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Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)
PDF Download Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)
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Review
From the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."―MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." ―Allen Stenger (The Mathematical Association of America, June, 2008)
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From the Back Cover
For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.Review from the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."―MATHEMATICAL REVIEWS
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Product details
Series: Undergraduate Texts in Mathematics
Hardcover: 412 pages
Publisher: Springer; 2nd ed. 2013 edition (April 17, 2013)
Language: English
ISBN-10: 1461462703
ISBN-13: 978-1461462705
Product Dimensions:
6.1 x 0.9 x 9.2 inches
Shipping Weight: 1.6 pounds (View shipping rates and policies)
Average Customer Review:
3.7 out of 5 stars
29 customer reviews
Amazon Best Sellers Rank:
#74,867 in Books (See Top 100 in Books)
Consensus on this book changes depending on how you like to do things.Quick rundown. Real analysis (at the undergraduate level) is an axiomatization of all concepts of single-variable calculus.This is a class that changes in difficulty surprisingly according to how you learn it (took it at UC Berkeley, math 104 fall 2017). Our class used Principles of Mathematical Analysis by Rudin and it was a horrendous experience. Everything I write will be from that point of view.The good:Ross’ elementary analysis is a really forgiving textbook. He explains all results thoroughly (almost to a fault), but that’s good for people who are completely new to this. Topic-wise, he covers only the most basic parts of analysis, but he explains every theorem thoroughly and I really like how he starts with explaining the real numbers and keeps the scope of the book in real numbers. That’s one thing Ross does very well, he keeps the scope of the book very centered on the real number system and it’s properties (completeness, Archimedean property, Q as a dense subset, etc.) and it serves the reader very well. I thought it was a really easy read, but that’s probably because I’ve read through Rudin chapters 1-7 about 5 times. Not much to say content-wise, but it’s really solid. No one section is outstanding, but they are all of good quality and it feels like he’s trying to develop all concepts in equal weight.The bad:Not as much to say here, but I think he’s a little too verbose and not enough math going on. He has a tendency’s to almost converse as he’s writing the material to you and it makes it kind of bad as a reference text. If I need a theorem or part of a proof really quickly while I’m doing a physics problem or other math, I certainly do not want to read 3 pages explaining 2 theorems when the proof+theorems would take half the page at most. But that’s really a matter of opinion and what level you’re at. Obviously, if you’ve never seen analysis before, you want as verbose an explanation as possible so you have more guidance and less racking your brain for explanations. But if you’re already past that level, then it’s not as good a text for you. I also didn’t like that Ross didn’t develop topology of the real numbers initially. I feel like that belonged in chapter 2 after he developed properties of the real numbers. The idea of open and closed sets and compactness and boundedness are all really important and could have been used immediately to shorten up proofs and I think it’s generally a better way to have analysis students think. A point of view with topology is extremely valuable. Results from real analysis can be quickly generalized with little trouble and slight adjustment if defined topologically.Overall, I recommend for undergraduates who have never seen analysis before. It will have you sufficiently prepared for future math.
This book is well organized, sentence structure is clear, and there are plenty of examples. The author takes his time to explain analysis concepts. I would have probably failed my analysis class if I did not get this book. If you are looking for an easy to read beginners analysis textbook, get this one.
I got the kindle version. Definitely wish I had gotten a hard copy. You will be flipping back and forth between pages, and doing it on a kindle or PC is really tedious. Difficult content, but if you enjoy upper level mathematics, more power to you
Everyone learns differently, hence there will be different biases on different analysis books. However, I appreciated reading this book throughout real analysis as it wasn't too difficult.
A very good book
Absolutely fantastic book introducing real variables and their associated proofs.
nice book
Great book and delivery time
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