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