Mathematical Analysis Volume II

TL;DR

This textbook volume provides a comprehensive analysis of multivariable functions, covering foundational concepts, theorems, and advanced topics like Fourier analysis, for a two-semester mathematical analysis course.

Contribution

It offers an extensive, structured presentation of multivariable analysis topics, integrating classical theorems with modern techniques in a pedagogical format.

Findings

Detailed coverage of multivariable calculus concepts

Inclusion of Fourier series and transforms

Structured approach suitable for coursework

Abstract

This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets and closed sets, limits and continuity, uniform continuity, connectedness, compactness, intermediate value theorem, extreme value theorem, partial derivatives, differentiability, chain rule, mean value theorem, first and second order approximations, local extrema, inverse function theorem, implicit function theorem, constrained extrema problems and Lagrange multipliers, Riemann integrals of functions of several variables, Jordan measurable sets, iterated integrals, Fubini's theorem, change of variables theorem, Fourier series and its convergence, Fourier transforms.