Calculus II
Code
1302
Academic unit
null
Department
null
Credits
7,5
Teacher in charge
Patrícia Xufre; Pedro Chaves
Teaching language
Portuguese and English
Objectives
The course develops the fundamental tools of differential calculus in R, that enable the mathematical formulation and study of models in Economics, Business and Finance.
Prerequisites
Mandatory Precedence:
- 1301. Calculus I
Subject matter
1.Space R.
Topological notions.
2.Functions from R into R.m
Examples in Economics/Business; domain; level curves; limits and continuity.
3.Differentiation in R.
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, 2011.
Simon C.P., Blume L., Mathematics for Economists, W.W. Norton & Company, Inc, 1994.
Xufre P., Silva, P., Mendes D., Análise em R, 2ª edição, 2014 Pearson Educación, S.A.
Resources
Further readings and pedagogical and teaching material is available on Moodle.
Teaching method
Theoretical classes; practical classes; resolution and proposal of problems and exercises; mini-tests, midterm test and final exam.
Evaluation method
The final exam is mandatory a nd must cover the entire span of the course. Its weight in the final grade can be between 30 to 70%. The remainder of the evaluation can consist of class participation, midterm exams, in class tests, etc. Overall, written in class assessment (final exam, midterm) must have a weight of at least 50%.