Learning outcomes |
Students should acquire Calculus concepts (both in R and R^n) in order to formulate and solve Economics and Management problems. Differentiate basic Topology concepts in R Characterize and interpret real functions of one real variable Determine and interpret composition and inverse functions Define, determine and interpret limits, continuity and differentiability of real functions of one real variable Compute and interpret derivatives of composition and inverse functions Determine extreme values of real functions of one real variable
Determine primitives: immediate, by parts, by substitution and of rational functions Geometrically interpret the Fundamental Theorem of Calculus and Barrow’s rule
Graphically represent domains of real functions of two real variables Define, determine and interpret limits, continuity and differentiability of real functions of several real variables Determine and interpret partial and directional derivatives and also the Jacobian matrix Apply and interpret the chain rule and the implicit function theorem Determine and interpret second order derivatives and the Hessian matrix
|
Main Bibliography |
Recommended Pires, Cesaltina, Cálculo para Economistas, McGraw-Hill, 2001; Stewart, James, Cálculo, Volumes I e II, Thomson Learning, 2001;
Additional references Abreu, Miguel, Fernandes, Rui L. e Ricou, Manuel, Folhas de Cálculo Diferencial e Integral I, Departamento de Matemática do IST, 2008; e Silva, Jaime C., Princípios de Análise Matemática Aplicada, McGraw-Hill, 1994; Dias Agudo, F. R., Análise Real, Escolar Editora, 2ª edição, 1994; Ferreira, J. C., Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1997;
|
Teaching Methodologies and Assessment Criteria |
Theoretical-practical classes. In the first part of the class, the teacher exposes mathematical concepts and solves exercises. Subsequently, in the second part of the class, students solve exercises from the adopted bibliography, under the guidance of the teacher.
|