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{SECT 0 {EXCHG {PARA 259 "" 0 "" {TEXT -1 14 "\nMaple Basics\n" }}
{PARA 0 "" 0 "" {TEXT -1 274 "Here are some basic Maple examples. T
hey illustrate the syntax\nof some useful commands for calculus. You
can make\nthe commands ``happen'' by hitting RETURN at the end of an
y input\nline. Input lines are in red on a color monitor, and they
start\nwith a > symbol." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT -1 53 "\n\nDefine an expression to work with in variou
s ways:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f := x^2*sin(x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&)%\"xG\"\"#\"\"\"-%$sinG6#F'F)
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 255 "\n\nNote that every command \+
ends with a semicolon. Having\ndefined f , we can use it in various
ways. Maple will remember\nwhat's meant by the symbol f.\n\n\nNow l
et's try doing some calculus-style things to f, such as differentiati
ng\nf with respect to x.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(
f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"-%$sinG6#F%F&
\"\"#*&)F%F*F&-%$cosGF)F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Lo
ok what happens if we use another variable than x :\n" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "diff(f,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Do you agree with the an
swer? (You should.) \n\nLet's do something else.\n" }}{PARA 0 "> "
0 "" {MPLTEXT 1 0 14 "g := int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"gG,(*&)%\"xG\"\"#\"\"\"-%$cosG6#F(F*!\"\"*&F)F*F+F*F**(F)F*F(F*-
%$sinGF-F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "The previous comm
and defined g as a new expression ---\n an antiderivative of f. \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0
10 "diff(g,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG\"\"#\"\"\"-
%$sinG6#F%F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 98 "That's reasssurin
g ... \nLet's try plotting something. Maple can plot all kinds
of things.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot( f, x=-3..3 )
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 378 "As you see, a new window po
ps up. You can do various things with the buttons\nin the menu at th
e top of the plot window, such as changing the style of axes.\nWhen yo
u're done with the window you can use the File menu to close\nit or k
ill it.\n\nThere are many variations on the plot command. To find ou
t more, use\nthe built-in help system. To do so, give a command like
this:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 455 "A help window pops up, with lots more informat
ion than you want. The most\nuseful stuff is often the examples at t
he bottom of the window. Note that you \ncan try any example by h
ighlighting it with the mouse, then moving to an\ninput position in th
e Maple window, and pressing the middle mouse button. (This\ncopies t
he highlighted stuff from one window into the input position.)\n\nHere
are a few more plot examples, to illustrate the possibilities:\n " }}
{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 -1 429 "The plot above is a parametric
plot---it produces a semi-circle.\nIf the plot doesn't look right to \+
you, try something in the Projection\nmenu in the plot window to se
e what it does.\n\nNote carefully how the square brackets are used. \+
In particular, the\nt-range is included INSIDE the square brackets,
for some reason.\n\nIn the next example, the last two bits of informa
tion control the ``window''\nin which the plot is drawn.\n" }}{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 34 "plot( [sin(t),cos(t
), t=0..2*Pi]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "\nTry playing
with any of the commands above, by using the mouse and\narrow keys to
change whatever you want. \n" }}{PARA 259 "" 0 "" {TEXT -1 15 "Plot
ting in 3d\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT
-1 146 "Maple is especially useful for plotting surfaces and other obj
ects in three dimensions.\n\nThe basic 3-d plotting command has the f
ollowing form:\n\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d( x^2+y
^2, x=-3..3, y=-3..3 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 510 "\nThe
result is a surface in xyz-space, as you'd expect. Note that you m
ight\nhave to fool with some of the menu items at the top to get axes,
different\ncolor schemes, etc. After you've made new choices for s
uch things, either click \nagain on the picture (use the MIDDLE mouse
button) or type ``p'' to get\nthe new plot.\n\nTry clicking on the \+
picture and dragging the bounding\nbox around to see the surface from \+
different angles. \n\n\nTry changing the function or the domain r
egion to see what happens." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0
"" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 24 "\nOther 3d plot
ting tools" }}{PARA 0 "" 0 "" {TEXT -1 93 "\n Maple has many other 3d \+
plotting tools. To get access to most of them, use\nthis command:\n
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with( plots );" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 86 "\nThis loads a lot of new plotting functi
ons into Maple. For example, you can type\n\n" }}{PARA 0 "> " 0 ""
{MPLTEXT 1 0 41 "contourplot( x^2+y^2, x=-3..3, y=-3..3 );" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 286 "\nThe result is a set of level curves fo
r the function. (You may want to experiment\nwith some of the menu i
tems at the top of the plot window to get axes, etc.)\n\nFor more info
rmation about any function, such as contourplot , you can\nalways us
e the Maple help system. Type, e.g., \n\n" }}{PARA 0 "> " 0 ""
{MPLTEXT 1 0 12 "?contourplot" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 125
"\nYou'll get a window full of information. The bottom of the window
often contains\nthe most useful information and examples." }}{PARA
260 "" 0 "" {TEXT -1 24 "\n\n\n\nDefining functions \n" }}{PARA 0 ""
0 "" {TEXT -1 288 "\nAbove we showed how to define f and g as \+
EXPRESSIONS. Doing\nso can save a lot of typing and retyping, but i
t does NOT define f and g\nas FUNCTIONS in the usual mathematica
l sense. For example,\nwe might like to find f(3), but Maple \+
won't do this properly (yet):\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 200 "We got some nonsense, but not what we wanted.\n\nHere's \+
how to define f as a FUNCTION, not an expression. Notice\nthe use
of the ``arrow''---it's actually just a hyphen and a greater than \+
sign.\n\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f := x -> x^2*sin(x);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Now we've defined f succes
sfully as a function in the usual sense. \n\n" }}{PARA 0 "> " 0 ""
{MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "To get a
decimal form of the answer above, type something like this:\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 0 "" 0 "" {TEXT
-1 234 "The evalf command tries to evaluate anything to a decim
al (or ``floating \npoint'') number. The percent sign represents \+
the previous output.\n\nIf you feed f a decimal number to start wi
th, it will give a decimal output.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1
0 7 "f(3.0);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19 2 0
" 113 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }