Calculus: One Variable

When I first started this book, it made very little sense. Persistance paid off for me and it will pay off for you. You will obtain a deeper understanding of calculus that won't go away after you complete the course. If you're having difficulty understanding the material in this book, you need to take a step back and visualize what the book is saying. As the book says in the beginning, calculus is just high school math with limits.

The solutions manual is useful if you get stumped.


very helpful supplement   February 20, 2002
ihgmd2b (New York, NY)
Despite the highly theoretical way of writing, this book acts as an excellent supplement either as a review, or as part of a class. The examples are concise and clear. There are many examples detailing how a certain problem should be done.

The problems at the end of each section vary between relatively easy and incredibly difficult.


I would consider adopting it if I were teaching calculus   September 15, 2006
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
One variable calculus books are almost identical in content and organization. In terms of organization, there is a brief explanation of the new topic of the section, any new definitions or theorems pertaining to the topic, several examples followed by worked solutions and the section ends with a set of exercises. Solutions to the odd-numbered exercises are given in an appendix at the end of the book. This book does not deviate from that organization.
In terms of content, the chapters in this book are:

*) Precalculus review
*) Limits and continuity
*) Differentiation
*) The mean-value theorem and applications
*) Integration
*) Applications of the integral
*) The transcendental functions
*) Techniques of integration
*) The conic sections; polar coordinates; parametric equations
*) Sequences; indeterminate forms; improper integrals
*) Infinite series

As can be seen, the content is routine, both in order and in topics.
Therefore, the obvious question to ask is, "What if anything, differentiates this book from the other calculus books?" There is no overwhelming answer to this question, just a few minor differentiating factors.

*) There is not a great deal of time spent under any heading resembling "Using technology." A few problems at the end of the sections are noted with a calculator symbol, but there is no time spent on teaching how an item of technology is used to solve the calculus problems. While others may not agree, in my opinion this is a major positive. The goal is to teach the principles of calculus. With the large number of topics that need to be introduced in the first two semesters, and the difficulties that some of the students have, spending time on technology solutions is largely a waste of time.
*) This book contains only single variable calculus. This makes it easier on the students as calculus books are rapidly reaching the point where they could be used as weights by members of the football team.
*) The authors do not engage in exercise overkill, where the exercises at the end of the sections seem to go on and one. Simply adding additional exercises that cover the same material is not an improvement.

As a consequence of these positive aspects that differentiate it, this is a book that I will consider adopting the next time that I am scheduled to teach calculus.


Typical coverage, not as rigorous as some other books, no "using technology" sections, I would use it as a text   September 20, 2006
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
This book is a continuation of "Calculus: One Variable" by the same authors. Therefore, it starts on page 706 with chapter 12. However, since the material is the traditional coverage for the third semester course in calculus, it is possible to use this book if you didn't use their single variable calculus book. It may not be easy, if your two-semester sequence in single variable calculus did not get through all the topics, then some filler would be required.
In terms of content, calculus books that cover either single variable or multi-variable calculus all have the same coverage. The topic differences that you see between them are very small. All have exercises at the end of each section with answers either to the even or the odd numbered ones included in an appendix. With one exception, this book is no different from the pack in that regard. The exception is in the number of exercises at the end of the sections. Some authors seem to think that they are engaged in an arms race regarding the number of exercises they include. So much so that it becomes overkill. Salas and company are just about right in the number of exercises they put at the ends of the sections.
The method of presentation is an explanation of the new concept(s) followed by an example/solution pair. A theorem/proof pair is rarer in this book than in others. Most of the time the authors are content to simply give a formula and then use it rather than present a more formal proof. This is not necessarily wrong, if you are interested in getting your students to the point that they can solve calculus problems then this is ideal. However, if you want to be more rigorous in your presentation, then you most likely will find this book lacking.
One feature that is left out is one that I am strongly in favor of. There is very little in the way of "using technology." I find problems that rely on a calculator or a symbolic math program to be unnecessary filler. I find it so difficult to cover all of the material that should be included in the three semester calculus sequence that I avoid the technology option. While I agree that some concepts can be better illustrated with a dynamic diagram, I don't believe that such a diagram is essential to the understanding. By avoiding what can sometimes be considered the crutch of technology, I can concentrate on filling their mind with calculus concepts rather than having them learn a sequence of buttons to push or mouse clicks to execute.