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{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }
{TEXT 256 0 "" }{TEXT 257 27 "Brief Introduction to Maple" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }{TEXT 268 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 270 0 "" }{TEXT 271 62 "
1.  Be sure you have opened this Maple worksheet as a Maple 10" }
{TEXT 273 0 "" }{TEXT -1 1 " " }{TEXT 274 17 "Classic Worksheet" }
{TEXT 275 0 "" }{TEXT 276 0 "" }{TEXT 277 0 "" }{TEXT 278 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 77 "   (a)  You should save this file to your
 U: drive after clicking on the link" }}{PARA 0 "" 0 "" {TEXT -1 42 " \+
  (b)  Start \"Maple 10 Classic Worksheet\"" }}{PARA 0 "" 0 "" {TEXT 
-1 57 "   (c)  Open this worksheet, on your U: drive, from Maple" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}{TEXT 279 0 "" }{TEXT 280 102 "2.  Once you have opened this workshee
t, do a \"Save\" to your U: drive, and then do them every so often" }
{TEXT 281 0 "" }{TEXT -1 0 "" }{TEXT 286 1 "." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 282 0 "" 
}{TEXT 283 121 "3.  If you ever need to add another command line, you \+
can pull down the \"Insert\" menu and click on \"Add Execution Group.
\"" }{TEXT 284 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 0 "" }{TEXT 262 25 "4.
 Maple as a Calculator." }{TEXT 263 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 64 "First, remember that all Maple commands end with a s
emi-colom, ;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 104 "You may use Maple as a calculator.  Just put your cursor anywh
ere on the following lines and hit return." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 6 "1 + 2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 
"3.4 * ( 3 + 4 ) / 2 - 16.5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "sqrt(2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Note, that to fo
rce a Maple to give you a numeric answer, you can use the " }{TEXT 
259 5 "evalf" }{TEXT -1 9 " command." }{TEXT 258 0 "" }{TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( sqrt(2) );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "1 + 2;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 74 "For convenience, you can refer to the last result Ma
ple calculated with a " }{TEXT 260 1 "%" }{TEXT -1 2 " ." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "% + 4;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 264 0 "" }{TEXT 265 31 "5. Defining functions in \+
Maple." }{TEXT 266 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 32 "Let's define a function, f(x) = " }
{XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#" }{TEXT -1 3 "   " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f:=x-> x^2;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 101 "Using incorrect syntax when defining a funciton in \+
Maple is one of the most common mistakes in Maple." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 267 90 "Notice that the f(x) in \+
mathematical notation is replaced by  f := x - >  in Maple syntax." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "To confir
m that the definition of f(x) is correct, check it at a few values of \+
x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(1);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "f(-4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 154 "One th
ing to remember when writing a mathematical expression is that when tw
o terms are being multiplied, you must type in the multiplication oper
ator, *." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
26 "So, try to define g(x) = 3" }{XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#
" }{TEXT -1 19 " correctly in Maple" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Evaluate the \+
function g(x) at three values of x." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 287 0 "" }{TEXT 288 13 "6.  For-loops" }{TEXT 
289 0 "" }{TEXT 290 1 "." }{TEXT 291 0 "" }{TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 171 "One of the classic \+
structures in a programming language is the \"for-loop.\"  In Maple, w
e will use a \"for-loop\" to generate several function values.  Note t
hat we will use " }{TEXT 292 0 "" }{TEXT 293 1 "i" }{TEXT 294 0 "" }
{TEXT -1 154 " as the loop-control or \"dummy\" variable.  Below, the \+
loop calculates f(0), f(1), ... , f(10), and prints this value along w
ith the loop-control variable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 48 "for i from 0 to 10 do\n   print (i,f(i));\nend do;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "Write a similar loop to print g(0), g(1),
 ..., g(10)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 83 "If you want to continue a line, without hitting \"enter,\" you \+
can hit \"shift-enter.\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 295 0 "" }{TEXT 296 
31 "7.  Sequences stored in arrays." }{TEXT 297 0 "" }{TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 84 "Now, cons
ider the sequence we discussed in class for the number of edges of n b
oxes." }}{PARA 0 "" 0 "" {TEXT -1 21 "4, 7, 10, 13, 16, ..." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 
299 11 "closed form" }{TEXT -1 23 " for this sequence was " }{XPPEDIT 
18 0 "a[n] = 3*n+1;" "6#*$/&%\"aG6#%\"nG,&*&\"\"$\"\"\"%\"nGF,F,F,F,F,
" }{TEXT -1 8 " , for  " }{XPPEDIT 18 0 "1 <= n;" "6#1\"\"\"%\"nG" }
{TEXT -1 3 "  ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 66 "The for-loop below will print the first 10 terms of this \+
sequence." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for n from 1 t
o 10 do\n   print(n,3*n+1);\nend do;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 92 "Maple also allows you to store the values of the sequence in an
 array, as in the code below." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 66 "a:=array(1..10);\nfor n from 1 to 10 do\n   a[n] := 3*n + 1;\nen
d do;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Now we can display a few
 values of the array a." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a
[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[5];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[6];" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 22 "Finally, consider the " }{TEXT 298 11 "recursively" }
{TEXT -1 18 " defined sequence " }{XPPEDIT 18 0 "b[n] = b[n-1]+4;" "6#
/&%\"bG6#%\"nG,&&F%6#,&F'\"\"\"F,!\"\"F,\"\"%F," }{TEXT -1 9 " , where
 " }{XPPEDIT 18 0 "b[1] = 5;" "6#/&%\"bG6#\"\"\"\"\"&" }{TEXT -1 2 " .
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "Fill \+
in the code below, which fills an array \"b\" with the first 10 terms \+
of this sequence." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "b:=arr
ay(1..10);\nb[1]:=     \nfor n from 2 to 10 do\n   b[    ] := b[n-1] +
   ;\nend do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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