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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 63 "Conclusion: Parti
al Differential Equations, Analysis, and Maple" }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT
-1 477 " Since the time when Maple IV was created, I have tried t
o push Maple up the curriculum. Before retiring from Georgia Tech, I p
articipated in a project to create worksheets for every course in the \+
first two years of undergraduate mathematics. At the same time, high s
chools in metropolitan Atlanta began to include Maple as a part of the
preparation of their students for college mathematics. I was also ask
ed to assist in creating materials for those pre-college courses." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 396 " Bu
t it has always been my perspective that Maple is more than a teaching
tool. It is a working tool. If Maple were used through the calculus a
nd in an ordinary differential equations class and then were put aside
, then its real power would be lost. Maple is a tool that should be re
adily at hand for making models and for analyzing the implications of \+
the models in any field on the campus." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 94 " Toward accomplishing that goal,
Maple must move across the campus and up the curriculum." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 243 " E. Yeargers
, R. Shonkwiler, and I took Maple across the campus in one direction t
hrough our cross listed, team taught course in Mathematical Biology. T
he result of that endeavor is included in the text published by Birkha
user and titled " }{TEXT 257 74 "An Introduction to the Mathematics of
Biology with Computer Algebra Models" }{TEXT -1 200 ". The idea of ca
rrying computer algebra systems into the curriculum of the Life Scienc
es is wide spread among those who have seen the power of Maple as a wo
rking tool. These efforts must be continued." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 768 " Using Maple in a study o
f undergraduate ordinary differential equations is common. There are m
any authors who have worked to make materials available for doing this
. Writings in partial differential equations using Maple are less comm
on. Yet, every engineering, physics, or chemistry student uses partial
differential equations to model physical phenomena in their area. Und
ergraduate courses in partial differential equations might take an ent
ire academic year. Major topics would be methods of Fourier Series, ch
aracteristics, Green's functions, Laplace transforms, and numerical an
alysis. These would be introduced while examining linear systems. Yet,
the world is non-linear, and we need a year of graduate partial diffe
rential equations to begin that topic." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 615 " The first question facing any w
riter deciding to make notes for partial differential equations is wha
t to include. The reader can get a glimpse of my decisions by looking \+
over the titles of the Sections. The omissions stand out. Where are Gr
een's functions? How can we discuss the method of characteristics and \+
not illustrate shocks arising in first order systems? Where are numeri
cal methods for three dimensional diffusion equations. One colleague r
eading the notes pointed out my initial omission of time dependent bou
ndary conditions for the diffusion equation using the methods of separ
ation of variables." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 224 " The list goes on. Thinking of the list, the prob
lem changes: where is the stopping place in constructing a set of lect
ure notes for a first look at using Maple in an undergraduate partial \+
differential equations course." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 18 " I stop here." }}}{MARK "0 1" 63 }
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