Teaching Methodologies
Classes are taught in a theoretical-practical regime, in accordance with the curriculum plan.
In the theoretical part, the expository methodology is used to present the concepts, fundamental results and methods for solving the mahthematical problems under study.
The practical part is aimed at carrying out exercises to apply the concepts transmitted under the guidance of the teacher, but encouraging autonomous work or in small groups. Some of these exercises are based on real-life practical problems, allowing an interaction between theory and practice.
In some classes, it is intended to integrate the use of technology, using suitable software, to improve mathematical understanding and facilitate problem solving.
Learning Results
Goals:
– 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.
Skills:
– use mathematical knowledge of integration of functions, namely in its application in the calculation of areas of plane regions and in theresolution 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
3.4 Numerical integration: Trapezoidal rule
4 Real-valued function of two real variables
4.1 Definitions
4.2 Limits and Continuity
4.3 Partial derivatives
4.4 Differentials. Calculation of approximate values
4.5 Free extrema of two variable functions
4.6 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:
Harshbarger, R. J., Reynolds, J. J. (2018). Mathematical Applications for the Management, Life and Social Sciences. (12th ed.). Cengage Learning.
Stewart, J. (2015). Calculus: Metric Version. Cengage Learning Brooks Cole.
Swokowski, E.,(1979). Calculus with Analytic Geometry. Taylor & Francis.
Sydsæter, K., Hammond, P., Strøm, A. (2012). Essential Mathematics for Economic Analysis. (4th ed.). Pearson Education Limited.