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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 55 "Maple Solutions to the Ch
emical Engineering Problem Set" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 19 "" 0 "" {TEXT -1 11 "Ross Taylor" }}{PARA 19 ""
0 "" {TEXT -1 34 "Department of Chemical Engineering" }}{PARA 19 "" 0
"" {TEXT -1 19 "Clarkson University" }}{PARA 19 "" 0 "" {TEXT -1 28 "P
otsdam, New York 13699-5705" }}{PARA 19 "" 0 "" {TEXT -1 27 "taylor@su
n.soe.clarkson.edu" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 225 "Maple is a computer algebra system or CA
S. Gonnet and Gruntz (Algebraic Manipulation Systems, in Encylcopedia \+
of Computer Science and Engineering, 3rd Edition, Van Nostrand Reinho
ld, 1991) define computer algebra as follows:" }}{PARA 0 "" 0 ""
{TEXT -1 1 "\n" }{TEXT 256 380 "\"Computer algebra (sometimes called a
lgebraic manipulation, or symbolic computation) can be defined to be c
omputation with variables and constants according to the rules of alge
bra, analysis and other branches of mathematics, or formula manipulati
on involving symbols, unknowns, and formal operations rather than with
conventional computer data of numbers and character strings.\"\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 605 "What this means is that Maple is \+
capable of far more than the simple (or not so simple) numerical solut
ion of the equations that arise during the modelling of chemical engin
eering operations. It can be used in all facets of problem solving fr
om helping us to derive and analyse the model equations in the first p
lace, computing numerical solutions when needed, and graphical visuali
zation of the results. In the worksheets written to solve the selectio
n of chemical engineering problems we have tended to gloss over the de
rivation and analysis part, since such was not considered part of the \+
assignment. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 428 "In creating the Maple solutions I considered w
hether or not to stick to standard Maple (i.e. Maple out of the box). \+
It is important to recognise that Maple is a very powerful programming
language in its own right and it is possible to teach Maple new trick
s. I decided not to pass on the opportunity to use some of the tools \+
that I have developed to make working with Maple somewhat simpler than
it might otherwise have been. " }{TEXT 257 4 "Some" }{TEXT -1 490 " \+
of the worksheets that accompany these notes therefore incorporate som
e commands that are not standard Maple. Readers can tell which workshe
ets fall into this category by the inclusion of a read statement follo
wed by a file name. There are three such files used in these worksheet
s: utils.mpl, newton.mpl, and besirk. The first of these contains vari
ous utility routines designed in part to make it easier to work with s
ubscripted and unsubscripted variables with the same root name (i.e. \+
" }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "x[
1]" "&%\"xG6#\"\"\"" }{TEXT -1 65 "). The other two files are describe
d in the following paragraphs." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 851 "Maple contains a large numbe
r of routines for solving equations. One of these routines is fsolve, \+
for obtaining numerical solutions to systems of equations. We use fsol
ve in several of the examples. However, in this authors opinion fsolve
is not very effective at solving systems of nonlinear equations (i.e.
more than one), largely because the procedure allows the user no cont
rol over the starting point, or over the iteration history. To deal wi
th this weakness in Maple I have implemented Newton's method for solvi
ng systems of equations in Maple. The procedure is moderately sophisti
cated and has numerous options that allow the user considerable contro
l over how the calculations are to be done. The code has been part of \+
the Maple Share Library (contributions by users) for some time. A more
up to date version is included with these examples. " }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 888 "
Maple out of the box is not capable of solving problems involving mixe
d systems of differential and algebraic equations (DAEs). However, in \+
view of their importance in what we do with Maple, we have implemented
a numerical method for solving DAE systems. Full details of the metho
d are available in the worksheet BSIRKPAP.MWS that has been included w
ith this collection of problem solutions. The code that implements the
method is contained in the file BESIRK and is loaded into the relevan
t worksheets using the read command. This method is also used in an al
ternative worksheet to one of the other examples where Maple's own dso
lve/numeric is another choice. Possible reasons for using BESIRK over \+
dsolve/numeric include the fact that BESIRK is many times faster. It c
an also be useful in solving systems of PDEs obtained when systems of \+
PDEs are approximated using the method of lines." }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 350 "The code \+
packages used here as well as the example files are available by anony
mous ftp from ftp.clarkson.edu in the \\pub\\maple directory. Utilitie
s are in the \\utils subdirectory, Newton's method in \\numerics, BESI
RK in \\besirk. Other exmaples are available in the \\chemeng subdirec
tory. The worksheets that follow are in the \\polymath subdirectory."
}}}}{MARK "11 0 0" 888 }{VIEWOPTS 1 1 0 1 1 1803 }