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The Calculus Lifesaver: All the Tools You Need to Excel at Calculus: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides) [Kindle Edition]

Adrian Banner
4.6 out of 5 stars  See all reviews (118 customer reviews)

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  • Print ISBN-10: 0691130884
  • Print ISBN-13: 978-0691130880
  • Edition: 1
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Book Description

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
  • 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

Editorial Reviews


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


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 )

Product Details

Customer Reviews

4.6 out of 5 stars
4.6 out of 5 stars
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Most Helpful Customer Reviews
182 of 187 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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128 of 130 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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68 of 68 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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37 of 37 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
5.0 out of 5 stars Five Stars
Received as expected!
Published 10 hours ago by Cesar
2.0 out of 5 stars Makes me fall asleep
Maybe it's a good book but it did not do it for me. I've been out of school for a while and needed something to help me review some of the calculus I last saw nearly a decade ago. Read more
Published 13 days ago by A. ENYIOMA
1.0 out of 5 stars One Star
About 2 inches thick...not the thing to throw to a drowning man!
Published 1 month ago by Patricia MacDonald
5.0 out of 5 stars Five Stars
The best book on Calculus. Period
Published 1 month ago by oludayo kehinde
4.0 out of 5 stars but it appears to be written in an easy to understand manner
I haven't read it yet, but it appears to be written in an easy to understand manner. Thank you
Published 2 months ago by Gerald L. Johnson
4.0 out of 5 stars Four Stars
Very good book.
Published 2 months ago by Matheus Fontaine
3.0 out of 5 stars Do *buy* the *hardcover* version. Do *not* buy the paperback...
...unless u enjoy attempting to glue a book back together from
a pile of pages. After buying thousands of books in my life,
i can safely say that the binding on this... Read more
Published 3 months ago by zuzu
5.0 out of 5 stars Awesome book!
Super helpful book! The author also has video lectures online. Helped me pass my calculus series. I am forever grateful!
Published 4 months ago by Jeffrey wayne weber
5.0 out of 5 stars Become a Calculus Master
If you are looking for a very good book to enhance your calculus skills, this is the book. Adrian Banner covers pretty much what you will see in Calculus I & II. Read more
Published 4 months ago by Randolph Eck
5.0 out of 5 stars Awesome Book.
Amazing book for reviewing for your Calculus 1 and 2 exams, as well as for a self learner. The author is clear and very explicative in all the topics covered.
Published 4 months ago by Marl Ferd
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