Mathematical Analysis II
In this curricular unit, is intended that students develop their logical thinking ability and calculus, and learn the instruments that allow the formulation and resolution of problems within the scope of their study plan. The main goals are the acquisition and consolidation of the fundamental knowledge of differential and integral calculus in IR^n.
Maria Helena da Costa Guerra Pereira
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 Evaluation Scheme (1st season):
Continuous assessment consists of conducting, during the academic semester, 2 tests in person, T 1, T 2 and one final exam in person, E. The tests have no minimum grade. The exam has a minimum grade of 8.5 values.
The final grade is calculated as follows: 20% T 1+ 20% T2+ 60% E.
If, exceptionally, it is not possible to carry out an assessment in person, there will be the possibility of do the same online followed by an oral exam, but the situation will be analyzed case by case.
Examination regime (only 2nd season):
Final exam in person (100%)
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.
Programs where the course is taught: