Real Analysis

Abstract

Real analysis starts with a treatment of sequences and series, including, among other things, applications to the Cauchy criterior of convergence, the Chesáro-Stolz theorem, Cantor’s nested intervals theorem, and the telescopic method. This is followed by a long treatment of one-variable real analysis: limits, continuity, differentiability, convexity, and computations and applications of integrals, with a discussion of Taylor and Fourier series. The subchapter on multivariable real analysis contains applications of partial derivatives, computation of integrals, and the theorems of Green, Kelvin-Stokes and Gauss-Ostrogradsky. The chapter concludes with functional and differential equations.