Basic Analysis 1: Introduction to Real Analysis

Jiří Lebl

Volume II continues into multivariable analysis. Starting with differential calculus, including inverse and implicit function theorems, then differentiation under the integral and path integrals, which are often not covered in a course like this, and multivariable Riemann integral. There is also a chapter on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier series. Together the two volumes provide enough material for several different types of year-long sequences. A student who absorbs the first volume and the first three chapters of volume II should be more than prepared for graduate real and complex analysis courses.