普林斯顿微积分读本（修订版）

by [美]Adrian Banner, 杨爽 (Translator), 赵晓婷 (Translator)

本书阐述了求解微积分的技巧，详细讲解了微积分基础、极限、连续、微分、导数的应用、积分、无穷级数、泰勒级数与幂级数等内容，旨在教会读者如何思考问题从而找到解题所需的知识点，着重训练大家自己解答问题的能力。
　　本书适用于大学低年级学生、高中高年级学生、想学习微积分的数学爱好者以及广大数学教师，即可作为教材、习题集，也可作为学习指南，同时还有利于教师备课。

Genres: Mathematics, Science, Calculus, Nonfiction, Textbooks, Reference, Education

668 pages, Paperback

First published March 5, 2007

Reviews

[Bob · Rating 5 out of 5]

I bought this to go through calculus to gain a thorough understanding. About 40 years after taking it as an undergrad. I learned a great deal from this book, and I feel it was well worth the vast hours it took to go through all the material.

[Q* := Q - {0} · Rating 3 out of 5]

Clear exposition of single-variable calculus with plenty of worked examples. Stands as a noteworthy supplement to a standard Cartesian-centric, single-variable textbook, but its treatment of other mathematical areas is lacking, making it difficult to recommend it (even at nearly 700 pages!) as a stand-alone reference. The calculus of polar and exponential forms, for example, feels very rushed and incomplete, and the brief section on complex numbers doesn’t even mention DeMoivre’s theorem when discussing complex exponentiation and nth roots.

In the end, the “Calculus Lifesaver” has some redeeming qualities and will be helpful as a study aid for a Calc I/II seminar, but you’d do much better to stick with the classic textbooks as the meat of your training (e.g., Stewart, Varberg, etc.).

[Snorlax · Rating 5 out of 5]

I think if you want a textbook that is easy to understand, this is one of the best. You probably can't find a simpler one. The author tries his best to make sure you understand the concepts, thus sometimes he has to go through some real life examples and try to explain from different perspectives.

I think this book is good for :
* High school education on Calculus.
* Self-study.
* Your first Calculus book.
* College education, though it has a good competitor : https://www.goodreads.com/book/show/1.... I think read this book first, then Thomas' calculus is the best learning path to build a solid fundamentals about Calculus.

There are some places that can be improved:

1 . On page 45, it's better say that the limit doesn't exist than saying the "limit is infinity", as infinity is not a valid limit value.
2. Sometimes it's better to show the proof the formula when the proof is not verbose. For example, the Quotient rule on page 106.

[Nicole · Rating 5 out of 5]

Literally saved my life.

[John Michael Strubhart · Rating 3 out of 5]

If the topics in the extensive Appendices had been included within the relevant chapters and some practice problems had also been included, this would have made a particularly good textbook. The author is careful to point out that this is essentially a review book, and as such, it is excellent. If you have the paper edition or a quality PDF version, read no further - this is an excellent calculus book.

My two very big complaints are that...

(1) This is a very poorly formatted kindle book. I would point the reader to The Feynman Lectures on Physics as an example of how to properly format a technical Kindle book. As I understand it, that 3 volume collection uses scalable vector graphics to display equations. It involves much more work to be sure but doing so would justify an increase in the price of the book. The Lectures are not cheap. The Calculus Lifesaver was cheap when I bought it. I see that it is now an e-text book and much more expensive. Hopefully, it's a pdf book. Don't buy it if it is not.

(2) Rather than gradually increasing the difficulty of guided examples, the auther makes a leap from simple to extraordinarily complicated examples. Now, given that this is a review book, one can fairly argue that doing so isn't all that bad, but I personally find it a harsh way to guide practice.

In short, get the paper edition and have a good textbook as backup.

[Wing · Rating 5 out of 5]

This is a great book. It explains very clearly the theory (with proofs) behind calculus. The author then teaches the reader techniques to solve problems. He states step by step what goes through his mind when he manipulates and utilises identities, rules, and equations. Obviously, a lot of practice is needed to recognise patterns and possibilities efficiently if not reflexively. The book does not have many exercises but that's not its purpose. He also highlights formulas and equations that deserve commitment to memory. The pace of the book does speed up a bit as it progresses from differentiation to integration. There is also a chapter on complex number but complex analysis is beyond the scope of this book. When Euler's Identity is stated, the reader should find it obvious. It is still awe inspiring. At around 700 pages and really well written and organised, this is truly value for money. There is a collection of online lectures delivered by the author that accompany the book. Five stars.

[Matt Stump · Rating 5 out of 5]

This is a great companion book to both derivative and integral calculus. I recommend using in conjunction with a calculus text book, as it does not contain many calculus problems to work out. It is a very good theory book, and I wish I had this when I was taking calculus the first time. Life would have been much simpler.

[James · Rating 3 out of 5]

Too early to tell how this book will help me. Read this one to be primed on calculus before I take it this Fall. To be frank I was confused for a majority of this book. Probably because I have not been solving the problems. I will review this book again once I finish my calculus courses. And will also use it as a reference.

[Monika]

Thorough summary w/helpful hints for students. Highly recommend. Princeton University.
See also: Probability & Real Analysis

[Ehud · Rating 1 out of 5]

Too many words, not many problems to solve. too simplistic and somehow dense.

[Darin · Rating 5 out of 5]

This is one of the best math books I have ever read, and I did read all of the chapters of this book. One of the ways I assess a textbook is by how much understanding I gain. Many math books follow the form "Here is an equation and here is how to manipulate it" with no motivation for why it's this way. Every page of The Calculus Lifesaver is packed full of insight.

Every example felt like the author put thought into how it helped you understand the concepts. While some of the examples used are standard, and really need to be in some cases, many others were much different than what I have seen in other calculus books. In fact, some were complex enough that the author needed several pages to explain them.

So, as much as I love this book, I would not necessarily recommend it as a first book on calculus. There are no end of chapter problems and I do feel that to learn math you need to spend a lot of time working problems. Even then, the book is about 700 pages long. Also, some of the examples are probably too hard for most people seeing calculus for the first time.

While I do believe that understanding should be promoted when learning math, a person has to know some things in order to understand other things. Therefore, I think this book is better suited for either a second pass through the topics or as a supplement to a more traditional book.

My final comment is that I think I only noticed two typos in the entire book, and they were in the text (i.e., not the equations) and therefore fairly easy to spot. This shows the attention to detail that the author put into the book.

Note that I believe (and follow) the meanings Goodreads gives for what each number of stars means. Therefore, the majority of my ratings are 3 stars ("liked it").

[Jeff · Rating 4 out of 5]

I've used this to review basic calculus in preparation for the PRAXIS II Mathematics Content Knowledge test, and it has been a great resource. Not only catching me up on calculus it has a good overview of trigonometry, functions, exponentials, and logarithms which have all been perfect for my needs. Not to mention Banner uses a rather off the cuff style that makes the reading a little less dry than it would be other wise.

[Ross · Rating 5 out of 5]

Most readable textbook ever. Didn't exactly "finish" it in the sense of reading cover to cover, just reviewed some topics I haven't had to think about in a while. Still, quite impressed by how they made Calculus fun again.

[Todd · Rating 4 out of 5]

Great companion book for College calculus, geared more for Calc I, then Calc II...but very helpful with filling in the gaps of the textbook.

[Travis · Rating 4 out of 5]

I found it to be very helpful for both calculus I and II. however I was disappointed that multivariable calculus was left out completely.

[Tim Verstraete · Rating 3 out of 5]

Finally finished this one … haar stukje really good things on there and was fun!

[Betina · Rating 5 out of 5]

The title says it all - a lifesaver! I passed my calculus exam thanks to this book.