{VERSION 4 0 "IBM INTEL LINUX22" "4.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 0 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "10x20" 1 20 0 0 0 0 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R 3 Font 3" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 0 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 4" -1 259 1 {CSTYLE "" -1 -1 "Courier" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 5" -1 260 1 {CSTYLE " " -1 -1 "Courier" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {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 }