| Code |
9093
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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 |
Knowledge acquired in secondary education in Mathematics A.
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Mode of delivery |
Face-to-face with the use of an e-learning platform
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Work placements |
Not Applicable
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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.
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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
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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.
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Teaching Methodologies and Assessment Criteria |
The teaching-learning methodology is centered on the student, who, throughout the semester, will acquire and apply the concepts, with his autonomous work. In this way, particular importance is given to the periodic assessment that allows the student to demonstrate, throughout the semester, the skills acquired through his/her work in stages. To this end, it is planned to carry out three mini tests (each one individually and in person in the classroom) and a global individual and in person attendance. Each exam consists of a written and in person test, with a maximum score of 20 points.
The student uses a basic calculator in the study of Linear Algebra and a graphing calculator in the study of Numerics. In the global frequency and exam, the graphing calculator is used.
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Language |
Portuguese. Tutorial support is available in English.
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