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# Linear Algebra and Numerical Analysis

 Code 12500 Year 1 Semester S2 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements Knowledge of Mathematics A (Secondary Education of the Science and Technology Course) and Calculus I. Mode of delivery Face to Face Work placements Not applicable. Learning outcomes The main objective of this curricular unit (CU) is to provide the student with an introduction to the basic concepts and techniques of Linear Algebra and Numerical Analysis. At the end of this UC, the student must: - understand the fundamental properties of matrices, including determinants and inverse matrices, and solve systems of linear equations by direct methods;- understand and know how to calculate eigenvalues ??and vectors of a matrix:- know how to describe and analyze numerical methods for solving nonlinear equations, systems of linear equations and nonlinear equations, methods for polynomial interpolation, methods for approximating integrals and methods for approximating solutions to simple ordinary differential equations (initial value problems). Syllabus 1 - Matrix algebra: types of matrices, operations with matrices, inverse matrix, elementary operations and condensation, characteristics, calculation of the inverse matrix using the condensation method.2 - Systems of Linear Equations: solving systems, classifying systems without and with parameters.3 - Determinants: definition, properties, adjoint matrix and inverse matrix, Cramer's rule.4 - Values ??and Eigenvectors: values, vectors, diagonalization.5 - Introduction to numerical analysis: preliminaries on computing: elementary concepts, errors and convergence.6 - Non-linear equations: Bisection, Newton-Raphson, Secant and Fixed point methods.7 - Systems of linear and non-linear equations: Jacobi, Gauss-Seidel, Newton-Raphson methods.8 - Polynomial interpolation: Lagrange and Newton polynomials.9 - Numerical differentiation and integration, Richardson Extrapolation.10 - Initial value problems for ODE. Main Bibliography [1] Serôdio, R., Linear Algebra, book to support Linear Algebra and Numerical classes.[2] Cabral, I., Perdigão, C., Saiago, C., Algebra Linear, Escolar Editora, 2018.[3] Magalhães, L.T., Linear Algebra as an Introduction to Applied Mathematics, Texto Editora, 1993.[4] Burden, R.I. & Faires, J.D., Numerical Analysis, Brooks-Cole Publishing Company, 2011.[5] Pina, H., Numerical Methods, Mc Graw-Hill, 2010.[6] Valença, M.R., Numerical Methods, INIC, 1988.Material available on Moodle; Central library in section M-2.4 Language Portuguese. Tutorial support is available in English.

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Optometry and Vision Sciences
Last updated on: 2024-06-17

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