Analysis of manifolds

James R. Munkres9780201315967, 0201315963

This book is intended as a text for a course in analysis, at the senior or first-year graduate. A year-long course in real analysis is an essential part of the preparation of any potential mathematician. For the first half of such a course, there is substantial agreement as to what the syllabus should be. Standard topics include: sequence and series, the topology of metric spaces, and the derivative and the Riemannian integral for functions of a single variable. There are a number of excellent texts for such a course, including books by Apostol [A], Rudin [Ru], Goldberg [Go], and Roy den [Ro], among others.