What do you think?
Rate this book
The Calculus Lifesaver: All the Tools You Need to Excel at Calculus
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an inner monologue--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an inner monologue--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
754 pages, Paperback
First published March 5, 2007
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 17 of 17 reviews
March 4, 2014
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.
April 27, 2020
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.).
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.).
January 31, 2021
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.
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.
October 5, 2019
Literally saved my life.
November 11, 2020
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.
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.
May 14, 2023
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.
January 3, 2018
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.
March 21, 2019
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.
Read
August 21, 2019Thorough summary w/helpful hints for students. Highly recommend. Princeton University.
See also: Probability & Real Analysis
See also: Probability & Real Analysis
August 7, 2020
Too many words, not many problems to solve. too simplistic and somehow dense.
October 25, 2021
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").
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").
June 7, 2009
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.
September 16, 2016
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.
January 9, 2011
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.
August 25, 2011
I found it to be very helpful for both calculus I and II. however I was disappointed that multivariable calculus was left out completely.
May 8, 2019
Finally finished this one … haar stukje really good things on there and was fun!
December 14, 2024
The title says it all - a lifesaver! I passed my calculus exam thanks to this book.
Displaying 1 - 17 of 17 reviews