Analysis over Rn

Topology and analysis in metric and vector spaces, with an emphasis on R^d and on spaces of continuous functions. Classical theorems about the latter space: Ascoli-Arzèla, Stone-Weierstrass. Fréchet derivatives in vector spaces, its properties and Taylor series. Implicit and inverse function theorems. Sketch of the theory of submanifolds in R^d. Null measure and Sard’s theorem. Multidimensional integrals and the Riemann-Lebesgue theorem.

References:
J. Munkres, Analysis on Manifolds (Westview Press)
S. Lang, Undergraduate Analysis (Springer).
R. I. Oliveira, notas de aula
W. Rudin, Princípios da Análise Matemática (Ao Livro Técnico).

* Standard program. The teacher has the autonomy to make any changes.