{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "" -1 256 " " 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 1 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 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 1 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 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 1 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 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Headi ng 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 10 "Tutorial 1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "This command clears Maple's memory. It is good \"Maple hygiene\" to begin every new worksheet with " }{MPLTEXT 0 21 8 "restart:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 161 "The M aple environment is a rich one, and may be slightly intimidating to th e beginner. To aid in exploring the environment, choose \"Help/Balloon Help\" to switch " }{TEXT 258 12 "Balloon Help" }{TEXT -1 81 " on. (I f it gets into your way at any later time, toggle it off in the same w ay.)" }}{PARA 0 "" 0 "" {TEXT -1 147 "If you would like the lettering \+ to appear larger, click on one of the magnifying glass icons in the sh ortcut bar (the top middle bar) to reset the " }{TEXT 268 12 "zoom fac tor." }}{PARA 0 "" 0 "" {TEXT -1 48 "Now tyype in your first command a nd press Enter:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "2/3 + 5/ 11" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "The error message indicates that you need to tell Maple the" }{TEXT 281 18 " end of a command." } {TEXT -1 142 " This is usually done by a semicolon (;). If you want Ma ple to execute the command, but to \"hide\" the output, you can use a \+ colon (:) instead." }}{PARA 0 "" 0 "" {TEXT -1 60 "Now go back and edi t the previous command, so that it reads:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 11 "2/3 + 5/11;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Did you ask yourself the question how the text got into this workshee t?" }}{PARA 0 "" 0 "" {TEXT -1 3 "To " }{TEXT 259 11 "insert text" } {TEXT 260 0 "" }{TEXT -1 58 ", click in any input line (starting with \+ the input prompt " }{MPLTEXT 0 21 1 ">" }{TEXT -1 58 "), then click th e \"T\" button on the shortcut bar. You can " }{TEXT 261 20 "insert an input line" }{TEXT -1 21 " by clicking on the \"" }{MPLTEXT 0 21 2 "[ >" }{TEXT -1 9 "\" button." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Not ice that Maple uses exact (not approximate decimal) arithmetic. \+ " }}{PARA 0 "" 0 "" {TEXT -1 15 "Now calculate " } {XPPEDIT 18 0 "(2/5)^10;" "6#*$*&\"\"#\"\"\"\"\"&!\"\"\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "(2/5)^10;" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 115 "This is a fraction with big numbers in numerator and d enominator. To get a sense of the magnitude of the fraction, " }{TEXT 262 24 "convert it to a decimal:" }{TEXT 263 0 "" }{TEXT -1 154 " Cop y and paste the previous command into the next line (use the icons in \+ the shortcut bar, the Edit menu, or Ctrl+c resp. Ctrl+v), then edit it to read:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf( (2/5)^1 0 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "The spaces are not necess ary, but make the input easier to read for the human eye. " }{TEXT 269 20 "Use spaces liberally" }{TEXT -1 101 ". Exception: no spaces ar e permitted within the name of a command or object; also constructions like " }{MPLTEXT 0 21 2 ":=" }{TEXT -1 41 " (the assignment operator, see below) or " }{MPLTEXT 0 21 2 "->" }{TEXT -1 53 " (to define funct ions) cannot be separated by spaces." }}{PARA 0 "" 0 "" {TEXT -1 177 " If 2/5 is entered as a decimal, Maple will calculate the result immedi ately as a decimal. Note, however, that in this case Maple uses approx imate arithmetic (like a calculator)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "0.4^10;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Maple \+ can also handle much bigger numbers exactly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(2/5)^50; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Let's convert this to a decimal as well:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "(2/5)^50; evalf( % );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }{MPLTEXT 0 21 1 "%" }{TEXT -1 8 " is the " } {TEXT 270 20 "\"previous\" operator " }{TEXT -1 246 "and can be used a s a short notation for the result of the previous calculation. It shou ld be used cautiously: As a rule of thumb, type it in the same input l ine as the command it refers to - that way, both commands are executed at the same time. " }}{PARA 0 "" 0 "" {TEXT -1 124 "If you want to ke ep only the decimal answer in your worksheet, you can replace the semi colon in the last command by a colon:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "(2/5)^50: evalf( % );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Maple calculates both the exact and the decimal answer, \+ but the output from the first calculation is now hidden." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "To " }{TEXT 265 15 "see more digits" } {TEXT -1 39 " in the decimal approximation, use the " }{MPLTEXT 0 21 5 "evalf" }{TEXT -1 35 " command with the following option:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "(2/5)^50; evalf( %, 30 ); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Now enter the expression " } {XPPEDIT 18 0 "2*x^2;" "6#*&\"\"#\"\"\"*$%\"xG\"\"#F%" }{TEXT -1 1 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "2x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Notice the blinking cursor between the 2 and th e x. It indicates that a" }{TEXT 271 22 " * must always be used" } {TEXT -1 1 " " }{TEXT 256 18 "for multiplication" }{TEXT -1 1 "." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2*x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 " Now let's " }{TEXT 264 13 "assign a name" }{TEXT -1 20 " to this expression." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "q := 2*x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Whenever " } {MPLTEXT 0 21 0 "" }{TEXT -1 1 " " }{MPLTEXT 0 21 1 "q" }{TEXT -1 11 " is used, " }{XPPEDIT 18 0 "2*x^2;" "6#*&\"\"#\"\"\"*$%\"xG\"\"#F%" } {TEXT -1 41 " will be substituted (until the value of " }{MPLTEXT 0 21 1 "q" }{TEXT -1 50 " is reassigned or cleared). To check the value \+ of " }{MPLTEXT 0 21 1 "q" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Now let's d raw " }{XPPEDIT 18 0 "y = 2*x^2;" "6#/%\"yG*&\"\"#\"\"\"*$%\"xG\"\"#F' " }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plot( q , x );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 130 "The graph has appeared in your worksheet. (To put it into an extra window, choose Options/Pl ot Display/Window from the menu bar.) " }{TEXT 266 21 "Make the graph \+ active" }{TEXT 267 0 "" }{TEXT -1 92 " by clicking somewhere in it. No tice that the lowest top bar, the context bar, has changed. " }}{PARA 0 "" 0 "" {TEXT -1 3 "To " }{TEXT 272 45 "obtain the approximate coord inates of a point" }{TEXT -1 90 ", click on it: the coordinates appear in a little box at the very left of the context bar." }}{PARA 0 "" 0 "" {TEXT -1 101 "If the parabola doesn't seem narrow enough, that's be cause the scales on the axes are different. For " }{TEXT 273 23 "equal units on the axes" }{TEXT -1 78 ", click the \"1:1\" button on the co ntext bar, or choose Projection/Constrained." }}{PARA 0 "" 0 "" {TEXT -1 48 "The plotting region within the worksheet can be " }{TEXT 274 6 "resize" }{TEXT -1 322 "d: Notice how the cursor changes its shape whe n you rest it over one of the little boxes in the corners or in the mi ddle of each side of the frame around the plotting window. Hold the le ft mouse button down and drag the frame to the desired dimensions. (Th is feature can be useful when you include pictures in a printout.)" }} {PARA 0 "" 0 "" {TEXT -1 273 "How does Maple draw the graph? It calcul ates a number of points on the graph and then connects the dots by sho rt line segments. If you want to see which points Maple used for our p arabola, choose Style/Point. Notice that more points are used where th e graph is more curved." }}{PARA 0 "" 0 "" {TEXT -1 60 "We could have \+ obtained the same plot by simply typing in ..." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "plot( 2*x^2, x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 136 "... but it's always a good idea to check the expression \+ you are plotting for misprints (or missing parentheses, see the exampl es below)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 227 "In the previous pl otting commands, Maple used the default interval [-10,10] for the x-va lues, and adjusted the y-values according to the given function. (In o ur case, the smallest y-value is 0, and the largest 2*10^2=200.) To s " }{TEXT 275 48 "pecify a different x-interval resp. a y-interval" } {TEXT -1 6 ", use:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot( q, x=-6..6 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot( q, \+ x=-6..6, y=-1..10 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 " Next, le t's plot " }{TEXT 276 1 "y" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "1/(x+1) ;" "6#*&\"\"\"\"\"\",&%\"xGF%\"\"\"F%!\"\"" }{TEXT -1 17 " . Did you t ry..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "1/x+1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Enter the expression with correct parenth eses..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q1 := 1/(x+1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "...then plot it on the default \+ interval." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot( q1, x ); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 135 "The picture looks strange, b ecause the scales on the x- and y-axes are so different. Restricting t he x-values to a smaller interval... " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot( q1, x=-5..3 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "... helps just a little. Let's choose a reasonable y-inte rval:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot( q1, x=-5..3, y=-20..20 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 164 "Does the graph \+ look right? What about the vertical line? Can you explain how it gets \+ into the picture? (Hint: Switch to Point Style.) To remove it, use th e option " }{MPLTEXT 0 21 12 "discont=true" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot( q1, x=-5..3, y=-20..20, disco nt=true );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 " Next, plot the cub e root function. Did you try:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x^1/3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q2 := x^(1/3 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot( q2, x=-3..3 ); \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 30 "What is wrong with this graph?" }}{PARA 0 "" 0 "" {TEXT -1 529 "Maple has omitted the entire negative branch of the grap h. (It acts like many scientific calculators, which can't evaluate rat ional powers of negative numbers, because they look at them in terms o f an exponential function.) Moreover, Maple didn't plot points close t o 0 -- that's because it calculated function values over the x-interva l [-3,3], and didn't happen to use x=0. Morale: You can't always belie ve the computer! The code to draw the correct picture is given in the \+ next (hidden) paragraph; you won't need it right now." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 43 "The correct graph of the cube root functi on" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Plot " }{XPPEDIT 18 0 "y = x^ (1/3);" "6#/%\"yG)%\"xG*&\"\"\"\"\"\"\"\"$!\"\"" }{TEXT -1 46 " over [ 0,3]. Store the plot under the name p1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot( q2, x=0..3 ); p1 := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Plot the corresponding negative branch by the follo wing algebraic trick, and store the plot under the name p2." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot( -(-x)^(1/3), x=-3..0 ) ; p2 := %:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "The two plots can now be displayed in the same picture by use of the " }{MPLTEXT 0 21 7 "display" }{TEXT -1 37 " command, which must first be loaded:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with( plots ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "display( p1, p2 );" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "The following command illustrates how " } {TEXT 277 48 "to plot several function together in one picture" } {TEXT -1 24 " (over the same domain):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot( [ 3*x, 2*x^2, x^3 ], x=-3..3, y=-10..10 );" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Curly set braces (" }{MPLTEXT 0 21 3 "\{,\}" }{TEXT -1 40 ") may be used in place of the brackets (" } {MPLTEXT 0 21 3 "[,]" }{TEXT -1 90 "); however, the brackets give you \+ more options: They group the expressions together in an " }{TEXT 278 7 "ordered" }{TEXT -1 127 " list, and different attributes (like color s, thickness of the lines, solid or dashed line) can be specified in t he same order." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot( [ 3 *x, 2*x^2, x^3 ], x=-3..3, y=-10..10, color=[blue, red, green]);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 280 21 "A family of functions" }}{PARA 0 "" 0 "" {TEXT -1 261 "Say we would like to know how the graphs of even powers of x change when the exponent changes. In other words, we want to compare functions defined by very similar formulas: a family of f unctions that depends on a parameter (the exponent). Here is a nifty w ay:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Define a function p which, for any given value of n, outputs a plot of " }{XPPEDIT 18 0 "x^n;" " 6#)%\"xG%\"nG" }{TEXT -1 51 " over [-3,3], with y-values restricted to [-10,10]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "p := n -> plo t( x^n, x=-3..3, y=0..10 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Th is allows to quickly produce the desired graphs and explore the differ neces:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p(2); # plots x^2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p(4); # plots x ^4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Finally, let's go to the mo vies. We will use the " }{MPLTEXT 0 21 3 "seq" }{TEXT -1 103 " command to create a sequence of frames for the movie. Here's an illustration \+ of how the command works:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "seq( n, n=1..10 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "s eq( 2^n, n=0..12 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "seq( 2*n, n=1..10 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "We can easily plot many of the even powers of x together in one picture by:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "display( seq( p(2*n), n=1..10 ) ); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "To get a sense of how " } {XPPEDIT 18 0 "x^(2*n);" "6#)%\"xG*&\"\"#\"\"\"%\"nGF'" }{TEXT -1 73 " changes as n increases, it's nice to see the graphs one after the oth er:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "display( seq( p(2*n) , n=1..10 ), insequence=true );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 15 "The Undo button" }} {PARA 0 "" 0 "" {TEXT -1 255 "Imagine the following situation: You hav e highlighted a command to copy it, and accidentally you hit \"c\" ins tead of \"Ctrl\"+\"c\". Fortunately, not all is lost! Just click the U ndo button on the shortcut bar; this is the button showing a left-curv ing arrow. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 279 16 "Saving your work " }}{PARA 0 "" 0 "" {TEXT -1 325 "When you have to exit Maple, but are not done with your work, it's a good idea to save only commands and t exts, and remove all output. This way, when you resume your work at a \+ later time, you will not be confused as to what Maple knows: it has fo rgotten everything. Moreover, graphical output would make your file ve ry large." }}{PARA 0 "" 0 "" {TEXT -1 180 "To remove all output, choos e Edit/Remove Output/From Worksheet. When you resume, you can quickly \+ re-execute the commands to start where you left off: choose Edit/Execu te/Worksheet." }}{PARA 0 "" 0 "" {TEXT -1 236 "Of course, when you hav e completed a report, you leave all relevant output in the worksheet! \+ Before printing, don't forget to set the zoom factor to 100% (smallest magnifying glass); otherwise, you might quickly use up your print quo ta!" }}}}{MARK "60 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }