Calculus. Single variable. 2nd ed. (English) Zbl 0892.26001

Hughes-Hallett, Deborah; Gleason, Andrew M.; Flath, Daniel E.; Lock, Patti Frazer; Gordon, Sheldon P.; Lomen, David O.; Lovelock, David; McCallum, William G.; Quinney, Douglas; Osgood, Brad G.; Pasquale, Andrew; Tecosky-Feldman, Jeff; Thrash, Joe B.; Tucker, Thomas W.; Thrash, Karen R.

New York, NY: Wiley. xvii, 647 p. (1998).

Table of contents of the first edition (1994): 1. A Library of Functions. 2. Key Concept: The Derivative. 3. Key Concept: The Definite Integral. 4. Short-cuts to Differentiation. 5. Using the Derivative. 6. Reconstructing a Function from its Derivative. 7. The Integral. 8. Using the Definite Integral. 9. Differential Equations. 10. Approximations.
Appendices: A. Roots and Accuracy. B. Continuity and Bounds. C. Polar Coordinates. D. Complex Numbers.
We confine our review to changes from the first edition. The Rule of Three has been expanded to the Rule of Four: Where appropriate, topics should be presented geometrically, numerically, algebraically and verbally. There are more easy and medium level problems, but as in the first edition, the problems are varied and challenging, and most cannot be done by following a template in the text. There are short answers in the back to those odd-numbered problems that have them. Each chapter concludes with a review of the main points, and there is a list of useful formulas on the endpapers. One or more projects are included at the end of each chapter; a wider selection is in a new appendix. New (optional) Focus on Theory sections discuss the concepts of axiom, definition and mathematical proof, and give a more theoretical treatment of limits, differentiability and the definite integral. Chapter 4 has a new section on local linearity and limits, which includes L’Hôpital’s rule. Chapter 5 has a new section on hyperbolic functions. Chapter 7 has an expanded treatment of partial fractions. Chapter 8 has a new subsection on center of mass. Chapter 9 has new material on using the ratio test to find radius of convergence of power series, and new material on the harmonic and alternating series. There is a new appendix on parametric equations. Various sections have been shortened or expanded, or moved.
See also the following review.

Reviewer: Gerald A.Heuer (Moorhead)

MSC:

26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
26A06	One-variable calculus
00A06	Mathematics for nonmathematicians (engineering, social sciences, etc.)

Keywords:

calculus; one variable; textbook

Citations:

Zbl 0892.26002