TI-89Workbook

# TI-89Workbook - TI-89 WORKBOOK for HONORS CALCULUS by...

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TI-89 WORKBOOK for HONORS CALCULUS by Professor James Keesling Department of Mathematics University of Florida Table of Contents Introduction………………………………………………………………… 2 1. Elementary Calculations. .................................................................... 4 2. Functions and Graphs………………………………………………. 5 3. Limits………………………………………………………………. . 6 4. The Derivative and Tangent Lines…………………………………. . 7 5. Applications of the Derivative………………………………………. 9 6. Integrals as Limits…………………………………………………… 12 7. Antidifferentiation and the Fundamental Theorem…. ........................ 15 8. Numerical Integration………………………………………………. . 17 9. Applications of Integration…………………………………………. . 19 10. Remarks…. .......................................................................................... 20

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2 Introduction. In recent years the design, speed, and power of modern computers have increased significantly. Along with the increased capabilities, computers have been assigned new tasks. These tasks are beyond anything conceived a few years ago. Until recently, computers were seen as powerful calculators whose sole contribution to mathematics was to work out complicated numerical examples with great precision and speed. However, with the advent of Macsyma, Mathematica, Maple, Derive and other computer programs capable of symbolic calculations, the computer has become an indispensable help in performing logical functions and algorithms as well as numerical calculations. Now the computer can solve algebraic equations exactly, can compute derivatives and integrals symbolically, and can even compute exact limits. For almost the whole history of calculus, these have been the skills that students learned in calculus courses. Now there is danger that those skills may become outmoded. No one uses tables of logarithms or trigonometric functions or learns manual methods of approximating these functions. Calculators and computer determine the values of these functions with greater accuracy than these tables would give us anyway. In the same way some would argue that the techniques of differentiation and integration may be on the way to being antiquated. This is not to say that there is no need for calculus or a course in calculus. It is just that the skills that were taught in the past need to be reevaluated. One still needs to understand the principles of calculus even to make use of one of the symbolic programs and apply it properly. If we make proper use of the new technology our calculus courses can be more interesting and relevant. There will be less emphasis on mastering certain algorithms and more concentration on understanding the underlying principles of calculus. Would one say that word processing has eliminated the need to learn to write and spell properly? Not at all! However, one would be disappointed if word processing technology were not incorporated in a modern course in creative writing. Where would we be without cut and paste and spell checking?
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## This note was uploaded on 07/14/2011 for the course MAC 3472 taught by Professor Jury during the Spring '07 term at University of Florida.

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TI-89Workbook - TI-89 WORKBOOK for HONORS CALCULUS by...

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