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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "Maple Basics\n" }}{PARA 
258 "" 0 "" {TEXT -1 265 "Here are some basic Maple examples.    They \+
illustrate the syntax of some useful commands for calculus.   You  mak
e the commands ``happen'' by hitting  RETURN at the end of any input l
ine.   Input lines are usually shown in red, and  they start with a   \+
 >  symbol." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 25 "Calculator-style c
ommands" }}{PARA 0 "" 0 "" {TEXT -1 78 "You can use Maple as a \"calcu
lator\", simply by typing the desired commands.   " }{TEXT 270 47 "Not
e that every command ends with a semicolon. " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "(2+3)/7 + cos(Pi/4);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 31 "sin(3.2) + cos(4.5) + ln (5.6);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 21 "1+2+3+4+5+6+7+8+9+10;" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 16 "sum(k, k=1..10);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "sum(1/k, k=1..100);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 49 "A strange result.   Let's see it in decimal form:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 6 "The   " }{TEXT 271 5 "evalf" }{TEXT -1 39 "   comm
and  tries to evaluate anything " }{TEXT 272 14 "numericallyI, " }
{TEXT -1 8 "to give " }{TEXT -1 108 "a decimal (or ``floating point'')
  result.   The  percent sign represents the most recent previous outp
ut.\n\n" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 23 "Calculus-style command
s" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 66 "To begin let's  define an \+
expression to work with in various ways:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "f :=  x^2*sin(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 4 "    " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 30 "Having defined our expression " }{XPPEDIT 18 0 "f;" "6#%\"fG" }
{TEXT -1 38 ", we can use it in various ways, and  " }{TEXT 256 47 "Ma
ple will remember what's meant by the symbol " }{XPPEDIT 18 0 "f;" "6#
%\"fG" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT 257 49 "First let's try  some calculus-style things with " 
}{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT 258 72 ",  such as differentiatio
n and integration with respect to the variable " }{XPPEDIT 18 0 "x;" "
6#%\"xG" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "
diff(f,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Look what happens i
f we use another variable than  " }{XPPEDIT 18 0 "x;" "6#%\"xG" }
{TEXT -1 3 " :\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(f,y);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Do you agree with the answer?   (Y
ou should.)    Let's try integration:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g := int(f,x);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "The previous command   defined  " 
}{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 47 "  as a new expression --- \+
an antiderivative of " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 40 ".  \+
  The following command calculates a " }{TEXT 269 10 "definite  " }
{TEXT -1 9 "integral:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "in
t(f,x=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(g,x);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "That's reasssuring --- we're \+
back where we started." }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 14 "Basic p
lotting" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Let's try plotting som
ething.    Maple can plot all kinds of things." }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot( f, x=-3.
.3 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 141 "If you click on the gra
ph you can do various things with the graphical menu buttons, such as \+
changing the style of axes and the aspect ratio." }}{PARA 0 "" 0 "" 
{TEXT -1 145 "  \nThere are many variations on the plot command.   To \+
find out more, use\nthe built-in help system.   To do so, either give \+
a command like this:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 545 "or experiment with the Help  menu
 at the top of the screen.   A help window pops up, often with much mo
re information than you want.   The most useful stuff is often the exa
mples at the bottom of the window.   Note that you  can try any exampl
e in the help system  by highlighting it with the mouse, then moving t
o an input position in the Maple window, and pressing the middle mouse
 button.  (This copies the highlighted stuff from one window into the \+
input position.)\n\nFollowing  are some  more plot examples, to illust
rate the possibilities:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "plot( sin(x), x=-Pi .. Pi, -2 .. 2 );" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot( sin(x), x=-Pi
 .. Pi, -5 .. 5 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(
 [sin(t),cos(t), t=0..Pi] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "T
he preceding plot is a " }{TEXT 259 10 "parametric" }{TEXT -1 246 " pl
ot---it produces a semi-circle. If the plot doesn't look semicircular \+
 to you,  click on the graph and then  try something in  the Projectio
n menu  to see what it does.   Notice carefully how the square bracket
s are used.   In particular, the " }{XPPEDIT 18 0 "t;" "6#%\"tG" }
{TEXT -1 19 "-range is included " }{TEXT 260 6 "inside" }{TEXT -1 145 
" the square brackets, for some reason.\n\nIn the next example  the la
st two bits of information control the ``window'' in which the plot is
 drawn.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot( [sin(t),
cos(t), t=0..Pi] , -5..5, -5..5);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "plot( [sin(t),cos(t), t=0..Pi],scaling=constrained);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 "\nTry playing with any of th
e commands above,  use the mouse and arrow keys to change whatever you
 want.   \n" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 11 "3D plotting" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 259 "" 0 "" 
{TEXT 262 144 "Maple is especially useful for plotting surfaces and ot
her objects in three dimensions.  The basic 3-d plotting command has t
he  following form:" }}}{EXCHG {PARA 259 "" 0 "" {TEXT 261 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot3d( x^2+y^2, x=-3..3, y=-3..3);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "The result is a surface in " 
}{XPPEDIT 18 0 "xyz;" "6#%$xyzG" }{TEXT -1 355 "-space, as you'd expec
t.    Note that you might have to fool with some of the menu items at \+
the top to get axes, different color schemes, etc. Also, try clicking \+
on the picture and dragging the bounding box around to see the surface
 from different angles.      \n\nTry changing the function or the doma
in region in the preceding command to see what happens." }}}{EXCHG 
{PARA 4 "" 0 "" {TEXT -1 23 "Other 3d plotting tools" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Maple \+
includes countless other 3d plotting tools.   To get access to most of
 them, use this command:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(
 plots );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "\nThis loads a lot o
f new plotting functions into Maple.    For example, you can type" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "contourplot( x^2+y^2, x=-3..3, y=-3..3 );" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 178 "\nThe result is a set of level curves for the functio
n.   (You may want to experiment\nwith some of the menu items at the t
op of the plot window to manipulate axes, colors, etc.)\n\n" }}}
{EXCHG {PARA 4 "" 0 "" {TEXT -1 18 "Defining functions" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 31 
"Above we showed how to define  " }{XPPEDIT 18 0 "f;" "6#%\"fG" }
{TEXT -1 8 "  and   " }{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 6 "   as
 " }{TEXT 263 11 "expressions" }{TEXT -1 65 ".   Doing so can save a l
ot of typing and retyping,  but it does " }{TEXT 264 3 "not" }{TEXT 
-1 9 " define  " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 6 "  and " }
{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 4 " as " }{TEXT 265 9 "function
s" }{TEXT -1 76 "  in the  usual  mathematical sense.    For example, \+
we might like to find  " }{XPPEDIT 18 0 "f(3);" "6#-%\"fG6#\"\"$" }
{TEXT -1 47 ",   but   Maple  won't do this properly (yet):\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 69 "We got some nonsense, but not what we wanted.  Here's how
 to define  " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 9 "   as a  " }
{TEXT 266 8 "function" }{TEXT -1 126 ", not an expression.  Notice esp
ecially the use of the  ``arrow'  (it is actually just a hyphen and a \+
greater than  sign.).  \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f :=  \+
x -> x^2*sin(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Now we've def
ined   " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 52 "  successfully as
 a function in the usual sense.  \n\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 5 "f(3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Let's get a " }
{TEXT 267 7 "decimal" }{TEXT -1 27 " form of the answer above:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 17 "Recall that the  " }{TEXT 268 5 "evalf" }{TEXT 
-1 144 "  command  tries to evaluate anything to a decimal number, and
 that the percent sign represents the most recent previous output.\n\n
If you feed   " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 65 "  a decima
l number to start with, it will give a decimal output.\n" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 "f(1.23);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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