Calculus of One Variable

?"A richly textured, flexible text with a variety of options in addition to a solid core of standard material." — Current Science

A well-respected treatment of one variable calculus, this book also covers plane analytic geometry and infinite series. Its comprehensive nature allows instructors to use it in many ways, and the rigorous approach provides intuitive insights and a feeling for the way the calculus is applied.
Geared toward undergraduate students of mathematics, the text requires a solid command of high school mathematics, including algebra, geometry, and trigonometry. Topics include the use of basic theorems on limits; techniques of differentiation; the characterization of real numbers as a complete, ordered field; mean-value theorems and their applications; a new perspective on the Riemann integral; transcendental functions; techniques of integration; and more. Numerous illustrative examples and figures appear throughout the volume, along with problems of many types and of varying levels of difficulty.

Joseph W. Kitchen received his PhD in Mathematics from Harvard University in 1963. He is Associate Professor Emeritus of Mathematics at Duke University. Dr. Kitchen is also the author, with Ethan D. Bokler, of First Year Calculus.

1. Preliminaries
2. Analytic Geometry of Straight Lines and Circles
3. Limits
4. Techniques of Differentiation
5. Completeness of the Real Numbers
6. Mean-Value Theorems and Their Applications
7. Antidifferentiation and Its Applications
8. The Riemann Integral
9. Transcendental Functions
10. Techniques of Integration
11. Higher-Order Mean-Value Theorems
12. Plane Curves
13. Infinite Series