Teaching Methodologies
Classes are taught under theoretical and practical regime. An expository methodology is used for the presentation of the concepts of the course, supported by the resolution of proposed exercises of application of the concepts transmitted. Some of these exercises are based in real-life practical problems.
Learning Results
Promote logical/deductive reasoning, providing students with some knowledge of Logic and Set Theory, in order to provide them with a support for the algorithmic construction and research in databases.
Provide mathematical matrix calculation, in particular its application in solving systems of linear equations.
Make the study of real functions of a real variable to allow students to its application in various problems such as the optimization of functions, among others.
Encourage the use of analytical methods in solving practical problems through the application of acquired knowledge.
Program
Chapter 1 – Logic
Chapter 2 – Sets
Chapter 3 – Matrix calculation
3.1 Operations with matrices.
3.2 Condensation and matrix inversion – Elimination method Gauss-Jordan
3.3 Systems of linear equations
3.4 Determinants
Chapter 4 – Real functions of real variable
4.1 Composition of functions. Inverse function
4.2 Limits and continuity
4.3 Exponencial function and logarithmic function
4.4 Inverse trigonometric functions
4.5 Derivation function
4.6 Asymptotes
4.7 Study of functions
4.8 Taylor and MacLaurin polynomials
Internship(s)
NAO
Bibliography
[1] Amaro, M. F., Funções reais de variável real, ISCAC, 2008.
[2] Azenha, A., Jerónimo, M. A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw Hill, 1995.
[3] Carvalho, M., Cálculo Matricial, ISCAC, 2006.
[4] Ferreira, J. C., Elementos de Lógica Matemática e Teoria dos Conjuntos, IST, 2001.
[5] Giraldes, E., Fernandes, V., Smith, M. P., Álgebra Linear e Geometria Analítica, McGraw Hill, 1995.
[6] Leite, J., Rocha, M. C., Larguinho, M., Conjuntos, ISCAC, 2007.
[7] Martins, P. C., Neves, C., Leite, J., Carvalho, M. e Amaro, A., Matemática I, ISCAC, 2006.
[8] Swokowski, E., Cálculo com Geometria Analítica, 2ª ed., vol. 1, Makron Books, 1995.