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Calculus: Early Transcendentals

Michael P. Sullivan and Kathleen Miranda
W.H. Freeman
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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The main features of this calculus book are typical of such books. There are nearly 1,100 pages of content before you reach the first appendix. There are slightly less than 150 pages of appendices and then there is the index. All of this leads to a text that will build muscles while (hopefully) the brain is being filled with calculus. The coverage is the standard set of topics presented in the traditional three semesters of calculus; it begins with a brief review of precalculus and ends with differential equations. A large number of exercises are also included; there are some sections where there are over 10 exercises at the end for every page of new topics. The solutions to the odd-numbered exercises are found in an appendix.

Given all of these standard features, the most obvious questions to answer have to do with how this book is different from other calculus texts. The first is an omission: there is almost no reference to technology, either graphing calculator or symbolic mathematics package. I consider this a positive feature; if a lot of technology were included, the 2,000 page calculus book would become a potential reality. The second is the coloration of the figures; the three colors of red, blue and tan are very effectively used to create the images of the actions such as solids of revolution and other three-dimensional figures.

Other than these aspects, there is nothing to differentiate this book from other books designed for the three-semesters of calculus market. In many ways I find myself wishing that there would be a moratorium on new calculus books because the field seems to have hit a wall regarding anything new in textbooks. I could have used this book to teach calculus 20 years ago and I could use my book of twenty years ago to teach it now and the outcomes would not be significantly different. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

P. Preparing for Calculus
1. Limits and Continuity
2. The Derivative
3. More about Derivatives
4. Applications of the Derivative
5. The Integral
6. Applications of the Integral
7. Techniques of Integration
8. Infinite Series
9. Parametric Equations; Polar Equations
10. Vectors; Lines, Planes, and Quadric Surfaces in Space
11. Vector Functions
12. Functions of Several Variables
13. Directional Derivatives, Gradients, and Extrema
14. Multiple Integrals
15. Vector Calculus
16. Differential Equations

Appendix A  Precalculus Used in Calculus
Appendix B Theorems, Proofs, and Definitions