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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "File: depart\\math\\maple
\\misc\\combine.mws Date: 20-nov-1997 By: bob jantzen" }}}{EXCHG
{PARA 18 "" 0 "" {TEXT -1 80 "Unexpected output for the particular sol
ution of a linear differential equation" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 133 "THIS HAS BEEN FIXED BY VERSION 8.0 WHICH DOES NOT EXPAND
THE TRIG FUNCTIONS IN THE ROUTINE, SO THIS WORKSHEET IS NO LONGER NEC
ESSARY." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "The differential equat
ion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "deq:=(D@@2)(q)(t)+8
00*D(q)(t)+250000*q(t)=120*cos(120*t);" }}{PARA 11 "" 1 "" {XPPMATH
20 "6#>%$deqG/,(---%#@@G6$%\"DG\"\"#6#%\"qG6#%\"tG\"\"\"--F,F.F0\"$+)-
F/F0\"'++D,$-%$cosG6#,$F1\"$?\"F=" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1
21 "The general solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
174 "### WARNING: `dsolve` has been extensively rewritten, many new re
sult forms can occur and options are slightly different, see help page
for details\nsol_gen:=dsolve(deq,q(t));" }}{PARA 12 "" 1 "" {XPPMATH
20 "6#>%$solG/-%\"qG6#%\"tG,6*&-%$cosG6#,$F)\"$+$\"\"\"-F-6#,$F)\"$?%F
1#\"#@\"&+T)*&F,F1-%$sinGF3F1#!\"\"\"%0U*&F,F1-F-6#,$F)\"$!=F1#\"\"*\"
&+\"[*&F,F1-F;FAF1#F=\"%0C*&-F;F.F1F@F1#F1FJ*&FLF1FHF1FD*&FLF1F2F1#F1F
>*&FLF1F:F1F6*(%$_C1GF1-%$expG6#,$F)!$+%F1F,F1F1*(%$_C2GF1FTF1FLF1F1"
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "The associated \"particular sol
ution\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sol_part:=subs(
_C1=0,_C2=0,sol_gen);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)sol_partG/
-%\"qG6#%\"tG,2*&-%$cosG6#,$F)\"$+$\"\"\"-F-6#,$F)\"$?%F1#\"#@\"&+T)*&
F,F1-%$sinGF3F1#!\"\"\"%0U*&F,F1-F-6#,$F)\"$!=F1#\"\"*\"&+\"[*&F,F1-F;
FAF1#F=\"%0C*&-F;F.F1F@F1#F1FJ*&FLF1FHF1FD*&FLF1F2F1#F1F>*&FLF1F:F1F6
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "combine(%);" }}{PARA
11 "" 1 "" {XPPMATH 20 "6#/-%\"qG6#%\"tG,&-%$cosG6#,$F'\"$?\"#\"%n<\"(
5_/%-%$sinGF+#\"#s\"'@XS" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 418 "This
is an example of where a little knowledge of how MAPLE works and of t
he underlying mathematical operations (expand, combine, etc) pays off.
We cannot hope to use a sophisticated tool effectively without having
more familiarity with basic operations. Clearly we cannot expect our \+
students to have the time to pick up this stuff, but we have to be the
wise sages who can explain these things when they do come up. " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 546 "I have t
o admit that I always forget the name of this \"combine\" command, but
the more I ask my students to explain what they are doing on paper in
terms of manipulation of expressions, the more I think it is useful t
o associate specific names like expand, combine, factor, etc with the \+
operations that we normally do in algebraic manipulation. If only we c
ould raise the level of mathematical communication from the expectatio
ns students currently have of just getting the answer to coherent comm
unication of the process used to reach that goal. " }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1065 "Vocabulary is important
since it makes what we are doing more precise. Yet students have a v
ery low literacy score on understanding mathematical terminology even \+
at the most basic level. We have to begin thinking about how to encour
age students in our lower level courses first (so that it can improve \+
in our own upper level courses) to change their attitude toward how th
ey document their mathematics. We hear all this talk about writing acr
oss the curriculum and writing intensive and enriched courses, but as \+
far as I know, no one has even raised the issue on the department or u
niversity level about how students communicate in technical subjects, \+
where WE (the math department) are the universal gateway. We need to \+
get the students to understand that we expect them to express themselv
es in a way that makes sense to another person, without having to rea
d their mind about what they did not put on paper. The only way to do \+
this is to make it count in our assessment activity and to give them f
eedback. But it has to be across the board or it cannot work." }}}}
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