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Matemática II

Código 16471
Ano 1
Semestre S2
Créditos ECTS 6
Carga Horária TP(60H)
Área Científica Matemática
Mode of delivery Face to face.
Work placements not applicable
Learning outcomes >> Specific objectives:
1. promote the learning of mathematical concepts in the field of differential and integral calculus in Rn;
2. provide the basic fundamentals of Linear Algebra usually applied in the various areas of Economics;

>> General objectives
3. develop the ability to interpret a problem, model it and solve it with the appropriate
mathematical knowledge and adequate techniques;
4. develop the capacity for abstract and logical reasoning, and linguistic rigor.
Syllabus 1. Functions of R^n in R^m (Part II)
1.1 Free and conditional extrema
1.2 Method of Lagrange multipliers
1.3 Integral calculus in R^n
1.3.1 Fubini's Theorem. Areas and volumes.

2. Topics of Linear Algebra
2.1 Matrices, Systems of linear equations and Determinants
2.1.1 Generalities and operations with matrices
2.1.2 Transpose and conjugate matrices. Symmetric and hermetic matrices
2.1.3 Ladder form and characteristic of a matrix
2.1.4 Systems of linear equations
2.1.5 Determinants: definition and properties
2.1.6 Calculating the inverse of a square matrix
2.1.7 Eigenvalues and eigenvectors of a square matrix
2.2 Vector Spaces
2.2.1 Definition, examples and properties
2.2.2 The n-dimensional Euclidean space
2.2.3 Linear dependence and independence
2.2.4 Generators and bases
2.3 Linear applications of R^n on R^m
2.3.1 Definition and examples
2.3.2 Matrix of a linear application of R^n in R^m
2.3.3 Eigenvectors of a linear application.
Main Bibliography Azenha, A., Jerónimo, M. A. (1995), Elementos de Cálculo Diferencial e Integral em R e R^n, McGraw-Hill.

Cabello, J. G. (2006), Álgebra Lineal. sus aplicaciones en Economía, Ingenierías y otras ciencias, Delta.

Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra Linear, Escolar.

DMAT-IST (2005), exercícios de análise matemática I e II, IST.

Hoffmann, L., Bradley, G. (2010), Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill.

Lay, D. C. (1999), Álgebra linear e suas aplicações, LTC.

Martins, A., Salomé, H., Silva, L., Pereira, J. (2018), Preparar o Exame 2019. Matemática A. 12.º, raiz.

Pires, C. (2001), Cálculo para Economistas, McGraw-Hill.

Santana, A. P., Queiró, J. (2018), Introdução à Álgebra Linear, gradiva.

Santos, R. (2010), Álgebra Linear, http://www.mat.ufmg.br/~regi/livros.html

Stewart, J. (2013), Cálculo, Volume 2, Cengage Learning.

Vários autores (vários anos), Testes e Exames, Moodle.
Language Portuguese. Tutorial support is available in English.

Regente

Imagem d@ Ana Catarina dos Santos Carapito [Ficheiro Local]
 Ana Catarina dos Santos Carapito

Curso

Economia
Data da última atualização: 2025-02-26
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