MAT357H1: Foundations of Real Analysis

Hours

36L

Function spaces; Arzela-Ascoli theorem, Weierstrass approximation theorem, Fourier series. Introduction to Banach and Hilbert spaces; contraction mapping principle, fundamental existence and uniqueness theorem for ordinary differential equations. Lebesgue integral; convergence theorems, comparison with Riemann integral, L^p spaces. Applications to probability.

Prerequisite
MAT257Y1/(MAT327H1 and permission of instructor)
Exclusion
MAT438H5
Distribution Requirements
Science
Breadth Requirements
The Physical and Mathematical Universes (5)