães, L.T., Álgebra Linear como Introdução à Matemática Aplicada, Texto Editora, 1993. 3) R.I. Burden & J.D. Faires , Numerical Analysis 7e, PWS-Kent, Boston, 2001. 4) H. Pina, Métodos Numéricos, Mc Graw-Hill, Alfragide, 1995. 5) M.R. Valença , Métodos Numéricos, INIC, Braga, 1988.
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Language |
Portuguese. Tutorial support is available in English.
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