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{SECT 0 {EXCHG {PARA 260 "" 0 "" {TEXT -1 10 "Lecture 1 " }}{PARA 264 
"" 0 "" {TEXT -1 13 "Click on the " }{TEXT 442 1 "+" }{TEXT -1 46 "'s \+
to open each section. You may click on the " }{TEXT 443 1 "-" }{TEXT 
-1 124 " to close the section. This will be useful for clearing up som
e space. But before printing make sure all sections are open. " }}
{PARA 264 "" 0 "" {TEXT -1 176 "As you read this lecture, experiment w
ith the commands.  Use the mouse to change symbols. Re-execute the com
mands by placing the cursor on the line of interest and hitting the " 
}{TEXT 428 6 "Return" }{TEXT -1 84 " key again. From time to time try \+
your hand at typing in and executing new commands." }}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 14 "What is Maple?" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "" 0 "" {TEXT 261 5 "Maple" }{TEXT -1 6 " is a " }
{TEXT 256 27 "Symbolic Computation System" }{TEXT -1 4 " or " }{TEXT 
257 26 "Computer Algebra  System. " }{TEXT -1 37 " That is, it manipul
ates information " }{TEXT 258 12 "symbolically" }{TEXT -1 4 " or " }
{TEXT 259 13 "algebraically" }{TEXT -1 122 " as opposed to just numeri
cally.  Nevertheless, it does have numerical manipulation abilities. I
n this course we will use " }{TEXT 260 9 "Maple 7. " }{TEXT -1 1 " " }
{TEXT 345 7 "Maple 6" }{TEXT -1 84 " was the previous version of Maple
 and it uses essentially the same syntax.  Before " }{TEXT 360 5 "Mapl
e" }{TEXT -1 1 " " }{TEXT 361 1 "6" }{TEXT -1 5 " was " }{TEXT 362 7 "
Maple V" }{TEXT -1 49 ". Significant changes were made when going from
  " }{TEXT 347 7 "Maple V" }{TEXT -1 4 " to " }{TEXT 348 7 "Maple 6" }
{TEXT -1 124 ", so you should be sure of the version you are using. So
me differences in syntax will be pointed out as we proceed. See the " 
}{TEXT 363 11 "Maple Links" }{TEXT -1 122 " on the course webpage or m
y homepage for more information about the history of Maple and Maple r
esources on the internet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 68 "For those who are interested, the kernel of Maple \+
is written in the " }{TEXT 262 2 "C " }{TEXT -1 150 "language. But mos
t of the functions in Maple are written in Maple and can be viewed and
 manipulated by the user. We will discuss how to do this later." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Perhaps t
he program most similar to " }{TEXT 366 5 "Maple" }{TEXT -1 4 " is " }
{TEXT 367 11 "Mathematica" }{TEXT -1 177 ". However, there are many ot
her such programs available. Some like Maple and Mathematica are quite
 general and some are more specialized. For a more comprehensive list \+
see the  " }{TEXT 364 34 "A List of Computer Algebra Systems" }{TEXT 
-1 69 " by Herng-Jeng Jou which may be found on the above mentioned we
bpage " }{TEXT 365 12 "Maple Links." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Maple as a \+
Calculator" }}{PARA 0 "" 0 "" {TEXT -1 30 "Maple may be used as simply
 a " }{TEXT 264 10 "calculator" }{TEXT -1 108 " with graphing capabili
ties:  We illustrate this capability first. Later we will show how to \+
use Maple as a " }{TEXT 265 22 "programming language.\n" }}{PARA 0 "" 
0 "" {TEXT -1 99 "To start Maple on most platforms just double click o
n the Maple icon. In Unix systems one may type " }{TEXT 349 6 "xmaple
" }{TEXT -1 82 " from a command line to open Maple. When Maple opens, \+
you are in what is called a " }{TEXT 344 15 "Maple worksheet" }{TEXT 
-1 45 ".  Names of Maple worksheets usually end in  " }{TEXT 346 4 ".m
ws" }{TEXT -1 71 ". I am now typing this lecture in a Maple worksheet \+
which I have named " }{TEXT 368 18 "lecture2002_01.mws" }{TEXT -1 2 ".
\n" }}{PARA 0 "" 0 "" {TEXT -1 346 "\"Execute\" each of the commands b
elow by placing the cursor anywhere on the line, then hitting the retu
rn key.  If you have done this correctly you should see the answer in \+
blue. Also the cursor will move to the next line. Hit the return key a
gain to execute the next line. Continue to do this. The first commands
 show how to do simple arithmetic." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 257 "" 0 "" {TEXT -1 48 "Note that each command ends with a semi
-colon.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
66 "Try to guess the output, before executing a command when possible.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 4 "3*4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2^5;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "12/2;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "11/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "11.0/2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Notice the effect
 of changing 11 to 11.0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "
3-4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3+4;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 351 24 "Maple is case sensitive." }{TEXT -1 114 
" So, for example, ABC, ABc, AbC, Abc, aBc, Abc, etc, are all differen
t so far as Maple is concerned. \n\nMaple uses " }{TEXT 350 2 "Pi" }
{TEXT -1 31 " (not pi) to denote the number " }{XPPEDIT 18 0 "pi:" "6#
%#piG" }{TEXT -1 44 ". We can get a floating point evaluation of " }
{XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 16 " by the command " }{TEXT 
371 9 "evalf(Pi)" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "Pi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval
f(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf(pi); #pi is
 not equal to Pi" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 324 "Note the # m
ay be used for comments as we just did. Everything following # on a li
ne is ignored by Maple. However, it looks better to use the text mode.
 Note that pi appears as the lower case Greek letter for p. Similarly \+
alpha, beta, gamma, etc., may be used as variables and will appear in \+
the output as the Greek letters " }{XPPEDIT 18 0 "alpha,beta,gamma;" "
6%%&alphaG%%betaG%&gammaG" }{TEXT -1 6 ", etc." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Notice that a Maple " }
{TEXT 266 9 "worksheet" }{TEXT -1 61 " (where we are now) is divided i
nto three different regions: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 352 18 "     input region " }{TEXT -1 9 "(in red
)," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 353 18 "  \+
   output region" }{TEXT -1 12 " (in blue), " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 354 16 "     text region" }{TEXT -1 
13 " (in black). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 18 "You can enter the " }{TEXT 453 9 "text mode" }{TEXT -1 
17 " by clicking the " }{TEXT 267 1 "T" }{TEXT -1 108 " on the menu at
 the top.  More about these matters will be given below. \n\nWe can ge
t 1000 decimal digits of " }{XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 
11 " as follows" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf[10
00](Pi);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf[10]" }
{TEXT -1 22 " is the same thing as " }{MPLTEXT 1 0 5 "evalf" }{TEXT 
-1 2 ".\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Note that Maple doe
s not give a floating point number unless you specifically ask for it.
 For example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/3);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 195 "We may get a floating point \+
evaluation of the previous output as follows. Note that % indicated th
e previous output. %% indicates the output before that. The one before
 that is indicated by %%%. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "We illustrate the
 use of % and %% below:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "3
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "2;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Se
e if you can predict what will be the output when the next line is exe
cuted." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "%%;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 14 "More examples:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "sin(Pi/5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 11 "sin(Pi/37);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf
(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sqrt(16);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(7);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 609 "Maple has very high precision arithmetic. However, if you push
 it too far, you will cause Maple to crash or, if you are lucky, just \+
to say, \" The object you asked for is too large.\"  When I attempted \+
to execute the following commands with Maple 6 on my Mac G-4 the first
 came back with a warning that I had used too much memory and should q
uit and restart Maple. The second caused Maple to crash. I would have \+
lost everything if I had not saved the worksheet before executing thes
e two commands. I will place # before them to guard against accidental
 execution. (Maple ignores everything on a line after a #.)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "# 353^10000000;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# 353^1000;" }}}{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 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 263 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 35 "Inserting prompts and Shortcut Keys" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 264 "" 0 "" {TEXT -1 88 "
You may insert new prompts before or after the cursor by clicking on t
he button labeled " }{TEXT 444 2 "[>" }{TEXT -1 46 " on the menu bar o
r by going to the menu item " }{TEXT 445 6 "Insert" }{TEXT -1 19 " and
 going down to " }{TEXT 446 15 "Execution Group" }{TEXT -1 21 " and ch
oosing either " }{TEXT 447 13 "Before Cursor" }{TEXT -1 4 " or " }
{TEXT 448 12 "After Cursor" }{TEXT -1 71 ".  If you do this a lot you \+
may want to learn the keyboard short cuts. " }}{PARA 264 "" 0 "" 
{TEXT -1 16 "Using Windows,  " }{TEXT 449 8 "Ctrl + J" }{TEXT -1 43 " \+
will insert a prompt after the cursor and " }{TEXT 450 8 "Ctrl + K" }
{TEXT -1 36 " will insert one before the cursor. " }}{PARA 264 "" 0 "
" {TEXT -1 41 "To see a list of all key shortcuts go to " }{TEXT 451 
18 "Help, Topic Search" }{TEXT -1 14 " and type in  " }{TEXT 452 13 "s
hortcut_keys" }{TEXT -1 92 ". Then click on the item for Macintosh, Wi
ndows or Unix depending on what computer you have." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 32 "Removing \+
Output from a Worksheet" }}{PARA 0 "" 0 "" {TEXT -1 88 "Sometimes one \+
want to clear the output from the worsheet when it becomes too clutter
ed. " }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 454 110 "YOU DO NOT WAN
T TO DO THAT NOW SINCE YOU WILL HAVE TO PRINT OUT THE OUTPUT IN THIS W
ORKSHEET FOR YOUR NOTEBOOK" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "This can be done by going to " 
}{TEXT 455 4 "Edit" }{TEXT -1 48 " on the menu at the top. Drag the mo
use down to " }{TEXT 456 13 "Remove Output" }{TEXT -1 43 " and with th
e mouse still held down select " }{TEXT 457 16 "From Worksheet. " }
{TEXT -1 69 "When you release the mouse button all of the output will \+
be removed.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 
1 {PARA 3 "" 0 "" {TEXT 268 31 "More Use of Built-in Functions:" }
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 174 "The following commands s
hould be self explanatory.  Execute each in turn. In some cases you ma
y guess the output. Note the different effect of Diff vs diff and of I
nt vs int." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(sin(x),x)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Diff(sin(x),x) = diff(
sin(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Diff(arctan(a
*x),x) = diff(arctan(a*x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "int(x^3,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(x^
3,x=1..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Int(x^3,x=1..2) = int(x^3,x=
1..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(2*x^3+x^2+x
-1=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Here I denotes the co
mplex number " }{XPPEDIT 18 0 "sqrt(-1);" "6#-%%sqrtG6#,$\"\"\"!\"\"" 
}{TEXT -1 79 ".  These three solutions can be converted to floating po
int numbers as follows:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "e
valf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Next we solve a diffe
rential equation. First we define the equation. We call it ODE." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ODE := diff(y(x),x)-y(x) = s
in(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "dsolve(ODE);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "We will discuss " }{TEXT 369 5 "so
lve" }{TEXT -1 5 " and " }{TEXT 370 6 "dsolve" }{TEXT -1 23 " in more \+
detail later. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "Elem
entary Plotting" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 98 "This is a brief introduction to the Maple plotting functi
ons. We will go into more details later. " }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "First we plot the graph of " }
{XPPEDIT 18 0 "y = x^3+x^2+x+1;" "6#/%\"yG,**$%\"xG\"\"$\"\"\"*$F'\"\"
#F)F'F)F)F)" }{TEXT -1 28 " for x in the range [-2,2] ." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(x^
3+x^2+x+1,x=-2..2); \n" }{TEXT -1 211 "After executing this line click
 on the plot with the cursor. Then drag the lower right corner of the \+
frame upward to the left to make the size of the plot smaller. This wi
ll help to save space in the worksheet. " }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 37 "Now we plot the graph of the surface " }{XPPEDIT 18 0 "z \+
= cos(x^2+y^2);" "6#/%\"zG-%$cosG6#,&*$%\"xG\"\"#\"\"\"*$%\"yGF+F," }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 51 "plot3d(cos(x^2+y^2), x=-Pi/2..Pi/2,y=-Pi/2..Pi
/2);\n" }{TEXT -1 349 "After executing the plot click on the picture. \+
 Then using the mouse you can rotate the surface. Also when you click \+
on the plot you will see a new row on the menu bar. Click on some of t
he icons to see the effect on the picture. Before continuing make this
 plot smaller also as you did the previous one to save paper  when you
 print this worksheet." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Later W
e will have lots more to say about ploting curves and surfaces." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Here are some more self-explanator
y built-in functions. Execute these." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "ln(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ev
alf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(ln(x), x=.3
..4);\n" }{TEXT -1 51 "After executing this command make the plot smal
ler." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 " Maple for " }{XPPEDIT 
18 0 "e^x;" "6#)%\"eG%\"xG" }{TEXT -1 7 "  and  " }{XPPEDIT 18 0 "e;" 
"6#%\"eG" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Note t
hat Maple does not recognize the number " }{TEXT 472 1 "e" }{TEXT -1 
5 " or  " }{XPPEDIT 473 0 "e^x;" "6#)%\"eG%\"xG" }{TEXT -1 22 " instea
d one must use " }{TEXT 474 6 "exp(x)" }{TEXT -1 5 " for " }{XPPEDIT 
475 0 "e^x;" "6#)%\"eG%\"xG" }{TEXT -1 5 " and " }{TEXT 476 6 "exp(1)
" }{TEXT -1 5 " for " }{XPPEDIT 477 0 "e;" "6#%\"eG" }{TEXT -1 49 ", a
s in the following. Note the output DOES give " }{TEXT 372 2 "e " }
{TEXT -1 3 "and" }{TEXT 480 1 " " }{TEXT -1 1 " " }{XPPEDIT 256 0 "e^x
;" "6#)%\"eG%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(1);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 23 "plot(exp(x), x=-1..2);\n" }{TEXT -1 51 "After execu
ting this command make the plot smaller." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 47 "But note the failure of the following commands:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(e);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 18 "plot(e^x,x=-1..2);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 157 "This is because Maple does not know what e^x is. It c
onsiders e to be some unknown number. However, is we replace e by a sp
ecific number there is no trouble:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "diff(2^x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "plot(2^x,x=-1..2);\n" }{TEXT -1 55 "Make the plot smaller after \+
executing the plot command." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 24 "Basic Worksheet Handling" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 256 "" 0 "" {TEXT 287 70 "Here I indicate
 how to start a new worksheet,  make a title, indicate " }{TEXT 286 
102 "author, insert Standard Math (that is,  a mathematical formula) i
n text, and how to save a worksheet. " }{TEXT 288 1 " " }{TEXT -1 2 "
\n\n" }{TEXT 280 9 "1. Under " }{TEXT 282 4 "File" }{TEXT 283 20 " on \+
the menu choose " }{TEXT 284 3 "New" }{TEXT 281 17 " or click on the \+
" }{TEXT 285 16 "blank page icon " }{TEXT 289 42 "on the menu bar.  Th
is opens a new page.  " }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 
"" 0 "" {TEXT 373 30 "2.  Next go to the menu named " }{TEXT 374 6 "Wi
ndow" }{TEXT 375 18 " and pull down to " }{TEXT 376 8 "Vertical" }
{TEXT 377 112 ". This will allow you to read this worksheet while foll
owing these directions in the new worksheet.  \n\n3. Under " }{TEXT 
270 6 "Insert" }{TEXT 290 8 " select " }{TEXT 271 5 "Text " }{TEXT 
291 16 "or click on the " }{TEXT 272 1 "T" }{TEXT 292 43 " icon on the
 menu bar. Then, where it says " }{TEXT 269 8 "P Normal" }{TEXT 293 
45 " pull down the menu at that point and select " }{TEXT 273 7 "P Tit
le" }{TEXT 333 2 ". " }{TEXT 294 18 "Type in the words " }{TEXT 378 
12 "Sample Title" }{TEXT 379 43 " and then hit return. This will put y
ou in " }{TEXT 274 8 "P Author" }{TEXT 295 34 " mode. Type your name a
nd the hit " }{TEXT 356 6 "Return" }{TEXT 357 2 ". " }{TEXT 296 19 "Yo
u will now be in " }{TEXT 334 8 "P Normal" }{TEXT 335 57 " text mode. \+
 Type the words \"Some sample Maple commands.\"" }}{PARA 256 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 343 17 "4. Next click on " }
{TEXT 275 2 "[>" }{TEXT 380 1 " " }{TEXT 297 10 "or choose " }{TEXT 
336 1 "I" }{TEXT 276 5 "nsert" }{TEXT 337 1 " " }{TEXT 298 5 " then" }
{TEXT 278 1 " " }{TEXT 338 15 "Execution Group" }{TEXT 339 1 " " }
{TEXT 299 4 "then" }{TEXT 279 1 " " }{TEXT 340 12 "After Cursor" }
{TEXT 341 2 ". " }{TEXT 300 53 "[Sometimes you may want to insert an e
xecution group " }{TEXT 277 6 "before" }{TEXT 342 11 " the cursor" }
{TEXT 301 50 "--especially if you are at the top of the page.]\n " }}
{PARA 256 "" 0 "" {TEXT 382 81 "When you see the prompt, i.e., >, then
 type in some mathematical command such as " }{MPLTEXT 1 0 6 "2^100;" 
}{TEXT -1 2 ". " }{TEXT 381 70 "Then hit return to execute this comman
d. Try a few more such command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 57 "5. Go back to the text mode by repeating \+
clicking on the " }{TEXT 383 1 "T" }{TEXT -1 29 " in the menu bar or g
oing to " }{TEXT 384 6 "Insert" }{TEXT -1 6 " then " }{TEXT 385 9 "Exe
cution" }{TEXT -1 1 " " }{TEXT 386 5 "Group" }{TEXT -1 6 " then " }
{TEXT 387 5 "After" }{TEXT -1 1 " " }{TEXT 388 6 "Cursor" }{TEXT -1 2 
". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Ty
pe in the words \"We now compute the integral\" .\n\nNext go to  " }
{TEXT 302 7 "Insert " }{TEXT -1 5 "then " }{TEXT 355 13 "Standard Math
" }{TEXT -1 103 ". You will see a ?.  Now type in int(x^2,x=1..2) you \+
will see this appear in a box under the menu bar. " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 167 "Now hit the T again to g
o back into ordinary text mode and continue to type the words \"as fol
lows\".  You should see the following:\n\n       We now compute the in
tegral " }{XPPEDIT 18 0 "int(x^2,x = 1 .. 2);" "6#-%$intG6$*$%\"xG\"\"
#/F';\"\"\"F(" }{TEXT -1 14 " as follows. \n" }}{PARA 0 "" 0 "" {TEXT 
-1 98 "6. Then click on [>  to go back into execution mode. When the c
ursor comes up type in the command " }{MPLTEXT 1 0 16 "int(x^2,x=1..2)
;" }{TEXT -1 45 " then execute the command by hitting return. " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "7. To sav
e your worksheet go under " }{TEXT 303 4 "File" }{TEXT -1 12 " and cho
ose " }{TEXT 304 4 "Save" }{TEXT -1 172 " (or click on the icon that l
ooks like a floppy disk on the menu bar). The first time you will be p
rompted to give a name. Use a single word with no spaces and end it wi
th " }{TEXT 306 4 ".mws" }{TEXT -1 16 ". For example,  " }{TEXT 305 
15 "YourName01.mws " }{TEXT -1 116 "would be a possible name for a Map
le file.  If you look at the top of this page you will see the name of
 this file: " }{TEXT 358 13 "lecture01.mws" }{TEXT -1 2 ". " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 95 "8. If you want \+
to start a new worksheet keeping what you already have in a named work
sheet use " }{TEXT 307 8 "Save As " }{TEXT -1 12 "instead of  " }
{TEXT 308 5 "Save " }{TEXT 389 133 "and give the worksheet a new name.
 This way you can keep your old worksheet and experiment with changes \+
without losing what you did. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Averting Disaster" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "A
fter a worksheet has been named, you should still save it frequently b
y clicking on the icon of the floppy disk or using " }{TEXT 458 4 "Sav
e" }{TEXT -1 7 " under " }{TEXT 459 4 "File" }{TEXT -1 137 " --to guar
d against losing work if Maple crashes. Note that you will not need to
 change the name after you have saved it the first time. " }}}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 35 "Using Several Worksheets at a Time." }}
{PARA 0 "" 0 "" {TEXT -1 26 "Under the menu item named " }{TEXT 390 6 
"Window" }{TEXT -1 33 " you will find the three options " }{TEXT 391 
41 "Cascade, Tile, Horizontal, and Vertical. " }{TEXT -1 268 "To see t
he effect of these first open several different worksheet in successio
n.  An easy way to do this is just by clicking on the blank page icon \+
on the menu bar. But  you may also open any worksheets. Then select ea
ch of these options. You will see what they do. \n\n" }{TEXT 392 15 "I
mportant Fact:" }{TEXT -1 215 " Assignments made in one open worksheet
 are recognized by all open worksheets. When switching worksheets be s
ure you have clicked your cursor in the worksheet you want to work in \+
before continuing in that worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 393 28 "Cutting, Copying and Pasting" }{TEXT 
-1 115 ": You may cut, copy and paste from a worksheet to itself or fr
om one worksheet to another using the commands unded " }{TEXT 460 4 "E
dit" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "
Maple's Built-in Help" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
257 "" 0 "" {TEXT 313 13 "Getting Help:" }{TEXT 309 129 " Perhaps the \+
easiest way is to use a question mark as follows: Here we suppose we f
orgot the command for differentiate. We guess " }{TEXT 315 11 "that it
 is " }{TEXT 310 71 "dif.  Type and execute the following command by h
itting the Return key." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?dif" }}}{EXCHG {PARA 257 "" 0 "" 
{TEXT 461 45 "This will bring up several options including " }{TEXT 
462 4 "diff" }{TEXT 463 1 "." }{TEXT -1 1 " " }{TEXT 359 23 " Now, you
 can click on " }{TEXT 466 4 "diff" }{TEXT 467 30 " or go back and add
 and extra " }{MPLTEXT 1 0 1 "f" }{TEXT 465 4 " to " }{MPLTEXT 1 0 4 "
?dif" }{TEXT 464 341 " and re-execute. In any event you will be lead t
o the help page for diff.  If you scroll down you will see a number of
 examples. This will often be enough. In some cases however you may ne
ed to read the entire help page carefully. If you execute a single que
stion mark (as follows) you will bring up some general information on \+
getting help." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "\nFor another example: Suppose th
at you want to know how to factor an integer or a polynomial: Then you
 could try:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 7 "?factor" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Not
ice that the help page that comes up says that " }{TEXT 311 6 "factor
" }{TEXT -1 67 " is used to factor polynomials and not integers. It te
lls you that " }{TEXT 312 7 "ifactor" }{TEXT -1 53 " is used to factor
 integers. Here are some examples.\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "factor(t^2-t-2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "factor(123456789);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "ifactor(123456789);\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 468 24 "Other ways to get help: " }{TEXT -1 37 "You may do a ful
l text search of the " }{TEXT 322 16 "Maple Help Files" }{TEXT -1 13 "
 by going to " }{TEXT 316 4 "Help" }{TEXT -1 34 " on the menu bar and \+
pull down to " }{TEXT 314 17 "Full Text Search " }{TEXT 469 2 "or" }
{TEXT 470 16 " Topic Search.\n\n" }{TEXT 317 59 "Another way is to sel
ect a word of interest and then go to " }{TEXT 318 4 "Help" }{TEXT 
319 34 " on the menu bar and pull down to " }{TEXT 320 15 "Help on Con
text" }{TEXT 321 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 
"" {TEXT -1 29 "The Use of := , = , : , and ;" }}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 67 "Assignment of the value 2 to the variable x is obtained
 by use of  " }{TEXT 330 2 ":=" }{TEXT -1 47 "  . This is a colon foll
owed by an equal sign. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 15 "The expression " }{TEXT 331 4 "x:=2" }{TEXT -1 38 " \+
means \"assign 2 to the  variable x.\" " }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 44 "Here is an example: We make two assi
gnments:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "x:=2; \ny:=3;" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Now let's see what the values o
f x and y are:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x,y;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Now x is 2 and y is 3 so far as Ma
ple is concerned. So if you try to solve the equation " }{XPPEDIT 18 
0 "x^2+x+1 = 0;" "6#/,(*$%\"xG\"\"#\"\"\"F&F(F(F(\"\"!" }{TEXT -1 20 "
  Maple is confused:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sol
ve(x^2+x+1=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Clearing x of
 the value 2 may be accomplished as follows:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "x:='x';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 4 "x,y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^2+x+1=
0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Note the use of " }
{TEXT 399 1 "=" }{TEXT -1 15 " as opposed to " }{TEXT 400 2 ":=" }
{TEXT -1 17 " in the equation " }{TEXT 401 15 "x^2 + x + 1 = 0" }
{TEXT -1 35 ".  We can even assign a name, say, " }{TEXT 402 4 "eqn " 
}{TEXT -1 17 "to this equation:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "eqn:=x^2+x+1=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
solve(eqn,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "The command " }
{TEXT 332 9 "restart; " }{TEXT -1 74 " as noted above, is useful for c
learing all variables and starting afresh." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "x:=2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r
estart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x,y;" }}}{EXCHG 
{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 323 29 "Note
 that if a line ends with" }{TEXT 326 3 " : " }{TEXT 329 12 " instead \+
of " }{TEXT 327 3 " ; " }{TEXT 328 12 "the command " }{TEXT 324 39 "is
 executed, but the output is not show" }{TEXT -1 2 ". " }{TEXT 325 11 
"Here is an " }{TEXT -1 8 "example:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "y:=14:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "t:=12;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "See what happens if \+
you forget the;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "t:=2" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 148 "You can go back to the line t:=2 and add the ; or you may add \+
it on the second line, where the cursor has moved to, before re-execut
ing the command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Did you notice the use of
 the comma above in " }{MPLTEXT 1 0 5 "x,y; " }{TEXT -1 84 "?  Execute
 the following to see the difference between the comma and the semi-co
lon." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 
"x:=2:\ny:=3:\nz:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x,y,
z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x; y; z;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 41 "Functions (Procedures) versus Exp
ressions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 62 "Maple has a large number of built-in functions (also know
n as " }{TEXT 396 10 "procedures" }{TEXT -1 17 ") . For example: " }
{TEXT 394 81 "sin, cos, tan, cotan, sec, csec, arcsin, ln, exp, abs, s
qrt, tan,  factorial, det" }{TEXT -1 151 " (determinant),  and many mo
re. These functions  behave pretty much as you would expect. You can a
lso make your own function which we illustrate below." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 183 "The \"obvious\" way t
o make a function, however, does not  work.  Suppose we want to define
 a new function f satisfying f(x) = x^2 + x + 1 for all x. Try execute
 the following command.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(x):=x^2+x+1;
\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 397 68 "This is NOT the way to do \+
it. Note what happens in the next command:" }{TEXT -1 1 "\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 11 "The object " }{TEXT 403 11 "x^2 + x + 1" }{TEXT -1 22 " is what
 is called an " }{TEXT 398 20 "algebraic expression" }{TEXT -1 141 ". \+
We may plot it, solve it, factor it,  integrate it, differentiate it, \+
and so forth, but it is NOT a function so far as Maple is concerned. \+
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "\nWhat we would like is for \+
f(2) to give us 7. Here are three correct ways to define such a functi
on.  You should learn each of these." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 257 "" 0 "" {TEXT -1 27 "Use of the arrow notation:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->x^2+x+1;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(a);" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 17 "\nUse \+
of unapply:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart: " 
}{TEXT -1 178 "(It is a good idea to restart after finishing one probl
em  and starting on another. This clears the internal memory. In this \+
case, it let's us clear the above definition of f. )\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=unapply(x^2+x+1,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(a);" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}
{PARA 257 "" 0 "" {TEXT -1 22 "Creating a procedure: " }{TEXT 395 62 "
(This is very useful for creating very complicated functions.)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f:=proc(x)
\n  x^2+x+1;\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f
(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(a);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 210 "We will use these ideas repeatedly in th
is course. So you should make absolutely sure you understand each of t
hese three methods for constructing a function. Now is a good time to \+
experiment with these methods." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 41 " Instructions for Printing this Worksheet" }}{EXCHG {PARA 0 "" 
0 "" {TEXT 429 58 "If you have closed any section open them now.  Then
 go to " }{TEXT 433 4 "File" }{TEXT 434 24 " on the menu and select " 
}{TEXT 435 5 "print" }{TEXT 436 62 ". Proceed to print this worksheet \+
before you start working on " }{TEXT 437 12 "Assignment 1" }{TEXT 438 
8 " below. " }{TEXT 439 148 "Keep a loose-leaf notebook with all the p
rint outs of the executed worksheets. The homework assignments will be
 printed out separately and handed in" }{TEXT 440 151 ".. After they a
re returned they should also be kept in the note book together with th
e solutions provides. I will check the notebook from time to time." }
{TEXT 432 1 " " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 265 "" 0 "" {TEXT -1 48 "After you have printed out the workshee
t. go to " }{TEXT 430 4 "View" }{TEXT -1 16 " and go down to " }{TEXT 
431 21 "Collapse All Sections" }{TEXT -1 77 ". Then print again. This \+
will give you a printout of just the section names. " }{TEXT 441 90 "Y
ou should place this before the executed worksheet to serve as a rough
 table of contents." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 37 "Assignme
nt 1 (Due Monday, January 14)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 404 10 "Problem 1." }{TEXT -1 50 " \n\n(a) Sta
rt a new worksheet. Make a title called " }{TEXT 407 12 "Assignment 1
" }{TEXT -1 11 " using the " }{TEXT 408 1 "P" }{TEXT -1 1 " " }{TEXT 
405 11 "Title style" }{TEXT -1 44 ". Follow the heading by your name u
sing the " }{TEXT 406 14 "P Author style" }{TEXT -1 34 ". [Look back a
t the above section " }{TEXT 409 24 "Basic Worksheet Handling" }{TEXT 
-1 108 " if you don't recall how to do this.] \n \n(b)  Still using th
e methods described above type in the following " }{TEXT 471 8 "verbat
im" }{TEXT -1 7 " using " }{TEXT 410 11 "Insert Text" }{TEXT -1 5 " an
d " }{TEXT 411 20 "Insert Standard Math" }{TEXT -1 94 " to do the comm
ent containing the integral: [Also execute each of the three Maple com
mands.]\n\n" }{TEXT 412 1 ">" }{MPLTEXT 1 0 9 " restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 22 "It is easy to compute " }{MPLTEXT 1 0 0 "
" }{XPPEDIT 18 0 "Int(x^2*sqrt(1-x^2),x = 0 .. 1);" "6#-%$IntG6$*&%\"x
G\"\"#-%%sqrtG6#,&\"\"\"F-*$F'F(!\"\"F-/F';\"\"!F-" }{TEXT -1 42 " usi
ng Maple. One simply types the command" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "int(x^2*sqrt(1-x^2),x=0..1);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 87 "To find the approximate floating point value of the in
tegral we apply evalf as follows:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 413 11 "\nP
roblem 2." }{TEXT -1 1 " " }{TEXT 414 3 " \n\n" }{TEXT -1 25 "(a) Show
 using Maple that" }{TEXT 415 1 " " }{XPPEDIT 18 0 "sqrt(2)+sqrt(3) = \+
pi;" "6#/,&-%%sqrtG6#\"\"#\"\"\"-F&6#\"\"$F)%#piG" }{TEXT -1 39 "  is \+
correct to three decimals digits, " }{TEXT 418 33 "but is not correct \+
to more than 3" }{TEXT -1 6 ". Use " }{TEXT 424 11 "evalf[3](x)" }
{TEXT -1 33 " to obtain x to 3 decimal digits." }}{PARA 0 "" 0 "" 
{TEXT -1 25 "\n(b) Assign the equation " }{XPPEDIT 18 0 "x^3-4*x^2-4*x
-5 = 0" "6#/,**$%\"xG\"\"$\"\"\"*&\"\"%F(*$F&\"\"#F(!\"\"*&F*F(F&F(F-
\"\"&F-\"\"!" }{TEXT -1 17 " to the variable " }{TEXT 425 3 "Eqn" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 8 "(c) Use " }{TEXT 423 5 "solve" }{TEXT -1 10 " to solve " }
{TEXT 426 3 "Eqn" }{TEXT -1 18 " for the variable " }{TEXT 427 1 "x" }
{TEXT -1 2 ". " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 416 9 "Problem 3" }{TEXT -1 63 ". \n\nUse Maple to find the valu
e of each of the following:\n\n(a) " }{XPPEDIT 18 0 "int(sin(x)*cos(x)
^2,x);" "6#-%$intG6$*&-%$sinG6#%\"xG\"\"\"*$-%$cosG6#F*\"\"#F+F*" }
{TEXT -1 28 " [indefinite integral]\n\n(b) " }{XPPEDIT 18 0 "int(sin(x
)*cos(x)^2,x = 1 .. 3);" "6#-%$intG6$*&-%$sinG6#%\"xG\"\"\"*$-%$cosG6#
F*\"\"#F+/F*;F+\"\"$" }{TEXT -1 106 " [definite integral exact value]
\n\n(c)  The floating point value of the integral in (b) to 10 digits.
\n\n(d) " }{XPPEDIT 18 0 "diff(x*exp(x)*sin(x),x);" "6#-%%diffG6$*(%\"
xG\"\"\"-%$expG6#F'F(-%$sinG6#F'F(F'" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 417 10 "Problem 4." }{TEXT -1 46 "  \n\nLet f \+
be the function defined by the rule " }}{PARA 0 "" 0 "" {TEXT -1 18 "
\n                 " }{XPPEDIT 18 0 "f(x) = sin(x)*(exp(x)+x^2+x+1);" 
"6#/-%\"fG6#%\"xG*&-%$sinG6#F'\"\"\",*-%$expG6#F'F,*$F'\"\"#F,F'F,F,F,
F," }{TEXT -1 3 ". \n" }}{PARA 0 "" 0 "" {TEXT -1 54 "Use each of the \+
three methods described in Lecture 1 (" }{TEXT 419 14 "arrow, unapply
" }{TEXT -1 5 " and " }{TEXT 420 4 "proc" }{TEXT -1 124 ") to define t
his function in Maple and find the value of f(x) to 10 digits for each
 of the following values of x:  0,  1.   " }{TEXT 421 36 "After each c
ase execute the command " }{MPLTEXT 1 0 8 "restart;" }{TEXT 422 27 "be
fore doing the next case." }{TEXT -1 0 "" }}}}{MARK "0 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }