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

**Adrian Banner** is Lecturer in Mathematics at Princeton University and Director of Research at INTECH.

"Banner's style is informal, engaging and distinctly non-intimidating, and he takes pains to not skip any steps in discussing a problem. Because of its unique approach, *The Calculus Lifesaver* is a welcome addition to the arsenal of calculus teaching aids."**—***MAA Online*

"This rather lengthy book serves as an excellent resource as well as a text for a refresher course in single-variable calculus, and as a study guide for anyone who needs or is required to know basic calculus concepts....Readers will find this book written for them, as calculus is presented in a very casual conversational tone; certainly, students who are not mathematics majors will benefit greatly."**—J.T. Zerger, ***Choice*

"Students who are having difficulty in calculus could use it as a resource in addition to their professor and teaching assistant."**—***Mathematics Teacher*

"I used Adrian Banner's *The Calculus Lifesaver* as the sole textbook for an intensive, three-week summer Calculus I course for high-school students. I chose this book for several reasons, among them its conversational expository style, its wealth of worked-out examples, and its price. This book is designed to supplement any standard calculus textbook, thus my students will be able to use it again when they take later calculus courses. The students in my class came from diverse backgrounds, ranging from those who had already seen much of the material to others who were struggling with basic algebra. They all uniformly praised the book for being one of the clearest mathematics texts they have ever read, and because it reviews the required prerequisite material. The numerous worked-out examples are an ideal supplement to the lectures. The only difficulty in using this book as a primary text is the lack of additional exercises in the text. However, there are so many sites and sources for calculus problems that this was not a problem. I would definitely use this book again."—Steven J. Miller, Brown University

"Banner's book is a chatty, user-friendly guide to calculus that will be a useful addition to the resources available to students. Banner does an exceptionally thorough job while maintaining an engaging style."—Gerald B. Folland, author of *Advanced Calculus*

"This is an engaging read. Each page engenders at least one smile, often a chuckle, occasionally a belly laugh."—Charles R. MacCluer, author of *Honors Calculus*

"This book is significant. The author's attempt to give an 'inner monologue' into the thought process that is needed to solve calculus problems rather than just providing worked examples is novel and is in line with his purpose of helping the reader get a deeper understanding of calculus. The book is well written and the author's examples are clear and complete."—Thomas Seidenberg, Phillips Exeter Academy