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The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide) [Paperback]

Adrian Banner
4.6 out of 5 stars  See all reviews (93 customer reviews)

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Book Description

March 25, 2007 0691130884 978-0691130880 1

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.

All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.

The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.

  • Serves as a companion to any single-variable calculus textbook
  • Informal, entertaining, and not intimidating
  • Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
  • More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
  • Theorems and methods justified and connections made to actual practice
  • Difficult topics such as improper integrals and infinite series covered in detail
  • Tried and tested by students taking freshman calculus

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The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide) + The Humongous Book of Calculus Problems
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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 Inside Flap

"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

--This text refers to an out of print or unavailable edition of this title.

Product Details

  • Series: Princeton Lifesaver Study Guide
  • Paperback: 728 pages
  • Publisher: Princeton University Press; 1 edition (March 25, 2007)
  • Language: English
  • ISBN-10: 0691130884
  • ISBN-13: 978-0691130880
  • Product Dimensions: 10 x 7.1 x 1.5 inches
  • Shipping Weight: 3.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (93 customer reviews)
  • Amazon Best Sellers Rank: #10,870 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
116 of 117 people found the following review helpful
5.0 out of 5 stars This is a Very Good and Interesting Book 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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156 of 161 people found the following review helpful
3.0 out of 5 stars From the perspective of self study April 5, 2010
By James A
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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59 of 59 people found the following review helpful
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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28 of 28 people found the following review helpful
5.0 out of 5 stars A great easy-going introduction to the subject March 25, 2008
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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Most Recent Customer Reviews
3.0 out of 5 stars Trying fo over-simplification?
Disappointed in the limited help offered on my topic of interest, and in his effort for simplicity, the explanation was too simplistic. Read more
Published 2 days ago by Bob K
5.0 out of 5 stars Very helpfull!
explanations are compose in a easy to understand format, also it help a lot if you read it while in calculus lessons
Published 2 months ago by arthur andrade
5.0 out of 5 stars Saved me up until calc 3
This book was enough to help me through calc 1 and 2 but not calc 3. I still HIGHLY recommend. The author does not use complicated terms or definitions - he just says it, why it is... Read more
Published 2 months ago by Joe C
4.0 out of 5 stars Good book. Additional online content is up reachable
The video lectures they provide are offline as of this writing and have been for some time. I'd rate higher if this were fixed.
Published 2 months ago by D. Messer
5.0 out of 5 stars Great practical guide to calculus
I checked this out of the local library to help me with my tutoring. After using it, I had to get my own copy. Read more
Published 2 months ago by Akcloudwoman
4.0 out of 5 stars Helpful book
It is truly a lifesaver. It saves me in calc 1 &2 college classes. Easy to understand and it has great suggestions! I highly recommend this book in college.
Published 3 months ago by Maggie Qiu
5.0 out of 5 stars Good!
Just the book needed for this course and I would thoroughly recommend it. Easy to understand as well. Try it!
Published 3 months ago by JEL
5.0 out of 5 stars The Best!
This book, combined with Dr. Banner's youtube (or MIT OCW) videos can save you from the maelstrom of confusion that is Calculus II. Read more
Published 4 months ago by Brandon J. Osborn
5.0 out of 5 stars A thoughtful and friendly overview of Calculus 1 and 2
Last fall my son enrolled in Calculus 1 as a college freshman. I thought that, having taken calculus 40 years ago, it might be an interesting time for me to try a refresher -- so... Read more
Published 4 months ago by Frank
5.0 out of 5 stars Fantastic!!
What my grade would have been if Ihad had this book available when I was in college. I never truly understood the Calculus until I started reading this bood. Read more
Published 4 months ago by Bernard K. Dack
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