Università Roma Tre

Sequences and Series of Functions: Uniform and Total Pointwise Convergence, Limit Passage in the Integral and Derivative, Uniform Convergence Criteria. Power Series and Analytic Functions. Matrix Exponential. Fourier Series: Basic Definitions, Bessel's Inequality, Riemann-Lebesgue Lemma. Pointwise Convergence of the Fourier Series for Piecewise Regular Functions.
Fundamentals of Topology in R^n. Functions of Several Variables, Limits, and Continuity. Open, Closed, Connected, and Compact Sets. Heine-Borel, Weierstrass, and Heine-Cantor Theorems. Functions of Several Variables: Differentiability of C^k Functions. Definition of the P-th Derivative Tensor. Taylor's Formula with Integral Remainder, Lagrange Remainder, and Peano Remainder. Local Maxima and Minima. The Implicit Function Theorem.

Analisi Matematica II, Giusti - Analisi Matematica II, Chierchia