Analysis II

Syllabus: 

Topology of the Euclidean Space. Differentiable applications. Derivative as linear transformation. The gradient. Chain rule. Paths in Rn. Cn class applications: Taylor's formula. Sequences and series of functions. Inverse function theorem; implicit functions; rank theorem; Lagrange multipliers. Multiple integrals. Variable changes in multiple integrals.

Bibliography

Mandatory: 

•    Lima, Elon Lages - Analysis Course I - IMPA; 
•    Lima, Elon Lages - Analysis Course II - IMPA; 
•    Lima Elon Lages - Real Analysis - IMPA. 

Complementary: 

•    Bartle, Robert - The Elements of Real Analysis; 
•    Elon Lages Lima. Lima, Elon Lages Analysis in the space JRll / Elan Lages J anciro: IMPA, 2004. 128 (Coleção Matemática); 
•    Lang, serve. Calculus of Several Variables (Undergraduate Texts in Mathematics); 
•    Fleming, Wendel. Functions of Several Variables - Springer Verlog; 
•    Courant, Richard. Introduction to Calculus and Analysig.