Mathematical Analysis

Tom M. Apostol

(from the preface) A glance at the Table of Contents will reveal that most of the topics which usually fall under the heading "Advanced Calculus" are treated in this book. The author's aim has been to provide a development of the subject matter which is honest, rigorous, up-to-date, and, at the same time, not too pedantic. Most of the "hard" theorems which are either omitted or treated rather skimpily in many texts on advanced calculus are proved here with great care. Some of them are ordinarily considered too difficult for a standard course in advanced calculus but too elementary for a course in real or complex function theory. With the inclusion of these theorems, the book helps to fill the gap between elementary calculus and advanced courses in analysis. More important than this, it introduces the reader to some of the abstract thinking that pervades modern mathematics.