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 and the use of mathematical language, providing students with a support for the resolution of problems and practical applications.
Provide mathematical knowledge of integration of functions, in particular its application in calculation of areas of plane regions and solving differential equations.
Make the study of real functions of two real variables to allow students to its application in various problems, among which are the optimization of functions.
Encourage the use of analytical methods in solving practical problems through the application of acquired knowledge.
Program
Chapter 1 – Integral calculus
1.1 Antiderivatives
1.2 Definite integral
1.3 Improper integrals
Chapter 2 – Differential equations
2.1 Differential equations with variables separable
2.2 First order linear differential equations
Chapter 3 – Real functions of two real variables
3.1 Limits and continuity
3.2 Derivatives
3.3 Optimization
3.4 Optimization with constraints. Application of Lagrange multipliers method.
Internship(s)
NAO
Bibliography
[1] Amaro, A., Carvalho, M., Equações Diferenciais, ISCAC, 2007.
[2] Azenha, A., Jerónimo, M. A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw Hill, 1995.
[3] Breda, A., Costa, J., Cálculo com funções de várias variáveis, McGrawHill,
1996.
[4] Carvalho, M., Leite, J. Funções reais de duas variáveis reais, ISCAC, 2006.
[5] Neves, C., Cálculo Integral, ISCAC, 2006.
[6] Saraiva ,M. A., Silva, M. A., Primitivação, Edições Asa, Rio Tinto, 1ª ed., 1990.
[7] Swokowski, E., Cálculo com Geometria Analítica, 2ª ed., vol. I,II, Makron Books, 1995.