82 of 83 people found the following review helpful:
5.0 out of 5 stars
This is a Very Good and Interesting Book, January 22, 2008
This review is from: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide) (Paperback)
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.
This is an excellent book for people like my self who need to quickly come back up to speed on subjects that may have become a bit clouded over the years.
This also is an excellent book for people who are learning Calculus for the first time. If you are in the process of learning Calculus the key to really understanding the subject is to work countless problems until the mechanics, concepts, and procedures are firmly ingrained in your mind. For these people I strongly recommend a companion text called "The Humongous Book of Calculus Problems" by W. Michael Kelly. A serious student could learn the concepts and procedures from Mr. Banner's book and then work many of the one thousand problems provided in Mr. Kelly's book to gain proficiency.
After having read Mr. Banner's book, would I purchase this book again? The answer is a definite yes. The money was well spent.
I am anxiously awaiting to see some follow on books from Mr. Banner treating the subjects of Differential Equations and Complex Variables.
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75 of 76 people found the following review helpful:
3.0 out of 5 stars
From the perspective of self study, April 5, 2010
This review is from: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide) (Paperback)
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 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.
STRENGTHS:
-- 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.
WEAKNESSES:
-- 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.
BOTTOM LINE:
-- 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.
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46 of 46 people found the following review helpful:
5.0 out of 5 stars
5 Stars. This book finally makes calculus comprehensible., January 18, 2008
This review is from: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide) (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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