{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 271 "Courier" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 } {PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "R3 Font 4" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 5" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 24 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 4 " -1 259 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 5" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {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 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }