The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides) 1st Edition

124 customer reviews
ISBN-13: 978-0691130880
ISBN-10: 0691130884
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Editorial Reviews


"Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, The Calculus Lifesaver is a welcome addition to the arsenal of calculus teaching aids."--MAA Online

"This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly."--J.T. Zerger, Choice

"Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant."--Mathematics Teacher

From the Back Cover

"I used Adrian Banner's The Calculus Lifesaver as the sole textbook for an intensive, three-week summer Calculus I course for high-school students. I chose this book for several reasons, among them its conversational expository style, its wealth of worked-out examples, and its price. This book is designed to supplement any standard calculus textbook, thus my students will be able to use it again when they take later calculus courses. The students in my class came from diverse backgrounds, ranging from those who had already seen much of the material to others who were struggling with basic algebra. They all uniformly praised the book for being one of the clearest mathematics texts they have ever read, and because it reviews the required prerequisite material. The numerous worked-out examples are an ideal supplement to the lectures. The only difficulty in using this book as a primary text is the lack of additional exercises in the text. However, there are so many sites and sources for calculus problems that this was not a problem. I would definitely use this book again."--Steven J. Miller, Brown University

"Banner's book is a chatty, user-friendly guide to calculus that will be a useful addition to the resources available to students. Banner does an exceptionally thorough job while maintaining an engaging style."--Gerald B. Folland, author of Advanced Calculus

"This is an engaging read. Each page engenders at least one smile, often a chuckle, occasionally a belly laugh."--Charles R. MacCluer, author of Honors Calculus

"This book is significant. The author's attempt to give an 'inner monologue' into the thought process that is needed to solve calculus problems rather than just providing worked examples is novel and is in line with his purpose of helping the reader get a deeper understanding of calculus. The book is well written and the author's examples are clear and complete."--Thomas Seidenberg, Phillips Exeter Academy


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Product Details

  • Series: Princeton Lifesaver Study Guides
  • Paperback: 752 pages
  • Publisher: Princeton University Press; 1 edition (March 25, 2007)
  • Language: English
  • ISBN-10: 0691130884
  • ISBN-13: 978-0691130880
  • Product Dimensions: 1.8 x 7.5 x 10.2 inches
  • Shipping Weight: 3.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (124 customer reviews)
  • Amazon Best Sellers Rank: #13,600 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

187 of 192 people found the following review helpful By James A on April 5, 2010
Format: Paperback Verified Purchase
There are a few things to note about this book:

1) It covers two semesters of calculus (math 103 and 104 equiv. at Princeton).
2) It's accompanied by about 48 hours of online video lectures, available at the book's website, via These lectures are of a "calculus review" nature, and are not the primary lectures for a calculus 1 or 2 course.
3) Those seeking a calculus review or a supplemental helper to an existing calculus course will benefit most; those doing self-study will likely need additional material, especially for practice and skill building.


-- Comes with ~48 hours of online video supplement.

-- Explains most first year calculus concepts in an accessible manner; there are a full two semesters of material in this book.

-- Concepts are accompanied by worked examples.

-- A value at twice the price for anyone seeking a calculus refresher or a supplement to an existing course/text.


-- Lacks progressive reinforcement of many concepts; the reader is generally referred to previous chapters/sections for review.

-- No practice problems or skill building exercises; only one worked exercise per variation is usually provided.

-- Could benefit from a few more diagrams amidst descriptions and notation.


-- If you are currently enrolled in calculus or looking for a review or a reference, chances are you'll love this book (note the 5 star reviewers).

-- If you are a solo student looking for a replacement for classroom study, you may find this book a little less than satisfying.
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129 of 131 people found the following review helpful By Richard N on January 22, 2008
Format: Paperback Verified Purchase
I purchased The Calculus Lifesaver book written by Adrian Banner when I discovered that my knowledge of Calculus was beginning to get a bit rusty and I wanted to clear up some of the mathematical cob webs in my head.

I read Mr. Banner's book cover to cover in a little less than 4 weeks. The book has 30 chapters consisting of 702 pages and has 46 pages of appendices.

Although the book illustrates each mathematical subject area with a great many solved problems, it does not contain any problem sets that are specifically intended for the reader to solve. This could be a draw back for some and it probably prevents this book from being used as a class room text, but for my purposes it worked well.

Mr. Banner gives an in depth treatment of all the standard stuff like limits, differentiation, integration, Taylor and MacLaurin series, and he gives an overview of topics such as parametric equations, complex numbers, arc lengths, surface areas, and volumes and differential equations.

All in all I feel that this book was well written, easy to read, and interesting. Mr. Banner's approach is quite different from the classical, almost stuff shirt approach that was typical of the math books that I used way back in my under grad days. He does interject some colorful language from time to time which initially surprised me, and then later on amused me, and always kept me interested.

This is an excellent book for those students looking for a second source to review for an up coming midterm exam. Treatment of specific subject areas is clear, concise and can be read and understood in short order.
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69 of 69 people found the following review helpful By JMS on January 18, 2008
Format: Paperback
I have reviewed dozens of calculus textbooks, and all are noble attempts at communicating something that is problematic for many students in simple-enough terms to be comprehensible. But most calculus textbooks books fail in their effort at simple communication. This book succeeds in that effort marvelously. The examples are worked through thoroughly so that when the reader has finished a section, he actually understands it. The concept of a function is explained as a sort of "machine" that transforms an input into an output. The concept of a limit is again clearly explained more simply and straightforwardly than I have seen it explained anywhere. The book is nevertheless non-trivial; it is solid and certainly not a "Calculus for Dummies" book. It is an easily understood but substantive introduction to calculus. If you've tried calculus several times using other books and in the end given up because the authors inevitably lost you at some unmarked turn in the road, get this book and give it a one more try. I think you'll find you are impressed with the resulting clarity of your understanding. Adrian Banner is gifted at explaining calculus.
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37 of 37 people found the following review helpful By Antonio Cangiano on March 25, 2008
Format: Paperback
Before I even start talking about the actual book, let me just tell you that this is a steal. I don't know what the publisher was thinking, but a 750 page, recently published book on Calculus never sells for such a low price. On Amazon it sells for $16, which is a ridiculously low price for this 5 star tome. The average Calculus book is far from cheap, so this excellent guide is a pure bargain. Now, let's talk about the content of the book.

I'm very exigent when it comes to Calculus books and usually like a very formal and rigorous style. Most people don't. Many tend to like accessible books that speak to them in plain English. And this book is marketed as such. This is supposed to be an extra aid, on top of a regular textbook, to make Calculus more accessible. However, it stands on its own, thanks to its comprehensiveness and clarity. If commonly adopted Calculus books puzzle you, or if you are studying on your own, this is the book for you. Every step is clearly explained and it doesn't fail when it comes to covering all the pre-requisites/fundamentals. Thanks to its style and approach, pretty much anyone who's willing to learn, will. I'd even recommend it to high school students who wish to learn more about this subject, because I don't think they would have any trouble following along. The tone is informal, friendly and often even funny, making it one of the least boring math books I've ever read. I highly recommend it to those who are struggling and would like to really understand the subject.
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