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 mathematical knowledge of integration of functions, namely in its application in the calculation of areas of plane regions and in the
resolution of differential equations;
– apply the study of real functions of two real variables in several problems, of which the optimization of functions stands out.
Program
1 Primitivation
1.1 Immediate primitives
1.2 Primitivation by parts
1.3 Primitivation of rational functions
1.4 Primitivation by substitution
2 Differential equations
2.1 Definitions
2.2 Separable differential equations
2.3 First order linear differential equations
3 Integral Calculus
3.1 Definite integral
3.2 Application of the definite integral to the calculation of areas of plane regions
3.3 Improper integrals
4 Real-valued function of two real variables
4.1 Definitions
4.2 Limits
4.3 Continuity
4.4 Partial derivatives
4.5 Differentials. Calculation of approximate values
4.6 Free extrema of two variable functions
4.7 Conditioned extremes. Application of the Lagrange multipliers method
Internship(s)
NAO
Bibliography
Bibliografia fundamental
Neves, Cidália, Textos de apoio e fichas práticas disponibilizados na plataforma NONIO, Edição do Autor.
Bibliografia complementar
Amaro, A., Carvalho, M., Equações Diferenciais, ISCAC, 2007.
Azenha, A., Jerónimo, M. A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw Hill, 1995.
Breda, A., Costa, J., Cálculo com funções de várias variáveis, McGraw-Hill, 1996.
Carvalho, M., Leite, J. Funções reais de duas variáveis reais, ISCAC, 2006.
Neves, C., Cálculo Integral, ISCAC, 2006.
Saraiva ,M. A., Silva, M. A., Primitivação, Edições Asa, Rio Tinto, 1ª ed., 1990.
Swokowski, E., Cálculo com Geometria Analítica, 2ª ed., vol. I,II, Makron Books, 1995.