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Linear Algebra and Numerical Analysis

Code 12807
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 with the use of an e-learning platform
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 computation: 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
Teaching Methodologies and Assessment Criteria The type of classes is theoretical + practical: in the first class of the week the teacher explains the theoretical part of the subject, interspersed with solving examples; In the second class of the week, it is intended that students, independently, analyze, discuss and apply, under the teacher's guidance, the main concepts covered.
The teaching-learning methodology is centered on the student, who, throughout the semester, acquires and applies the concepts, through their autonomous work. In this way, particular importance is given to periodic assessment, which allows the student to, throughout the semester, gradually demonstrate the skills acquired through their work.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2024-06-17

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