Teaching Methodologies
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;
Learning Results
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.
Program
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’Hôpitals 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.
Internship(s)
NAO
Bibliography
Guerreiro, J. S., Curso de Análise Matemática, Livraria Escolar Editora, Lisboa, 1989.
Tan, S.T., Matemática Aplicada à Administração e Economia, Pioneira Thomson Learning, São Paulo, 2003
Dowling, E. T., Cálculo para Economia, Gestão e Ciências Sociais, McGraw-Hill, Lisboa, 1994.
Campos Ferreira, J., Introdução à Análise Matemática, Ed. Fundação Calouste Gulbenkian, Lisboa, 1990
Piskounov, N., Cálculo Diferencial e Integral, Vol. 1, 2, Lopes da Silva Editora, Porto, 1986.
Apostol, T. M., Cálculo, Vol. 1, 2, Editora Reverté Lda, Barcelona, 1993.
Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 1, 2, McGraw-Hill do Brasil, S. Paulo, 1983.
Ostrowski, A., Lições de Cálculo Diferencial e Integral, Vol. 1, 2, Ed. Fundação Calouste Gulbenkian,
Lisboa, 1990.
Stewart, J., Cálculo, Vol.1, 2, Editora Pioneira