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TI89 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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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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 Spring '07
 JURY
 Calculus, Derivative, Limits

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