Customer Reviews

Advanced Calculus

5 star:		(5)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

This is a very good book. I recommend this book for anyone who wants to learn calculus on a rigorous level.

This text is very readable. Unlike most analysis texts out there that focus on rigor without any intuition, Fitzpatrick strikes the perfect balance. The topics are well spaced (via the sections) and exercises are accessible.

I also recommend this for non-math grad students like econ, stat, and engineering.

The section on Multivariate calculus is the best I have seen out there.

If you went through an analysis course in undergrad and did okay but never really grasped the concepts and

how they all fit, then this is the book for you. But just that you know this is not a book on the level of Royden.

To some extent its a little bit on the level of Rudin. (maybe a little bit lower)

This is my first time writing a recommendation for a book review, but I felt obligated to mention how useful

this book has been to me.

I will repeat If you have a strong analysis background you may want a different book with less intuition and examples. But if you are in the middle and you feel like you want a comprehensive, cohesive and readable real analaysis text then this is the right book for you.

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

Comes in handy for my class. I love math and this book will help. This book will put me on my way to my goal in mathamatics.

There are so many errors in this book and the exercises for first few chapters are relatively difficult compared to the later ones

I read it myself as a bridge between calculus and mathematical analysis. This book is a rigorous mathematical book, and it takes steps in developing theorems and results. The development of topics provides intuition to the readers. (e.g. the introduction of Jordan domain in chapter 18 provides a primitive idea of Riemann integrability in higher dimensional spaces.) As an expense to this end, this book becomes a bit wordy. It could be used as the text for a honor calculus course, or it could be used as a companion text for advanced students in a regular calculus course. In my opinion, it is very suitable for self study.

The book is written in a clear, concise, accessible style.

However the are too few examples and no answers to selected exercises. You might want to buy a supplementary book (such as Schaum's Outline) or look up additional examples online.

With this book Fitzpatrick has taken the time and care to present the most important topics from Adv Calc in a clear, readable way. Furthermore, it is a book that teaches you to think better about math rather than a book that feeds you formulas. I consider myself a talented math student and I have benefited immensely from this book.

I purchased this text because the text used in my Advanced Calculus II course was opaque to me (it was Friedman's Advanced Calculus). I immediately improved my understanding of calculus on R^n. Now I have gone back to the beginning and read Fitzpatrick's treatment of Adv Calc I material, and I realize that it is far superior to the book I used (which was Gaughan's Introduction to Analysis, a good but not great book). I cannot recommend Fitzpatrick's text enough. It is worth the money.

Here are the things I have understood more clearly from this book just in the last month: the nature of transcendental functions (trig and exp) as solutions of simple differential equations; the meaning, the importance and the depth of the Fundamental Theorem of Calculus, especially the role of the Second Fundamental Theorem of Calculus (differentiating integrals) in the solution of general differential equations; a proof that the number e is irrational; the proof of Newton's generalized binomial expansion; the motivation for Taylor Series; the proof of the Lagrange Remainder Theorem for Taylor Series as well as the Cauchy Integral Remainder Theorem for Taylor Series. I could go on and on but I'm getting tired of writing and I'd rather go back and read Fitzpatrick's book some more.

I'd give it 4.5 stars if I could. This is the text used in my Advanced Calculus class, a class which was my first really rigorous proof class and which serves as "discouragement" to students who aren't cut out to be math majors.

Fitzpatrick begins by giving the field and positivity axioms for the real numbers. Then we get the principle of mathematical induction, the Archimedean principle, and the completeness axiom. From there, we build the whole way up to derivatives--the quarter ended after the mean value theorem (Ch 4).

It is a great experience, helped along by really great exercises, and a great instructor. It's not easy, but I can say that I really appreciate the completeness of the real numbers, and am probably 5 IQ points higher than when I started! Fitzpatrick's clear (considering the material), rigorous and self-contained text helped make that happen.

I would, however, subtract half a star, since some of the proofs he presents are a little idiosyncratic and more complex than they need to be, for example the proof of the product property of limits. I suspect the intent is to display some diversity of reasoning, but I didn't really appreciate it. Similarly, there are things that could be presented differently, or named differently, i.e. the Bolzano-Weierstrass theorem is never called such, and is treated as a waypoint on the way to the sequential compactness theorem.

But these are really, really small gripes. Overall, the book is pedagogically excellent, with great exercises. After a hectic quarter with this book, I am much more confident in my ability to do math, I have a deeper understanding of the real line and what we can do on it, and can think with greater clarity and depth in general.

this is a good book in a sense that if you've already done rigorous proofs before. This book targets undergrads who've taken single variable calculus up to multivariable calculus. This book is meant to be taught in two semesters. I've never really done proofs except for simple proofs like trig or so. This book is really rigorous and i would not recommend it for those that have not taken a proof class. The author assumes you know the basics of proofs already and starts off with sequences and limits of sequences and introduces the the completeness axiom. One frustration i had with this book was trying to understand half of his definitions. I could not find a solutions manual so I don't even know if most of my solutions are correct. So if you've never done proofs, stay away from this book until you're comfortable and want a challenge. The only reason i have this book is the class i'm taking requires this book. If you're really good at proofs then this might be your favorite book. IF your weak at proofs then try looking for an easier book that spoon feed you cause you'll pull out all your hair out before you even get halfway. But don't get me wrong, this isn't a bad book; its more rigorous.