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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "Partial Differential Equa
tions PowerTool" }}{PARA 19 "" 0 "" {TEXT -1 16 "by Dr. Jim Herod" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 63 "Conclusi
on: Partial 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 t
ried to push Maple up the curriculum. Before retiring from Georgia Tec
h, I participated in a project to create worksheets for every course i
n the first two years of undergraduate mathematics. At the same time, \+
high schools in metropolitan Atlanta began to include Maple as a part \+
of the preparation of their students for college mathematics. I was al
so asked to assist in creating materials for those pre-college courses
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 396 "   \+
   But it has always been my perspective that Maple is more than a tea
ching tool. It is a working tool. If Maple were used through the calcu
lus and 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 readily at hand for making models and for analyzing the implication
s 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 di
rection through our cross listed, team taught course in Mathematical B
iology. The result of that endeavor is included in the text published \+
by Birkhauser and titled " }{TEXT 257 74 "An Introduction to the Mathe
matics of Biology with Computer Algebra Models" }{TEXT -1 200 ". The i
dea of carrying computer algebra systems into the curriculum of the Li
fe Sciences is wide spread among those who have seen the power of Mapl
e as a working tool. These efforts must be continued." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 768 "      Using Maple in \+
a study of undergraduate ordinary differential equations is common. Th
ere are many authors who have worked to make materials available for d
oing this. Writings in partial differential equations using Maple are \+
less common. Yet, every engineering, physics, or chemistry student use
s partial differential equations to model physical phenomena in their \+
area. Undergraduate courses in partial differential equations might ta
ke an entire academic year. Major topics would be methods of Fourier S
eries, characteristics, Green's functions, Laplace transforms, and num
erical analysis. These would be introduced while examining linear syst
ems. Yet, the world is non-linear, and we need a year of graduate part
ial differential equations to begin that topic." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 608 "     The first question \+
facing any writer deciding to make notes for partial differential equa
tions is what 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 Green's functions? How can we discuss the method of characte
ristics and not illustrate shocks arising in first order systems? Wher
e are numerical methods for three dimensional diffusion equations. One
 colleague reading the notes pointed out the omission of time dependen
t boundary conditions for the diffusion equation using the methods of \+
separation of variables." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 224 "      The list goes on. Thinking of the list, the
 problem changes: where is the stopping place in constructing a set of
 lecture notes for a first look at using Maple in an undergraduate par
tial differential equations course." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 18 "      I stop here." }}}{MARK "3 0" 0 }
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