0203-386: The Colorado School of Mines Weekly Calculus Projects (August 1993)
Author: Jack K. Cohen
The Colorado School of Mines uses Mathematica in all sections of
the campus-wide required first year calculus sequence.
This is a collection of weekly Mathematica projects designed to
demonstrate the realistic use of Mathematica in scientific work.
Mathematica is introduced at a measured pace and competence is
built steadily. There are occasional references to the Edwards
and Penney text, Edition 3, but the material is not tied to this
text in any essential way.
Calculus.m:
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Mathematica package implementing several different methods of
approximate numerical integration; including Riemann Sum, left and
right endpoint rules, trapezoid rule, midpoint rule, Simpson's
rule, and Newton's method. Also contains a fix for the infamous
cube root problem (i.e., the negative root, instead of a complex
one is selected for (-1)^(p/q), when q is odd and p/q is in lowest
terms).
This file is intended to be part of the student environment via
init.m. It is also available separately as MathSouce item 0202-352.
Projects and Notebooks:
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The Projects are accompanied by Notebooks that allow the students
to "cut and paste" the Mathematica command sequences referred to
in the Projects. This obviates many of the early syntax errors
made by students who are not yet sensitive to the strict requirements
of computer languages ("why can't I say f(x) instead of f[x_]?",
etc.). The Notebook crutch is gradually withdrawn throughout the year.
Answers exist for the projects---more information is provided at
the end of this file.
Sermons:
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The Sermons contain the author's opinions about the teaching of
Calculus and the use of the materials in this directory. Dialog
is welcome and I hope you get a chuckle or two as well.
Tutorial:
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This is the FIRST Mathematica Notebook the students work through.
It provides an introduction to the NeXT front end including moving
about within the Notebook using the arrow keys and the mouse,
editing and deleting text, and executing some basic commands. (This
tutorial is also available separately as MathSource item 0203-476.)
Worksheets:
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This is a collection of worksheets (and answers) designed to be
used for cooperative education or as homework to accompany the
Edwards and Penney text, Edition 3. The worksheets are aimed to
emphasize good scientific practice in solving problems and to
introduce Mathematica at a measured pace.
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Copyright (c) Colorado School of Mines, 1993.
Permission is granted to use these materials for classroom and other
pedagogical purposes. This includes the right to reproduce and modify
these materials for your classes.
Jack K. Cohen, 08/09/93.
jkc@dix.mines.colorado.edu
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Update History:
08/13/93 original installation
08/16/93 Projects, Notebooks 12-15 enhanced (actually 13 is new)
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Purpose: Gradual introduction of Mathematica and good scientific thinking.
The latter is much more important than the former!
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I've made both 300dpi and 400dpi versions of the postscript files
to try to make them portable. However, there may still be trouble
if your printer doesn't have all the requisite fonts. There may
also be trouble for other reasons that I have no hope of understanding.
If all else fails, send me your US-mail address and I will have
hard copy mailed at cost of materials + epsilon.
The Notebooks are all NeXT .ma files. If that's of no use to you,
be consoled that they contain only the Mathematica statements
contained in the project. Their purpose is to allow the students
to "cut and paste", thus avoiding the need to explain a lot of
syntax at the outset.
The Sermons contain my philosophy and addition information about
using the materials.
Answers exist for the projects, but since students know how to use
anonymous ftp too, they aren't included in the public distribution.
If you care about having them, direct mail hard copy under the
above terms is the best I can offer.
jkc@dix.mines.colorado.edu
Jack K. Cohen
Center for Wave Phenomena
Colorado School of Mines
Golden, CO 80401
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