Advanced Calculus: A Course in Mathematical Analysis [Hardcover]

Patrick M. Fitzpatrick (Author)

Book Description

ISBN-10: 0534926126 | ISBN-13: 978-0534926120 | Publication Date: August 21, 1995 | Edition: 1

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.

Editorial Reviews

About the Author

Patrick M. Fitzpatrick is Professor and Chair of Mathematics at the University of Maryland, College Park.

Product Details

• Hardcover: 576 pages
• Publisher: Brooks Cole; 1 edition (August 21, 1995)
• Language: English
• ISBN-10: 0534926126
• ISBN-13: 978-0534926120
• Product Dimensions: 9.6 x 7.6 x 1.1 inches
• Shipping Weight: 2.5 pounds (View shipping rates and policies)
• Average Customer Review: 2.8 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #721,659 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

3.0 out of 5 stars it's fair, not great tho, October 21, 2003

By 

george (chicago) - See all my reviews

This review is from: Advanced Calculus: A Course in Mathematical Analysis (Hardcover)

Fitz's Advanced calculus is a fair textbook. It's not great and the Rn is somewhat ponderously developed. Furthermore, there are typo errors that one can occasionally find in the book reading each section. Excercises vary in difficulty, number (some sections only have 10 problems and others have 30 problems) and quality. From my experience with this text, as a TA, the problems really don't develop the skills neccesary for learning higher math; rather, it bludgeons the reader to recall simple ideas and rehash them out in a proof (the Principle of Mathematical Induction is one example, a beautiful tool, but poorly used). Furthermore, certain proofs, like the Triangle Inequality, aren't rigorously laid out in the text. They simply sketch a proof and leave it at that. There are also small, but not inconsequential holes, in other proofs. If one does not have a brilliant lecturer to go along with this mediocore book, then the student could leave the class with terrible skill, or lack thereof, in proofs. Lastly, if one must purchase a Real Analysis text, go with Walter Rudin's Principles of Mathaematical Analysis. If that seems like a very big jump in mathematical difficulty and maturity level, then try Spivak's "Caluclus," Serge Lang's "Undergraduate Analysis," or Apostol as well. This text is a fair book, but certainly not outstanding or worth the price they're asking for.

BTW, if Real Analysis is the reader's first introduction to proof based mathematics, then he might do well to purchase a copy of "An Introduction to Mathematical Reasoning." It's a small book for roughly $30, but it's a wonderful piece to properly develop the skills needed in theoretical math.

4 of 4 people found the following review helpful:

3.0 out of 5 stars Good treatment: Unfortunately this is a textbook, April 8, 2001

By 

Kenghis Khan (nprvl,il,usa) - See all my reviews

This review is from: Advanced Calculus: A Course in Mathematical Analysis (Hardcover)

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.

4 of 4 people found the following review helpful:

3.0 out of 5 stars it's not a bad text, May 6, 2000

By A Customer

This review is from: Advanced Calculus: A Course in Mathematical Analysis (Hardcover)

This is not a bad introduction to mathematical analysis. It provides a clear, concise, and often intuitive discussion of many of the fundamental topic in the field: sequences and series of reals, convergence, subsets, compactness, connectedness, differentiation, integration, the inverse and implicit function theorems and even a brief (not fully satisfactory ) discussion of metric spaces. Certainly it lacks rigour (it even neglects to properly develope the real number field), but it is nonetheless valuable as an introduction to mathematical reasoning. For those seeking more rigorous treatments of the subject at a more reasonable price I would have to agree with some of the other reviewers that Kolmogorov & Fomin's and Haaser & Sullivan's texts are wonderful. David Sprecher's text "The Elements of Analysis" is also well worth a look.