The Calculus Lifesaver: All the Tools You Need to Excel at Calculus

This books over-takes any other Calculus book by leaps and bounds. I took neither a Pre-Calculus nor AP-Calculus course, yet I found myself easily understanding everything. The tone of the book is playful, yet at the same time informative. The book after all is there to teach you about Calculus, NOT random tidbits of entertaining information. Of course there are some chapters that require one or two reviews but that is fairly expected since after all, it's Calculus! In addition, this book has 48 hours worth of video-lectures, corresponding to actual chapters, to watch. I mean, where else could you get that? I guess the greatest compliment I could pay this book would be to say that my once irrational fear and distaste for anything to do with functions, has slowly been replaced by a feeling of friendly acquaintance, and that my initial intimidation by the very word "Calculus", has been overcome by a sense of puzzlement at my previous unfounded apprehension. As you can probably tell, I can't recommend this book strongly enough. If you have no idea what Calculus is except for the fact that it would be cool to Master, this is definitely the book for you.

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.

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.

Many calculus textbooks are dry and teach calculus without giving the background motivation of why certain concepts have been discovered in a certain order in time and also how these concepts all relate to each other. Dr. Banner has done a great job at shedding light on the topic of calculus as it should be seen by anyone who really wants to understand the subject and walk away confident in their knowledge.