Top-down Calculus

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S. Gill Williamson

Top-down Calculus (first published in 1987 and now out of print) was developed in the 1980's for a summer session program in the Department of Mathematics at the University of California, San Diego, for high school calculus teachers. They needed to develop intuition and technical skills to lead class discussions and answer questions. Exercises follow the pattern of a prototype exercise set with solutions and discussion, followed by numerous variations on this theme. A first pass through the material studying the prototype questions and solutions followed by a second pass working selected variations is recommended.

Complete Book Plus Individual Chapters as pdf Files

The book, Top-down Calculus, contains five chapters. The first four chapters constitute the core calculus course. Chapter five develops infinite series. 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. Interested in tutoring calculus? The notes TUTORING INTEGRAL CALCULUS below will get you through the most difficult part. Chapter 5, Infinite Series, is given below as an unedited pdf file.

Chapter 1: LINEAR FUNCTIONS AND DERIVATIVES

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Download Book PDF

Chapter 2: COMPUTING DERIVATIVES

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Chapter 3: APPLICATIONS OF DERIVATIVES

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Chapter 4: INTEGRALS

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Appendix 3: SOLUTIONS, PARTIAL SOLUTIONS AND HINTS TO EXERCISES

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Appendix 1: MATH TABLES

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CORRECTIONS

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Chapter 5: INFINITE SERIES

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For supplementary reading and freely accessible downloadable sources click HERE.

Interested in tutoring calculus? Differential calculus is usually not a problem for tutors. Integral calculus is harder. Here is a handout that I prepared for my tutors to help them.

TUTORING INTEGRAL CALCULUS

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