- 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: 4.5 out of 5 stars See all reviews (153 customer reviews)
- Amazon Best Sellers Rank: #27,090 in Books (See Top 100 in Books)
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The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guides) 1st Edition
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"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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Top Customer Reviews
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 princeton.edu. 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.
It's from the perspective of self-study that I write this review; I used this book as a primary source for learning calculus. In the interest of full disclosure, I'm still about 50 pages from finishing.
While The Calculus Lifesaver definitely teaches the material in an often accessible manner, there are some issues. The main drawback is a lack of practice problems. While there are lots of examples, many of which are dealt with in a step by step manner, typically there is only one example given for each variation or problem type. This means that the reader will sometimes be plunged headlong into a problem type, when a gentler approach would have been more helpful. Fortunately following the online video lectures will ease much of this.
Let me just say that calculus is hard. It is hard but not impossible. This is coming from someone who began with basic algebra less than two years ago. Often calculus subjects take time to sink in, so expecting to cover 20-30 pages per day is not reasonable for anyone broaching calculus for the first time (some days I could barely do 5). Be patient and give concepts time to assimilate. Often a day or two after banging your head against the wall can make all the difference. If you're having trouble with the material in the book, shift gears to the video lectures. For me, this often made a big difference in my ability to digest the material. I prefer seeing and hearing first (then sleeping) then review and problem solving via the book.
A review like this will generally depend on how well the reader believes they are learning, even mastering the material. For me, working through The Calculus Lifesaver cover to cover, I often found myself lacking confidence in my ability to solve calculus problems. And although there are many diagrams, more would have been justified. Often I had trouble following the descriptions and notation, where most likely a few more illustrations would have helped. For the first part of the book, chapters 1-17, I followed up by studying Paul Dawkins' online calculus notes, available at tutorial.math.lamar.edu. These were very helpful for practice problems, not to mention a different perspective on notation and proofs -- there are also cheat sheets for trig identities, derivatives, and much more, and everything is available in PDF format. I intend to use Paul's notes for calculus 2 as well (essentially chapters 18-30 in TCL) which I'll begin shortly.
There is no doubt that The Calculus Lifesaver will teach you the concepts of calculus, and make digesting other calculus material much easier. However, it's unlikely to be sufficient as a solo guide unless you've taken the subject in the past. In that case it will make for terrific review and a great reference. This book will best benefit those who are already enrolled in a calculus course, and are having trouble with their text or teacher. For those going solo, it's still a good book, but it doesn't quite stand on its own.
This is one of the best books to learn the intricacies of calculus, I have come across. Banner takes you step by step through the complexity of solving the problems. His explanations are very clear and the solutions are provided for all the sample problems. This is a must-read book for those who want to master calculus.
Now if you would like more problems to solve (with solutions), I wholeheartedly recommend The Humongous Book of Calculus Problems: For People Who Don't Speak Math by Kelley, W. Michael (2007) Paperback. This tome has the comprehensive solutions to about 1000 problems. The nice thing is that you can learn the theory in Banner's book, and then go to the corresponding chapter in the "Humongous" book for more practice problems. To make this easier, I have compiled a table for these books. (Too bad Amazon doesn't support formatting here)
Calculus Life Saver........Humongous Book of Calculus Problems
Chapter 1..................Chapters 1 - 6
Chapter 2..................Chapters 7 and 8
Chapters 3 and 4...........Chapters 9 and 10
Chapter 5..................Chapter 11
Chapters 6 and 7...........Chapters 12 and 13
Chapters 8 - 14............Chapters 14 - 16
Chapters 15 - 17...........Chapters 17 - 19
Chapters 18 - 21...........Chapters 20 - 21
Chapters 22 and 23.........Chapters 26 and 27
Chapters 24 - 26...........Chapter 28
Chapter 27.................Chapter 24
Chapter 29.................Chapter 22 and 23
Chapter 30.................Chapter 25
With these two books, you will be truly a master of calculus.