Teaching Methodologies
Classes are taught in a theoretical-practical regime.
The expository methodology is used for the presentation of the concepts of the curricular unit, supported by the realization of exercises to
apply the transmitted concepts. Some of these exercises are based on real-life practical problems, allowing the interaction between theory
and practice.
Learning Results
As a 1st year mathematics curricular unit, the main objective is to provide skills to support the work to be developed in other curricular units
of the course, namely:
– provide knowledge of the wide variety of problems that can be solved using mathematical concepts and results;
– foster logical/deductive reasoning and mental calculation;
– encourage the use of analytical methods in solving concrete problems through the application of acquired knowledge.
It is intended that students develop the following skills:
– use some notions of logic and set theory that support programming and database research;
– apply mathematical knowledge of matrix calculus, namely in solving systems of linear equations;
– apply the knowledge of real functions of real variables in several problems such as the optimization of functions, among others.
Program
1 Logic
1.1 Propositions and logical operators
1.2 Propositional expressions and quantifiers
2 Sets
2.1 Generalities
2.2 Real number intervals
2.3 Operations with sets
2.4 Cartesian products, binary relations and functions
3 Matrix Calculus
3.1 Matrix definition. Generalities
3.2 Operations with matrices. Invertible matrices
3.3 Condensation of matrices. Gauss-Jordan elimination method
3.4 Systems of linear equations
3.5 Determinants
4 Real-valued functions of a real variable
4.1 Generalities
4.2 Composition of functions. Inverse function
4.3 Limits and Continuity
4.4 Exponential function and logarithmic function
4.5 Inverse trigonometric functions
4.6 Derivatives. Applications of derivatives
4.7 Study of functions
4.8 Taylor and Mac-Laurin polynomials
Internship(s)
NAO
Bibliography
Bibliografia fundamental
Neves, Cidália, Textos de apoio e fichas práticas disponibilizados na plataforma NONIO, Edição do Autor.
Bibliografia complementar
Amaro, M. F., Funções reais de variável real, ISCAC, 2008.
Carvalho, M., Cálculo Matricial, ISCAC, 2006.
Leite, J., Rocha, M. C., Larguinho, M., Conjuntos, ISCAC, 2007.
Martins, P. C., Neves, C., Leite, J., Carvalho, M. e Amaro, A., Matemática I, ISCAC, 2006.
Azenha, A., Jerónimo, M. A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw Hill, 1995.
Ferreira, J. C., Elementos de Lógica Matemática e Teoria dos Conjuntos, IST, 2001.
Giraldes, E., Fernandes, V., Smith, M. P., Álgebra Linear e Geometria Analítica, McGraw Hill, 1995.
Swokowski, E., Cálculo com Geometria Analítica, 2ª ed., vol. 1, Makron Books, 1995.