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Advanced Calculus: A Course in Mathematical Analysis [Hardcover]

Patrick M. Fitzpatrick
2.9 out of 5 stars  See all reviews (16 customer reviews)

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Advanced Calculus Advanced Calculus 4.5 out of 5 stars (15)
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Book Description

August 21, 1995 0534926126 978-0534926120 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.

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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
  • Average Customer Review: 2.9 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #956,567 in Books (See Top 100 in Books)

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Customer Reviews

2.9 out of 5 stars
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Most Helpful Customer Reviews
9 of 9 people found the following review helpful
3.0 out of 5 stars it's fair, not great tho October 21, 2003
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.
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6 of 6 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 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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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
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.
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7 of 9 people found the following review helpful
3.0 out of 5 stars Not as bad as everyone says November 25, 2003
By Amanda
I feel like I have to defend this book a little having used it during my undergraduate years. Sure there are some valid complaints, Fitzpatrick's notation can be poor sometimes and his development of one variable analysis is needlessly cluttered with unnecessary machinery.
Those complaints aside, this text is quite thorough and does a good job motivating and explaining most of the big ideas (which is something that many analysis texts often refrain from doing unfortunately).
If you read the reviews on this page you'll see many complaints that Fitzpatrick doesn't baby his readers by cramming tons of examples into the text to illustrate each concept to death. He will also often omit the details of a proof, only giving a sketch and challenging the reader to complete the proof on his or her own. I agree that this can be a bit aggravating if you use this in your first class in rigorous mathematics. But if you've got a few upper level math classes under your belt and these things still bother you, then perhaps mathematics is not the field you should be specializing in.
OVERALL OPINION: this is not a bad book for a second undergraduate coarse in analysis. If you are looking for a good single variable analysis text and have not done much in term of rigorous math before, then there are plenty of more user friendly texts out there. If you are looking for a thorough and challenging overview of undergraduate analysis, then this text is one of the many possibilities you should consider.
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4 of 5 people found the following review helpful
By A Customer
Background: B.S. Econ, B.S. Math, Master's Econ classwork, starting Ph.D. Econ Fall 2004. Took undergrad metric spaces and single-var analysis and some graduate real analysis in the past.
Sat in on a quarter of undergrad Multivariable Analysis (a previous offering of the same class was cancelled last year before I graduated with the math degree). This book was the assigned text. I did all the class homework. The class covered the Differential part of the multivariable chapters, not the integral part, but skipped the metric spaces chapter.
I liked the book despite its several but ususally easily discernable typos. It covered the Multivariable stuff in Rn efficiently for me as an introduction. I can envision many uses in math and econ for the material and approaches used in the book. Now I'll go on to other texts that cover the same material and more but with a higher level of mathematical sophistication (like the Dover published, C.H. Edwards, Calc of Several Variables book they tried two years ago). Also, I'll return to some Optimization texts to get more out of them.
In order to get the most out of the multivar part of the book, you definitely need to have good comfort with concepts and proof techniques used in Single-var analysis and in basic set theory.
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Most Recent Customer Reviews
5.0 out of 5 stars This book is great.
I may disagree with many reviewers. For me, this book is great. The first thing you have to know is that this book is "Mathematical Analysis" book, not just multivatiables... Read more
Published 17 months ago by Thanawath1978
3.0 out of 5 stars Decent, but get something else
I've read over 75% of the book and worked through most of the problems. I have to say this book is ok at best. Read more
Published on April 23, 2006 by mathistheway
2.0 out of 5 stars A bad introduction lacking in "good proofs"
According to my instructor for this course, I would not receive an A (or probably a B) if I wrote my proofs like Fitzpatrick does. Read more
Published on April 5, 2005 by Silo 51
4.0 out of 5 stars A good mathematical analysis book for beginners
I have used this as a textbook several times. Fitzpatrick's book is very clear and well written. The progression is rather gentle. Read more
Published on October 14, 2004 by R. Schinazi
5.0 out of 5 stars People! Advanced calculus is not calculus!
I can tell why many people dislike this book. Please, this is not an introductory calculus book. See the title! It says "Advanced" calculus! Read more
Published on August 19, 2003
1.0 out of 5 stars Not a great book
This book is a bad introduction to mathematical analysis. The most serious problem is its lack of examples. Read more
Published on April 15, 2003
2.0 out of 5 stars this book
This book isn't all that great. You CAN learn from it of course, but it seems to lack rigor and the way he defines a lot of concepts is completely unclear. Read more
Published on September 17, 2001 by fred jack
3.0 out of 5 stars A really easy book to follow
The "Advanced Calculus" is one of the easiest text book on analysis you can find. I agree there are several typos, but the idea is clear & there is no... Read more
Published on April 22, 2000 by PoJen Huang
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