William R. Wade,
An Introduction to Analysis, 2nd Edition. Math 415 covers parts of Chapters 7, 14, 9 and 11.
Consult the Math
415 calendar web page for reading and homework
assignments.
In this course you will master the basic theorems on power series (including Taylor series) and Fourier series, and on differential and integral calculus in Euclidean space, with an introduction to Lebesgue's theory of integration.
A recommended list
of References for Advanced Calculus that can
be found in the Library.