Currículo

Mathematical Analysis III AM3-E

Contextos

ECTS

6.0 (para cálculo da média)

Objectivos

- Training in optimization methods and integration of multivariable functions defined in differential manifolds (with an emphasis in curves and surfaces); - Introduction to the Lebesgue integral and measure theory.

Programa

1. Riemann integral: - Integration in Rn; - Fubini theorem; - Change of variables theorem; - Classic coordinates and applications (volume, centroid). 2. Lebesgue integral - Jordan measure and Lebesgue exterior measure in Rn; - Measurable sets and Lebesgue measure; - Measurable functions; - Lebesgue integral and convergence theorems. 3. Line integral - Line integral in Rn; - Vector fields and Green theorem; 4. Manifolds in Rn - Tangent and normal spaces; - Representations of manifolds; - Integration in manifolds and divergence theorem; - Constrained extreme points and Lagrange multipliers.

Método de Avaliação

Lectures will be used to present the program material and the resolution of practical exercises. Students are motivated to work also at home by consulting the bibliography. The final grading is obtained from a written examination.

Carga Horária

Bibliografia

Não foi definida bibliografia principal

Disciplinas de Execução

2026/2027 - 1 Semestre