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{SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT -1 19 "An Introduction to " }
{TEXT 256 5 "Maple" }{TEXT 308 1 ":" }}{PARA 4 "" 0 "" {TEXT -1 62 "He
lp, Expressions, Functions, Substitutions, Solving Equations" }}{PARA 
256 "" 0 "" {TEXT 257 29 " Bob Bradshaw, Ohlone College" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT 
303 6 "Maple " }{TEXT -1 2 "or" }{TEXT 304 12 " Mathematica" }{TEXT 
-1 1 "?" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Both " }{TEXT 306 6 "Map
le " }{TEXT -1 4 "and " }{TEXT 307 11 "Mathematica" }{TEXT -1 301 " ar
e excellent software packages, with strengths and weaknesses. Learning
 one package will help you understand both packages. Developing a work
ing knowledge of either program is well within the abilities of the in
terested student. Becoming a master at either package will require bot
h time and effort." }{TEXT 305 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 4 "
Help" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 137 "Before starting to use Ma
ple, the first thing is to know how to get help. There is a HELP menu \+
on your screen but there is an easier way." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "If you are looking for help wit
h a particular command, simply type \"?" }{TEXT 259 14 "command name\"
 " }{TEXT -1 11 "For example" }}{PARA 0 "" 0 "" {TEXT 258 0 "" }
{MPLTEXT 1 0 6 "?solve" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "Restar
t" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "It sometimes becomes necessar
y to clear the " }{TEXT 260 5 "Maple" }{TEXT -1 27 " memory. Do this b
y typing " }{TEXT 267 8 "restart;" }{MPLTEXT 1 0 1 "\n" }{TEXT -1 77 "
Note that this does not completely release allocated memory. To do so,
 quite " }{TEXT 261 5 "Maple" }{TEXT -1 24 " and reboot the program." 
}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 6 "Syntax" }}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }{TEXT 262 5 "Maple" }{TEXT -1 143 " uses lower case \+
letters for most, but not all, commands and uses parentheses for the a
rguments of functions. Note it is required to capitalize" }{TEXT 268 
3 " Pi" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/4);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 151 "P
arentheses are used for both arguments of functions and for grouping s
ymbols. Square brackets are used for vectors and curly braces are used
 for sets." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 119 "A semicolon is required at the end of each statement unless yo
u want to suppress the output. In that case, use a colon." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "3+4;\n3*4:" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 102 "Multplication requires a multiplication symbol in all \+
instances and forgetting it is a frequent error." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 3 "3x;" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "
Expressions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "Expressions are th
e types of equations you normally see in a math course, such as the fo
llowing. Notice that " }{TEXT 265 5 "Maple" }{TEXT -1 12 " requires a \+
" }{TEXT 266 2 ":=" }{TEXT -1 30 "  in the assignment statement." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "y:=x^2+3;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Substituting a value for \+
" }{TEXT 263 1 "x" }{TEXT -1 6 " gives" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "x:=3;y;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 91 "However, trying to use this syntax with standard mat
h notation gives \nthe incorrect answer." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "y(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "y(7
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 46 "You must explicitly define the new value of x." }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "x:=1;y;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 28 "If you ask for the value of " }{TEXT 
264 1 "y" }{TEXT -1 69 ", the program returns the last value rather th
an the equation itself." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "To
 return to the equation for y rather than the last numerical value, us
e " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "x:='x';y;" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "You can also use t
he subs command to perform a substitution." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "subs(x=r^2,y);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
9 "Functions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Functions are decl
ared using the notation " }{TEXT 269 4 "name" }{TEXT -1 2 ":=" }{TEXT 
270 8 "variable" }{TEXT -1 4 " -> " }{TEXT 271 8 "equation" }{TEXT -1 
13 ". For example" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "z:=x->x^2+7;" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 
"This now works using standard mathematical notation" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "z(2);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 29 "To label a certain value, use" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 11 "z(5):=z(5);" }}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 16 "Numerical Values" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Si
nce " }{TEXT 279 5 "Maple" }{TEXT 280 0 "" }{TEXT 281 0 "" }{TEXT -1 
163 " performs exact arithmetic, you must tell it to give a decimal re
sult if that is what you are looking for. There are a couple of ways. \+
The usual way is to use the " }{TEXT 282 5 "evalf" }{TEXT -1 9 " comma
nd." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "myfractions:=1/3+7/1
7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalf(myfractions);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "
The " }{TEXT 283 5 "evalf" }{TEXT -1 62 " command can be used to get t
he first 50 decimal places of Pi." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "evalf(Pi,50);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 95 "Another way is to include a decimal i
n the original problem. However this does not always work." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1./3+7/17;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "Pi/4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "Pi/4.;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 17 "Solving Equations" }}{EXCHG {PARA 256 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 298 5 "Maple" }{TEXT -1 90 " wil
l solve equations with one or more variables and, if possible, return \+
an exact answer." }{MPLTEXT 1 0 27 "\nanswer1:=solve(a*x+b=c,x);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 300 5 "Ma
ple" }{TEXT -1 54 " will also return multiple answers where appropriat
e.\n" }{MPLTEXT 1 0 30 "answer2:=solve(x^2-5*x-7=0,x);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 51 "To verify that these are solutions, we ca
n use the " }{TEXT 309 4 "subs" }{TEXT -1 105 " command to substitute \+
the values back into the equation. The solutions need to be checked on
e at a time." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "checkthis1:
=subs(x=answer2[1],x^2-5*x-7);\ncheckthis2:=subs(x=answer2[2],x^2-5*x-
7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "simplify(checkthis1)
;\nsimplify(checkthis2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 54 "If you want a decimal value, use the \"fs
olve\" command." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "answer:=fsolve(x
^2-5*x-7=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 66 "It is also possible to specify the interval containi
ng the answer." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "eqn:=x^3-8*x^2-3
5*x+150;\nanswer:=fsolve(eqn=0,x);\nposanswer:=fsolve(eqn=0,x=0..infin
ity);\nneganswer:=fsolve(eqn=0,x=-infinity..0);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "When there are multi
ple answers, you can access the one you want by using " }{TEXT 277 4 "
name" }{TEXT -1 2 "[ " }{TEXT 276 13 "answer number" }{TEXT -1 1 "]" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "answer[2];" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "In some cases, " }
{TEXT 299 5 "Maple" }{TEXT -1 89 " is unable to give the exact solutio
n. Instead, it leaves the answer in the form \"RootOf\"" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 32 "first:=solve(x^5-x^3+2*x-9=0,x);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Use the " 
}{TEXT 278 5 "evalf" }{TEXT -1 35 " command to get the decimal values.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(first);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "In this instanc
e, using the \"fsolve\" does not give all the solutions." }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 34 "answer:=fsolve(x^5-x^3+2*x-9=0,x);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "It
 is also possible solve a system of equations in " }{TEXT 272 1 "x" }
{TEXT -1 5 " and " }{TEXT 273 3 "y. " }{TEXT -1 27 "First, reset the v
ariables " }{TEXT 274 1 "x" }{TEXT -1 5 " and " }{TEXT 275 1 "y" }
{TEXT -1 30 " and then write the equations." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "x:='x';y:='y';\ne1:=3*x+5*y=1;\ne2:=2*x-8*y=11;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "S
olve the equations with the solve command. Be sure to enclose both the
 equations and the variables in set notation \{ \}." }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 29 "answer:=solve(\{e1,e2\},\{x,y\});" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "To use th
e value of " }{TEXT 301 1 "x" }{TEXT -1 63 " should be straight forwar
d but, unfortunately, simply typing \"" }{TEXT 302 1 "x" }{TEXT -1 34 
"\" will not give the desired value." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}{MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 60 "Instead, you must use the \"assign\" command on
 your solution." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "assign(answer);x
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 
256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 "You Try It!
" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
25 "1.  Create an expression " }{XPPEDIT 18 0 "y = x^2+6*x-81;" "6#/%
\"yG,(*$%\"xG\"\"#\"\"\"*&\"\"'F)F'F)F)\"#\")!\"\"" }{TEXT -1 7 ".  Se
t " }{TEXT 288 1 "y" }{TEXT -1 52 " = 0 and solve for both exact and d
ecimal values of " }{TEXT 284 2 "x." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 28 "2.  Determine the values of " }{TEXT 
285 1 "x" }{TEXT -1 21 " in the interval 1 < " }{TEXT 286 1 "x" }
{TEXT -1 28 " < 12 that are solutions to " }{XPPEDIT 18 0 "2*x^5-29*x^
4-108*x^3+1611*x^2-3240*x;" "6#,,*&\"\"#\"\"\"*$%\"xG\"\"&F&F&*&\"#HF&
*$F(\"\"%F&!\"\"*&\"$3\"F&*$F(\"\"$F&F.*&\"%6;F&*$F(F%F&F&*&\"%SKF&F(F
&F." }{TEXT -1 5 " = 0 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 56 "3.  Create the following function and find the value
 of " }{TEXT 310 1 "f" }{TEXT -1 1 "(" }{TEXT 311 1 "x" }{TEXT -1 3 " \+
+ " }{TEXT 312 1 "h" }{TEXT -1 4 ") - " }{TEXT 313 1 "f" }{TEXT -1 1 "
(" }{TEXT 314 1 "x" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT 289 1 "f" 
}{TEXT -1 1 "(" }{TEXT 287 1 "x" }{TEXT -1 5 ") =  " }{XPPEDIT 18 0 "x
^2+6*x+9;" "6#,(*$%\"xG\"\"#\"\"\"*&\"\"'F'F%F'F'\"\"*F'" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "4. Solve the syste
m of equations" }}{PARA 0 "" 0 "" {TEXT -1 1 "3" }{TEXT 290 1 "x" }
{TEXT -1 4 " + 5" }{TEXT 291 1 "y" }{TEXT -1 4 " - 8" }{TEXT 292 1 "z
" }{TEXT -1 5 " = 10" }}{PARA 0 "" 0 "" {TEXT -1 1 "2" }{TEXT 293 1 "x
" }{TEXT -1 4 " - 8" }{TEXT 294 6 "y + z " }{TEXT -1 4 "= 12" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 295 1 "x" }{TEXT -1 4 " - 3" }{TEXT 
296 1 "y" }{TEXT -1 4 " + 7" }{TEXT 297 1 "z" }{TEXT -1 5 " = 13" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "10 3 2 4" 2 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }