Top-down Calculus |
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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. Google Books now hosts Top-down Calculus as a downloadable pdf file (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. |
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The Material on this Website |
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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. Interested in tutoring calculus? The notes TUTORING INTEGRAL CALCULUS below will get you through the most difficult part. |
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Chapter 1: LINEAR FUNCTIONS AND DERIVATIVES |
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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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For supplementary reading and freely accessible downloadable sources click HERE. |
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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. |
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TUTORING INTEGRAL CALCULUS | ||
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