Calculus II
Code
1302
Academic unit
null
Department
null
Credits
7,5
Teacher in charge
Patrícia Xufre
Teaching language
Portuguese and English
Objectives
The course develops the fundamental tools of differential calculus in ℝⁿ, that enable the mathematical formulation and study of models in Economics, Business and Finance.
Prerequisites
Mandatory Precedence:
- 1301. Calculus I
Subject matter
1.Space ℝⁿ
Topological notions.
2.Functions from ℝⁿ into ℝm
Examples in Economics/Business; domain; level curves; limits and continuity.
3.Differentiation in ℝⁿ
Partial derivatives; differentiation; Taylor?s theorem; derivative of the composite function; homogeneous functions and Euler?s theorem.
4.Inverse function theorem and Implicit function theorem.
5.Optimization
Free optimization; optimization with equality constraints; optimization with inequality constraints. Karush-Kuhn-Tucker conditions. Sufficiency and Necessity theorems. Envelope theorem.
Bibliography
?Pires, C., Cálculo para Economia e Gestão, Escolar Editora, 2010
?Campos Ferreira, J., Introdução à Análise em ℝⁿ, electronic publication (http://preprint.math.ist.utl.pt/files/iarn.pdf), DM, IST, 2003
?Xufre,P., Silva, P., Mendes, D., Análise em ℝⁿ, 2ª edição, 2014 Pearson Educación, S.A.
Teaching method
Theoretical classes; practical classes; resolution and proposal of problems and exercises; mini-tests, midterm test and final exam.
Evaluation method
Evaluation consists of two midterm test (20% each) and a final exam (60%). To pass the course, students must get at least 8.5 (over 20) in the final exam.