Customer Reviews

Advanced Calculus: A Course in Mathematical Analysis

5 star:		(1)
4 star:		(3)
3 star:		(6)
2 star:		(2)
1 star:		(3)

 

 

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.

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.

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.

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.

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.

OK, it has a few typos, it is kinda hard to read and not very rigorous at some points, but all in all it's still an useful book for an intro to intermediate level analysis course--and I found it concise and very thorough, especially since it has a couple chapters on one variable analysis.

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 "mistry" in this book. It might not be the best in the world, but I personly think that is a great book to get start in the analysis course.

I can tell why many people dislike this book. Please, this is not an introductory calculus book. See the title! It says "Advanced" calculus! Advanced calculus is supposed to engage in rigorous arguments of theorems and their proofs. And the author did a great job, I tell you. Not many examples? Come on, you are supposed to have seen lots of examples in your earlier calculus classes!

Let me tell you: It's not that this book is bad; most people just hate rigorous mathematical arguments as soon as they start seeing them in their advanced calculus text books. That's all. This book is very compherensive and especially author did a great job in presenting real functions of multi variables by using vector terminologies.

If this is a text book assigned in your class, stick to it and adopt yourself to the real world of math. It takes time any way. If you still hate it, just do your best to finish the class and prepare to get a job.

I have used this as a textbook several times. Fitzpatrick's book is very clear and well written. The progression is rather gentle. This is especially important for many students struggle with mathematical analysis the first time around. I only wish Fitzpatrick had included more problems, especially more challenging problems.

Proposition 1: Fitzpatrick is a moron. Proof: Easy. Turn to any page in this book and read it.

This has got to be the most expensive analysis book in the world -- yet it's worthless! The $10 Dover books are so much better. Instead of wasting your money on this book, buy Kolmogorov & Fomin's "Introductory Real Analysis" or Hasaar and Sulivan's "Real Analysis".