Advanced Calculus: A Course in Mathematical Analysis

by Patrick M. Fitzpatrick

Advanced Calculus is designed for the two-semester course on functions of one and several variables. The text provides a rigorous treatment of the fundamental concepts of mathematical analysis, yet it does so in a clear, direct way. The author wants students to leave the course with an appreciation of the subject's coherence and significance, and an understanding of the ideas that underlie mathematical analysis.

Genres: Mathematics

576 pages, Hardcover

First published August 21, 1995

Reviews

[Mike · Rating 1 out of 5]

I thought this book like many real analysis books is trash. I've already taken analysis and tried to use this book. It's clear this book was not written by a person(s) who actually knows how to explain math. The book just states theorems and the math that goes with it. The examples are terrible and you'll probably need to reference other books and the internet to clarify them. The problems are trash and I couldn't solve many. I skipped chapter 5 and gave up after chapter 6.3 Like many books it teaches problems and not concepts, so when you get to the problems you can't rely on what you've learned in the chapter to carry over. Keep in mind I am reading the earlier edition that is blue. I know a lot of people like this book, maybe the newer version is much better. College people are suppose to be smart, be smart and borrow the book from your library before you buy it. Many times I've gotten books that have a lot of excellent reviews, just to find out it's only popular because of who the author is, etc.

[Kenghis Khan · Rating 3 out of 5]

The treatment of analysis in several variables in this book is solid. Fitzpatrick does a decent job explicating the theory while mainting a very rigorous presentation. Unfortunately, this book is a textbook. His examples are trivial while his sample problems are significantly more difficult. Quite frankly, Fitzpatrick should incorporate more examples that require multiple applications of concepts in dealing with proofs other than those of theorems. For students unaccustomed to proof based mathematics, this work is a disastrous introduction to multivariable calculus. Finally, his chapter treating the Hessian Matrix is an abhorration. He fails to distinguish his variables and the confusion is discouraging. Nevertheless, for students with some background in proof-based mathematics, this is a good treatment of the subject.

[Andy Williamson · Rating 5 out of 5]

This is a great book on the subject of Real Analysis or theory of functions of a real variable.