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Advanced Calculus: A Course in Mathematical Analysis, by Patrick M. Fitzpatrick
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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.
- Sales Rank: #1310297 in Books
- Brand: Brand: Brooks Cole
- Published on: 1995-08-21
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 7.50" w x 1.00" l,
- Binding: Hardcover
- 576 pages
- Used Book in Good Condition
About the Author
Patrick M. Fitzpatrick is Professor and Chair of Mathematics at the University of Maryland, College Park.
Most helpful customer reviews
14 of 15 people found the following review helpful.
Very Good Bridge between Calc and Analysis
By T. Hartwig
This book is a proof-based calculus and a first Analysis. I've had experience with a few Analysis books and this is much more approachable while still containing rigorous definitions and proofs. The author takes care to give intuitive examples and motivation. That being said, it would be difficult (but not impossible) for someone who wasn't familiar with writing and closely reading proofs. If you intend to attempt this book without having had some sort of math reasoning course or background you should pick up an introduction to proofs book - I suggest Eccles "Intro to math reasoning":
An Introduction to Mathematical Reasoning
9 of 9 people found the following review helpful.
it's fair, not great tho
By george
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.
6 of 6 people found the following review helpful.
it's not a bad text
By A Customer
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.
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