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Mathematics II

Code 12083
Year 1
Semester S2
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements No.
Mode of delivery Face to face.
Work placements not applicable
Learning outcomes To develop student’s logical, critical and analytical reasoning, and to enhance students' autonomy in formulating and solving mathematical problems.
Syllabus 0.1 Motivation for Analysis

1. Functions from R^n to R^m
1.1 Free and constrained optimisation
1.2 Method of the Lagrange's multipliers

2. Integral calculus in R^n
2.1 Fubini's theorem
2.2 Areas and volumes

3. Real and complex numbers
3.1 The notion of field
3.2 General form and polar form of a complex number
3.3 Symmetric and conjugate of a complex number
3.4 Operations with complex numbers
3.5 Powers and roots

0.2 Motivation for Linear Algebra

4. Topics of Linear Algebra
4.1 Vector spaces
4.2 Linear dependence and independence
4.3 Generators and basis
4.4 Vector subspaces

5 Linear transformations and matrices
5.1 Kernel, image space and rank of a matrix
5.2 Eigenvalues and eigenvectors of a matrix
5.3 Determinants
5.4 Systems of linear equations > 0.1 Motivation for Analysis

1. Functions from R^n to R^m
1.1 Free and constrained optimisation
1.2 Method of the Lagrange's multipliers

2. Integral calculus in R^n
2.1 Fubini's theorem
2.2 Areas and volumes

3. Real and complex numbers
3.1 The notion of field
3.2 General form and polar form of a complex number
3.3 Symmetric and conjugate of a complex number
3.4 Operations with complex numbers
3.5 Powers and roots

0.2 Motivation for Linear Algebra

4. Topics of Linear Algebra
4.1 Vector spaces
4.2 Linear dependence and independence
4.3 Generators and basis
4.4 Vector subspaces

5 Linear transformations and matrices
5.1 Kernel, image space and rank of a matrix
5.2 Eigenvalues and eigenvectors of a matrix
5.3 Determinants
5.4 Systems of linear equations
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. > 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.
Last updated on: 2021-06-25

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