Mathematical Analysis: a Modern Approach to Advanced Calculus

by 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.

Genres: Mathematics, Textbooks, Academic, Calculus, Science, Nonfiction

Paperback

First published January 1, 1957

Reviews

[Douglas · Rating 5 out of 5]

Tom Apostol, who is still alive and ethusiastic about all kinds of mathematics, is well known for several textbooks on calculus at all levels. My first encounter was with his undergraduate text. I've had this book on my shelf for many years now and I regularly resort to it when I need clarification of points in analysis. Right now I'm using it as a reference for a study of what I call "Random Riemann Sums" wherein I am trying to combine my knowledge of Monte Carlo with analysis to better understand such things as sum distributions, partitions, bounded variation, etc. I find I can dip into Apostol's book more easily than other texts.

[Ross Lund · Rating 3 out of 5]

Probably the only mathematical text I have ever read cover-to-cover. A very good introduction to Analysis as long as you already have some maths background. Naturally as a pure maths text it is very dry, with some positively arid sections, even for one interested in learning the subject.

[Curtis Penner · Rating 5 out of 5]

Written in 1957, it has stood the test of time. It is still very good. Good explanations and proofs. This is an advanced Calculus book. I have read and enjoyed Apostol’s two Calculus books. I have also enjoyed this advanced calculus book.

[Pratik Gurung · Rating 5 out of 5]

Great book.

[Daniel Low]

An excellent text for my first-year analysis course.