| Code |
18103
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| Year |
1
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
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Learning outcomes |
The main objective of this curricular unit (UC) 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;
- 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) ;
- Apply the methods studied to solve mathematical problem.
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Syllabus |
CAP 1.Matrices: types of matrices, operations with matrices, inverse matrix, elementary operations and condensation, characteristics, calculation of the inverse matrix using the condensation method.
CAP 2.Systems of Linear Equations: solving systems, classifying systems without and with parameters.
CAP 3.Determinants: definition, properties, adjoint matrix and inverse matrix, Cramer's rule.
CAP 4.Values and Eigenvectors: values, vectors, diagonalization.
CAP 5.Introduction to numerical analysis: preliminaries on computation: elementary concepts, errors and convergence.
CAP 6.Non-linear equations: Bisection, False Chord, Newton-Raphson, Secant and Fixed-point methods.
CAP 7.Systems of linear and nonlinear equations: Jacobi, Gauss-Seidel, Newton-Raphson methods.
CAP 8.Polynomial interpolation: Lagrange and Newton polynomials.
CAP 9.Numerical differentiation and integration: Trapezium, Simpson, Gaussian quadrature methods.
CHAP 10.Initial value problems for ODE.
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Main Bibliography |
1] Serôdio, R., Álgebra Linear, livro de apoio às aulas de Álgebra Linear e Numérica.
[2] Cabral, I., Perdigão, C., Saiago, C., Álgebra Linear, Escolar Editora, 2018.
[3] Magalhães, L.T., Álgebra Linear como Introdução à Matemática Aplicada, Texto Editora, 1993.
[4] Burden, R.I. & Faires, J.D., Numerical Analysis, Brooks-Cole Publishing Company, 2011.
[5] Pina, H., Métodos Numéricos, Mc Graw-Hill, 2010.
[6] Valença, M.R., Métodos Numéricos, INIC, 1988.
Material available on Moodle and in the Central library (section M-2.4).
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Teaching Methodologies and Assessment Criteria |
Two mid-term tests are carried out. Students may use a basic calculator for the study of Linear Algebra and a graphic calculator for the study of Numerical Analysis. In the mid-term tests and exams, a graphic calculator may be used.
The first mid-term test (MT1) and the second mid-term test (MT2) are each worth 10 marks. The final mark for continuous assessment (CA) is given by the formula CA = MT1 + MT2, rounded to the nearest whole number (CA becomes a positive integer). If MT1 = 2.5 or MT2 = 2.5, the student is admitted to the exam. If CA = 10, the student is exempt from the exam. If MT1 < 2.5 and MT2 < 2.5, the student is not admitted to the exam. If CA = 17, the student may take an additional written test to achieve a final mark of 17 or higher.
Each exam consists of a written test with a maximum mark of 20. A minimum attendance of 70% is required only for students who are enrolled exclusively at UBI. Office hours may be held in person or online.
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Language |
Portuguese. Tutorial support is available in English.
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