Programa

Mathematical Analysis III

Licenciatura Bolonha em Applied Mathematics for Economics and Management

Licenciatura Bolonha em Management

Licenciatura Bolonha em Economics

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.