Top-down Calculus

HOME

S. Gill Williamson

Top-down Calculus (first published in 1987) was developed in the 1980's for a summer session program in the Department of Mathematics at the University of California, San Diego, to train high school teachers to teach calculus. These teachers had studied calculus, but they needed to sharpen their skills to be able to respond quickly in class discussions. Top-down Calculus is available as a free downloadable pdf file and is on the Creative Commons.

Exercises follow the pattern of a prototypical exercise set with solutions and discussion, followed by numerous variations on this theme. Students are encouraged to work one or two of the variation exercise sets and scan the remaining variations, noting the techniques required for each problem. The concise nature of this material works well for self study or a fast paced summer session course.

The Material on this Website

The book, Top-down Calculus, contains five chapters. The first four chapters constitute the core calculus course. Chapter five develops infinite series with an emphasis on intuition. The first four chapters are presented below. Each chapter (a pdf file) has its own Table of Contents and Index. In addition, separate pdf files for Appendix 1, Math Tables, and Appendix 3, Solutions, Partial Solutions, and Hints, have been provided. Some comments and hints to problems are being added to these files by the author. A list of Corrections to Top-down Calculus is provided below.

Chapter 1: LINEAR FUNCTIONS AND DERIVATIVES

PDF

Ch1Image

Chapter 2: COMPUTING DERIVATIVES

PDF

Ch2Image

Chapter 3: APPLICATIONS OF DERIVATIVES

PDF

Ch3Image

Chapter 4: INTEGRALS

PDF

Ch4Image

Appendix 3: SOLUTIONS, PARTIAL SOLUTIONS AND HINTS TO EXERCISES

PDF

Appendix 1: MATH TABLES

PDF

CORRECTIONS

PDF

For supplementary reading and freely accessible downloadable sources click HERE.

.