Mathematics I

The following teaching methodologies are used in this curricular unit:
1) Verbal methods (say), making use of the following educational resources: Exposition, Explanation, Dialogue and questioning;
2) Intuitive Methodologies (show), making use of the following educational resources: Demo, Audiovisual, written texts;

It is intended, with this curricular unit, to provide a working tool that allows an opening of mathematical reasoning in order to provide not only with the taste for mathematics, but also with the ability to solve real problems using analytical techniques.

Set theory: Sets: definition and representations; Subsets; Operations on sets; Cardinality; Partitions and potency of sets; Mathematical Induction; Cartesian product of sets; Relations: definitions, representations and properties; Functions: definition, injectivity, surjectivity and inversion.
Overview of Real Functions of Real Variable: Limit and Continuity of Real Functions of Real Variable.
Differential Calculus in IR: Rates of Change; Definition of derivative of a real function of real variable; Side derivative; N order derivative; Derivation rules. Derived function; Differentiability and continuity. Rolle and Lagrange Theorems. L’Hôpital’s rule. Differentials; Study of functions and their graphical representation; Maximum and minimum problems.
Integral Calculus in IR: Primitives of Real Functions of Real Variable; Definition of a primitive of a function; Immediate primitivation; Other primitivation methods; Application to the calculation of areas.

NAO

Ostrowski, A., Lições de Cálculo Diferencial e Integral, Vol. 1, 2, Ed. Fundação Calouste Gulbenkian,
Lisboa, 1990.

Apostol, T. M., Cálculo, Vol. 1, 2, Editora Reverté Lda, Barcelona, 1993.

Dowling, E. T., Cálculo para Economia, Gestão e Ciências Sociais, McGraw-Hill, Lisboa, 1994.

Guerreiro, J. S., Curso de Análise Matemática, Livraria Escolar Editora, Lisboa, 1989.

Stewart, J., Cálculo, Vol.1, 2, Editora Pioneira

Piskounov, N., Cálculo Diferencial e Integral, Vol. 1, 2, Lopes da Silva Editora, Porto, 1986.

Campos Ferreira, J., Introdução à Análise Matemática, Ed. Fundação Calouste Gulbenkian, Lisboa, 1990

Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 1, 2, McGraw-Hill do Brasil, S. Paulo, 1983.

Tan, S.T., Matemática Aplicada à Administração e Economia, Pioneira Thomson Learning, São Paulo, 2003