Top-down Calculus

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S. Gill Williamson

In the 1980's, ``top-down calculus'' workbooks were developed for a UCSD summer program for high school math teachers. These teachers needed to review calculus to perfect their intuitive and technical skills. We have reconstructed and updated these workooks below. Printed (pdf files) on 8.5 x 11 paper, they have wide margins for taking notes. Reviewing calculus is much more fun than learning it the first time! You can go over the material in any order, including backwards. When you work a problem don't feel obliged to use only ideas earlier in the book. Standard calculus books are full of problems rigged to show the usefulness of calculus. These problems, however, are unstable in that small changes can make them much more difficult. We address this instability through variations on prototype problem sets. Excellent online software for calculus is availble for free -- use it!

Top-down Calculus Workbook

For reviewing differential calculus use ----->

Derivatives Intuition Practice

Top-down Calculus Workbook

For reviewing integral calculus use --------->

Integrals Intuition Practice

For a concise review of integral calculus for prospective tutors of the subject use ------->

Tutoring Integral Calculus

Bound copy available on Amazon $10.00

Tutoring Integral Calculus

Original 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

Linear Functions and Derivatives

TDCcopy
Ch1Image
Download Book PDF

Chapter 2: COMPUTING DERIVATIVES

Computing Derivatives

Ch2Image

Chapter 3: APPLICATIONS OF DERIVATIVES

Applications of Derivatives

Ch3Image

Chapter 4: INTEGRALS

Integrals

Ch4Image

Appendix 3: SOLUTIONS, PARTIAL SOLUTIONS AND HINTS TO EXERCISES

Solutions

Appendix 1: MATH TABLES

PDF

CORRECTIONS

PDF

Chapter 5: INFINITE SERIES

Series

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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