Basic Analysis II: Introduction to Real Analysis, Volume II

The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green's Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series.
Table of Contents (of this volume II)
8. Several Variables and Partial Derivatives
9. One Dimensional Integrals in Several Variables
10. Multivariable Integral
11. Functions as Limits