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Linear Algebra and Numerical Analysis

Code 9093
Year 1
Semester S2
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements Knowledge acquired in secondary education in Mathematics A.
Mode of delivery Face-to-face with the use of an e-learning platform
Work placements Not Applicable
Learning outcomes The main goal of this curricular unit (CU) is to provide an introduction to the basic concepts and techniques in Linear Algebra and Numerical Analysis.
At the end of this CU, the student will be able to
- understand fundamental properties of matrices, including determinants and inverse matrices and solve systems of linear equations using direct methods;
- describe and analyse numerical methods for solving non-linear equations, systems of linear equations and of non-linear equations, methods for polynomail interpolation, methods for approximating integrals and methods for approximating solutions to simple ordinary differential equations (initial value problems);
- apply the methods discussed to solve mathematical problems in bioengenhary.
Syllabus CHAPTER 1 Matrices: Types of matrices, matrix and vector operations, elementary row operations, row-echelon form, rank of a matrix, inverse matrix, calculation of matrix inverse by the Gaussian elimination method. CHAP 2 Systems of linear equations: solving systems, system classification without and with parameters. CHAP 3 Determinants: definition, properties, calculation of matrix inverse using determinants, Cramer's rule. CHAP 4 Values ??and Eigenvectors: values, vectors, diagonalization. CHAP 5 Introduction to Numerical Analysis: computer preliminaries, elementary concepts, errors and convergence. CHAP 6 Nonlinear equations: bisection, false position, Newton-Raphson, secant and fixed-point methods. CHAP 7 Systems of linear and of nonlinear equations: Jacobi and Gauss-Seidel methods, Newton-Raphson methods. CHAP 8 Interpolation: Lagrange and Newton polynomials. CHAP 9 Numerical differentiation and integration: trapezoid, simpson, gaussian quadrature methods. CHAP 10 ODEs
Main Bibliography MAIN BIBLIOGRAPHY: Isabel Cabral, Cecília Perdigão, Carlos Saiago, Álgebra linear: teoria, exercícios resolvidos e exercícios propostos com soluções, Escolar Editora, 4ª edição, 2014 ; Material made available on Moodle: Numeric workbook.
BIBLIOGRAPHY:
Material made available on Moodle; Central library in section M-2.4
Howard Anton & Chris Rorres, Álgebra linear com Aplicações
Reginaldo J. Santos, Introdução à Álgebra Linear
Seymour Lipschutz, Álgebra linear: resumo da teoria, 600 problemas resolvidos, 524 problemas propostos
Burden, R.L. & Faires & J.D., Numerical Analysis, 9th Ed., Brooks/Cole, Cengage Learning, 2011
Pina, H., Métodos Numéricos, Mc Graw-Hill, 2010
Valença, M.R., Métodos Numéricos, INIC, 1988.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2023-06-19

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