Calculus II
Code
1302
Academic unit
null
Department
null
Credits
7,5
Teacher in charge
Patrícia Xufre e José Costa
Teaching language
Portuguese
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
Compulsory pre-requisite:
- 1301. Calculus I
Recommended pre-requisite:
- 1303. Linear Algebra
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. Kuhn-Tucker conditions. Sufficiency and Necessity theorems. Envelope theorem.
Bibliography
Teaching method
Evaluation method
Evaluation consists of three mini-tests, of which the average of the best two weighs 15% of the final grade, a midterm test (25%) and a final exam (60%).