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

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 we agreed to put our heads together now and then. Since the textbook (Stewart) was none too friendly, we soon started assembling background materials to help us along. We bought several books, including this one; "How to Ace Calculus: The Streetwise Guide" by Adams, Thompson and Hass; and "The Humongous Book of Calculus Problems" by Kelley. In addition, we picked up a copy of "The Calculus 1 & 2 Tutor" DVD by Jason Gibson, and checked out several of the many tutorials on YouTube. Now that the semester is over, I would say that Banner's book was the most thorough yet friendly treatment of calculus. If you are motivated to learn calculus really well, and have the time to put into it, his book does a vastly better job than most textbooks in explaining the material in an accessible way. At more than 700 pages, however, it is not a quick read. If you're looking for quick help here and there on tougher topics, "How to Ace Calculus" or the YouTube videos provide a faster fix. A number of other reviews here mention that the book does not provide much in the way of practice problems, and recommend "The Humongous Book" for that. To be honest we felt we were exposed to plenty of problems in my son's course textbook, the various videos, etc., and did not end up consulting "Humongous" extensively during the semester. But this may be an area in which everyone's mileage may vary. Also, although we like Banner's book quite a lot, we found the technical quality of his online videos made them hard to watch. They were basically produced by setting up a camera in a classroom, and both the video and audio quality were problematic. Even so, as mentioned Banner's book is the most comprehensive treatment of calculus we found at a reasonably accessible level -- and if you are committed to mastering the subject, I'd recommend it highly. I wish I had something like it when I went through calculus for the first time four decades ago (in a pre-calculator era, slide rules and printed log tables in hand ...)

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 bought this book in 2012 when I found Adrian Banner's Calculus I&II videos online. At that time I just did the videos as a refresher for my rusty calculus (being out of college for > 10 years). I was hooked by his informal yet highly enjoyable discourses, and found I was learning/refreshing a lot of material in every video (each of which is ~ 2 hrs long!). Eventually I bought the book and finished reading it after I had completed the videos. I have since then picked up the book often and found reading chapters at random to refresh some concepts. In other words, if I am conveying that this is one of my references for college calculus concepts then that is quite correct. I finally decided to post a review to convey how this book helps me more than my other undergrad calculus textbooks. Basically Adrian Banner focuses on conveying the relevant concepts in a (very) informal, conversational style. He does not provide too many proofs in the main text though the main ones are provided in the appendix (e.g., limits, Extreme Value Theorem, Rolle's Theorem, Simpson's Rule etc.). The thing is that Adrian gives you the straight dope right off the bat without beating around the bush. Its like Cliff's Notes on steroids, once you go through the whole book I believe you will have a great grasp of the concepts of freshman undergraduate calculus (there is no coverage of multivariable or vector calculus and only a single chapter on differential equations). For me the outstanding feature is that I fail to point to anything in the book that is superfluous - ALL the material is relevant and if you do buy the book make sure you cover every page of the 30 chapters and 11 appendices. The only reason you will be less than satisfied is that there are no problem sets in the book. There are several examples provided, but you certainly are left feeling disappointed for the lack of good problem sets. But as other reviewers have pointed out, this can be remedied by for e.g., picking up Schaum's 3000 solved calculus problems. This book will give you the background necessary to solve those problems! Now if only Adrian Banner would publish books to accompany his multivariable calculus III and linear algebra videos!

This book is pretty good. It is chucked full of hundreds of pages of our lovely dear friend Calculus. I didn't end up using it much. Not sure if it is because the book wasn't all that helpful...or perhaps I just didn't need the extra help :p I am still glad I bought it and would recommend it to those who need material outside of what their professor gives, or outside of what they can understand from their textbook. What I didn't like was how big the book is because it is hard to take places. It is really, really, really fat. It doesn't fit well in a bookbag, purse, etc. nor is it simple to carry in hand. That is the biggest drawback for me and why I took a star off. Single subject course supplemental material should make sense for the average student in terms of size, portability, etc. The author of the book literally put all of calculus into one single book...so...If you are in Calc I, then you are carrying around information for Calc II and Calc III. When you're already annoyed at the book's bulkiness, carrying around all that extra material is annoying and not necessary. I know these are just my opinions though, and I encourage you to still get the book if you are struggling, because in the end the material/info inside the book is what truly matters. A chunky fat book that is annoying to carrying around is worth it overall to get that A.

I am currently in a beginning college calculus class. It is the last class I need to graduate with my associates degree in science and tranfer to finish my education. I have always been a BC student in math classes. Conceptualizing mathematics even on a basic level takes a long time. SO...when I finally made it to this last math class ever (I hope), I was really worried I would not graduate when I started to fail the class. Since I bought this book, my class has been SO MUCH EASIER! Not only do I understand what specifically we are being taught, but also what they do, why they do it, and what are actual real world applications of calculus. The Calculus Lifesaver is 100% easier to understand than the rediculously technical writing presented in my textbook and by my professor. This book allows me to better understand the technical language,too! I bought The Calculus Lifesaver along with The Complete Idiot's Guide to Calculus, 2nd Edition by W. Michael Kelley off Amazon. I seriously felt like i must be an idiot after weeks of attending class, studying with classmates, attempting to do the homework, and going to the math tutoring center 4x a week. Together, these books have been the single most effective thing I have tried. I start with The Complete Idiot's Guide to Calculus, 2nd Edition by W. Michael Kelley to tell me what exactly each topic (like Limits or Derivatives) is, what they do and how they relate to one another in VERY BASIC ENGLISH. it has a few problems worked out step-by-step and explains what is happening while the problems are being solved. There are also a few practice problems. This book lays out the basic concepts. Then I move to the Lifesaver. The Calculus Lifesaver is a bit more technical than the Idiot's Gude, but after reading a chapter in the Idiot's Guide, I had no problem going through the coinciding chapter in the Calculus Lifesaver. The problems in the Calculus Lifesaver are of varying difficulty and are similar to the type and difficulty of the problems I am expected to be able to solve and evaulate in my class. If you are like me and just cannot think of anymore things to do to pass your calculus class, I HIGHLY RECOMMEND you buy both the The Complete Idiot's Guide to Calculus, 2nd Edition by W. Michael Kelley as well as The Calculus Lifesaver: All the Tools You Need to Excel at Calculus... by Adrian Banner you will not be disappointed.

I purchased this book as part of a summer math review before starting a PhD program. As mentioned in a couple of reviews above, this book does not contain actual problem sets. However, it does contain the most thorough and understandable explanations that I have seen to date. Most math textbooks, including the ones I purchased to accompany MIT's OpenCourseWare, are inconsistent in their explanations. More often than not, the author will present a solution with little to no work, leaving the student to puzzle out how the author reached it (which can be especially difficult if the author simplified his equation differently or used methods that he considers "common knowledge"). Banner specifically sets out to counteract this approach, taking the extra space and time needed to elaborate on sample problem solutions and tie those solutions to methods covered elsewhere in the text. The result is an extremely readable, easy to follow guide to calculus. For good measure, Banner also throws in some nice tricks that students can use to tackle complex problems. The lectures that accompany this book on the website are also very valuable, but I love this book in part because it requires no lectures to be understood. Banner does not punt on any topic in the book, unless he feels that the material is beyond the scope (and even then, there is a good deal of complementary explanation in the Appendices). My only complaint is that my calculus studies will take me beyond the Lifesaver. If Banner ever wants to write a book that presents some Calculus II material that is useful for graduate study (partial derivatives, for instance) or Linear Algebra, I will happily buy it.

This book was awesome. It helped me ace my second semester of calculus. Unfortunately, it doesn't really delve into multivariable calculus but it has done everything I wanted and more. Not only are the explanations and proofs great, but I was surprised by how well-written it is. Many math resources suffer from poor writing that do a terrible job at being clear about which variable they are discussing in which sentence. I found myself enjoying this and comprehending it well. My professor even let me teach my class a few times because I understood some stuff so well thanks to how well this book explained things. I was able to completely reproduce a long proof from this book in front of my class, not because I memorized the proof, but because I understood that well what the book had taught me. The professor gave me a ton of extra credit for teaching the class and I think my overall grade in the class ended up being like 120% in what most people told me was supposed to be the hardest calculus class. I'm getting a math minor (physics major) so I guess I'll find out how much harder it can get. I highly recommend this book to anyone interested in calculus.

This is the best calculus book I have ever read or used. I took Calculus I three times. The textbooks were not worth the lighter fluid I used to burn them. (I survived with Calculus Made Easy, by Silvanus P. Thompson F.R.S., published in 1910, and still in print.) Calculus Lifesaver (CLS) turns 180 degrees away from most textbooks. It is clearly written in an informal style. Princeton University Press has 24 free two hour lectures by the author on its website, press.princeton.edu/video/banner, which they say have been downloaded 92 million times as of 2010. CLC was published in 2007. Calculus Lifesaver has no exercises/problems at the end of sections and chapters, it is 718 pages of detailed explanation with exercises included in the text for the reader to test his understanding. Nevertheless, CLS is not a painless pill for acing a calculus course. One has to have a good knowledge of precalculus: algebra, geometry, trigonometry, and concentrate hard. Working many, many problems is absolutely necessary. 3000 Solved Problems in Calculus, Elliot Mendelson, Schaum's Solved Problems Series looks good and is inexpensive. Adrian Banner, the author, received his bachelors' and masters' degrees from the University of New South Wales (Australia); his Ph.D from Princeton University. He became CEO of the Janus Intech Mutual Funds in 2012. Intech uses mathematics extensively in selecting securities for its portfolios. IMO, 5 star ratings are given far too often,but the Calculus Lifesaver deserves one, without a doubt.

It's really a life saver in calculus. I am reading calculus after 20 years completing my Degree. The author has gone step by step, brushing up basics of functions, trignometry, intro to limits and then how to differentiate, etc. Really good book, worth buying.

One of te best books of calculus I've seen. After it, the next one should be "Calculus" writen by Kline. With both, a strong fundamental foundation will have been built

Super bouquin, malheureusement en anglais (pas de traduction connue en français, dommage) explique de manière détaillée tout ce qu'il faut comprendre pour pratiquer le calcul I et II. Pas besoin d'être un grand matheux, le niveau 1ère S ou T S est suffisant mais il faut prendre son temps et revenir en arrière quand on n'est pas tout à fait au point. Cela se lit tout seul (presque) comme un roman. ah, ah, j'exagère...Toutefois le format kindle n'est pas pratique, les formules sont écrites trop petit. Je vais donc commander la version papier qui est en grand format. Après avoir fini cet ouvrage il faudra compléter par un autre manuel avec des centaines d'exercices corrigés dans la série Schaum's outline of calculus ou encore Humongous book of calculus

I found out about this book by watching Adrian Banner's online lectures. The lectures are a wonder. Exceptionally easy to follow; assume little prior knowledge; do not miss out crucial steps that would be obvious to some (or many?) but are not obvious to me. The book is just the same and I'm very impressed. Like so many other physics and maths books, reading it on the Kindle Fire HDX is a miserable experience. Better than some but the problem is the same: Equations are tiny and do not zoom with the text. Amazon is very negligent in not providing a decent reader for this tablet. The iPad one is fine. Also fine on the PC. But not on the Kindle Fire HDX 8.9. (A Kindle for %^&* sake) Anyway - I always try to get this comment in and I would not want to mark the book down. I also happen to know that authors are just as frustrated as I by the obduracy of Amazon in respect of its arcane (I'm told) publishing process.

Purchased this from Amazon in Mar 2025. Excellent book on Calculus. However the print quality from the publisher leaves much to be desired. Multiple pages in the first 4 chapters contain very faint printing like the printer was running out of ink, as well as many pages containing smudged printing. The rest of the book was ok but overall the print was too light for my liking. Felt like the publisher was trying to save ink. Even though the book was fairly priced, it is not an excuse for such terrible printing. Really ruins the reading experience.