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A Graphical Tool for Analysis Courses

Jeffry L. Hirst

Department of Mathematical Sciences

Appalachian State University

Boone, North Carolina 28608

jlh@math.appstate.edu Phone:828-262-2861

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Abstract:

Due to the reform movement, many universities use technology in their calculus courses. By using
computer algebra systems in higher level courses, we can capitalize on skills students are learning
in their introductory courses. This paper describes a Maple procedure that illustrates the mechanics
of delta-epsilon proofs.

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Introduction:

There are several factors which motivated the development of this software.
First, many students have a difficult time writing their first few delta-epsilon
proofs. While most introductory analysis texts have some very useful
illustrations, such pictures are usually too general, too small in number,
and lack interactivity. Since it would be inappropriate to overburden analysis
texts with reams of illustrations, a special purpose software supplement
seems desirable.

Our solution is a Maple procedure:

which accepts as input
- a function (f is an expression in x)
- a point on the x-axis (a is a real)
- and expected limit (L is a real)
- a maximum value for epsilon (max is a positive real)

and outputs an animation showing the graph of the function f
with the appropriate lines drawn for various values of epsilon.

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Sample frames from animations generated by edmap.

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The Maple code for edmap in
text
form or as a Maple V release 4
worksheet.

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Tips
for distributing Maple code to students.

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Tips
for using the display command in Maple.