Mathematical Analysis II
This course is intended for students to develop their capacity for logical reasoning and calculation, and learn the tools for formulating and solving problems posed in its syllabus. The main purposes are the acquisition and consolidation of fundamental knowledge of differential and integral calculus in IRn.
Patrícia Santos Ribeiro
Weekly - Available soon
Total - Available soon
Portuguese. If there are Erasmus students, classes will be taught in English
Prerequisite recommended: Mathematical Analysis I
Pires, C., Cálculo para Economia e Gestão, Escolar Editora, 2010.; Sydsæter, K, Hammond, P., Essential Mathematics for Economic Analysis, 2nd ed., Prentice Hall, 2006.; Sydsæter, K. et al., Further Mathematics for Economic Analysis, Prentice Hall, 2005.; Dias Agudo, F.R., Análise Real, Livraria Escolar Editora, 2ª edição, 1994.; Azenha, A., Jerónimo, M.A., Elementos de Cálculo Diferencial e Integral em IR e IRn, McGraw-Hill, 1995.
Lectures and pratical sessions with exercises.
Continuous Assessment System (only 1st season):
Final grade is calculate by the following formula: 3 intermediate Tests (T1, T2, T3) during the semester (minimum grade in each test: 7,5 points)
Final Grade: 30%T1+40%T2+30%T3
Exam system (only 2nd season)
Final Exam (100%) (minimum grade: 9,5 points)
1. Space IRn (n>=1)
Notion of norm and notion of distance;
Brief notions of topology.
2. Real functions of n real variables
General concepts and definitions.
Domain. Level Curves.
Limits and continuity.
3. Differential Calculus in IRn
Partial Derivatives. Gradient.
Differentiability and differential.
Higher-order derivatives and differential.
Derivative of the composite function.
4. Integral Calculus in IRn
The Riemann Integral.
Calculation of double integrals. Application to the calculation of areas.
Some basic concepts.
Equality constrained optimization: graphics resolution; method of Lagrange multipliers.
Inequality constrained optimization: graphic resolution.