{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 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 " " -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 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 6 6 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 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Bullet Item" 0 15 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 1 2 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 "Helvetica" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 3" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 0 2 2 2 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 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 19 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 260 8 "day1.mws" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 58 " AN INTRODUCTION TO MAPLE: Basic computations and plotting" }}{PARA 19 "" 0 "" {TEXT -1 42 "Math 242 (sections 1 and 3) -- Spring 1998" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 19 "" 0 "" {TEXT -1 33 "Matt Mil ler (miller@math.sc.edu) " }}{PARA 19 "" 0 "" {TEXT -1 33 "Douglas Mea de (meade@math.sc.edu)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Objectives" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 39 "Enter mathematical expressions in Maple" }}{PARA 15 "" 0 "" {TEXT -1 30 "Plot a given function in Maple" }}{PARA 15 "" 0 "" {TEXT -1 32 "Extract information from a graph" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "W hat is Maple?" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 597 "Much of your mat hematical background has probably been focused on developing the abili ty to solve equations and explore functions. The sophisticated manipul ation of symbols and expressions that you use to solve equations and i nvestigate functions can also be performed by software packages called computer algebra systems (CAS). A CAS can be use to generate the exac t symbolic solutions you obtained by hand, the numerical approximation s you found using a calculator, and the graphs you have drawn. Maple i s one of several CAS's; other major examples are Mathematica, Macsyma, Derive, and MathCad." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 38 "How will Maple be used in this course?" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 522 "Our first, and larges t, use of Maple will be the graphical display of functions, including \+ the solution of one or more differential equations. In fact, this grap hical information is often more useful than a formula for the exact so lution. Sometimes we will use Maple just for demonstrations during re gular class; other times students will turn to the computers as needed to carry out caculations, both during class and outside of class. Yo u will also be expected to use Maple on the homework and even parts of the exams." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "Note: You might find Maple of use in other courses!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "Documentation and Online Help" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 244 "The on-line help for Maple is very good. The help pages descri be the syntax of each command, a brief description of the algorithm th at has been implemented, and a few examples illustrating the use of th e command. To obtain help on the command " }{TEXT 0 4 "func" }{TEXT -1 8 ", type: " }{TEXT 0 5 "?func" }{TEXT -1 366 ". To close a help w indow use the small button in the top left corner; to simply turn it i nto a small icon for later reference use the dot in the top right corn er (this works for any window actually, and the box next to it opens a window up to full size). The Help Browser, an interactive interface \+ to the entire Maple help system, can be brought up by clicking on " } {TEXT 258 4 "Help" }{TEXT -1 79 ", found at the top right of the Maple window. To get started trying activating " }{TEXT 259 12 "Balloon Hel p" }{TEXT -1 93 " under the Help Browser (this will be useful when you start to experiment with the Menu Bar)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Getting Sta rted" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 928 "You have already learned \+ how to open up a worksheet. After Maple is opened, position the cursor arrow on the menu item File and click the left button once. You can s elect New to obtain a fresh, empty worksheet. Or you can select Open t o choose an existing worksheet (the name will always end with .mws), e ither by double clicking on the name or by selecting the name and then Load. Once in a worksheet the current location is marked by a vertica l bar. You can move around by moving the mouse and then clicking the l eft button once, by using the arrow keys, or by using the scroll bar u p and down arrows on the right side of this window followed by finer a djustment with the mouse. A command (marked by the > symbol with words in bright red) is executed by positioning the cursor anywhere on the \+ desired line and pressing the return key. Briefly: use the mouse to \+ position yourself, and the return key to actually do something." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "It is pr obably a good idea to begin EVERY worksheet that you create with the f ollowing two commands." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "with(plots):" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 42 "Note for Math 242 (Differential Equations)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 111 "When working with differential equations, it is advis able to add the following command to the startup commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with( DEtools ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Information about these \+ commands can be found in the on-line help: " }{HYPERLNK 17 "?plots" 2 "plots" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "?restart" 2 "restart" "" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Basic Facts" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "Maple is a computer language; it cannot read your m ind. You need to learn how to communicate with Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "The fundamental symbol s:" }}{PARA 15 "" 0 "" {TEXT -1 27 "assignments are made with " } {TEXT 0 2 ":=" }{TEXT -1 9 " (plain " }{TEXT 0 1 "=" }{TEXT -1 132 " \+ has a different meaning) -- think of this as giving the value of the r ight hand side to the name that appears on the left hand side" }} {PARA 15 "" 0 "" {TEXT -1 46 "every command is terminated by a semi-co lon ( " }{TEXT 0 1 ";" }{TEXT -1 14 " ) or colon ( " }{TEXT 0 1 ":" } {TEXT -1 78 " ) -- with the latter the computation is done, but the re sult is not displayed" }}{PARA 15 "" 0 "" {TEXT -1 19 "the double quot e ( " }{TEXT 0 1 "\"" }{TEXT -1 64 " ) refers to the result of the imm ediately preceding computation" }}{PARA 15 "" 0 "" {TEXT -1 46 "Maple \+ is case sensitive -- that is, the names " }{TEXT 0 1 "x" }{TEXT -1 5 " and " }{TEXT 0 1 "X" }{TEXT -1 16 " are different, " }{TEXT 0 2 "pi" }{TEXT -1 5 " and " }{TEXT 0 2 "Pi" }{TEXT -1 23 " are not the same th ing" }}{PARA 15 "" 0 "" {TEXT 0 4 "\{ \}" }{TEXT -1 94 " -- set nota tion (mostly used in the context of plotting a bunch of functions simu ltaneously)" }}{PARA 15 "" 0 "" {TEXT -1 21 " as in " } {TEXT 0 6 "a .. b" }{TEXT -1 45 " -- this is how Maple indicates the i nterval " }{XPPEDIT 18 0 "[a, b]" "7$%\"aG%\"bG" }{TEXT -1 34 ", that \+ is, the real numbers from " }{XPPEDIT 18 0 "a" "I\"aG6\"" }{TEXT -1 6 " to " }{XPPEDIT 18 0 "b" "I\"bG6\"" }{TEXT -1 1 " " }}{PARA 15 " " 0 "" {TEXT 0 1 "?" }{TEXT -1 4 " or " }{TEXT 0 4 "help" }{TEXT -1 38 " -- a request to Maple for information" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 75 "The standard mathematical fun ctions are denoted by their standard names:\n " }{TEXT 0 1 "+" } {TEXT -1 10 " (plus) , " }{TEXT 0 1 "-" }{TEXT -1 11 " (minus) , " } {TEXT 0 1 "*" }{TEXT -1 11 " (times) , " }{TEXT 0 1 "/" }{TEXT -1 16 " (divided by) , " }{TEXT 0 1 "^" }{TEXT -1 25 " (raised to the power) \+ , " }{TEXT 0 3 "sin" }{TEXT -1 2 ", " }{TEXT 0 3 "cos" }{TEXT -1 2 ", \+ " }{TEXT 0 3 "tan" }{TEXT -1 2 ", " }{TEXT 0 3 "abs" }{TEXT -1 2 ", " }{TEXT 0 4 "sqrt" }{TEXT -1 5 ", ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "In the follo wing lines, use paper and pencil to first predict what you think Maple will do. Then execute the command and see what actually happens!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "number:= 4 * 6 + 12 / 6 - \+ 1 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "power:= (-3)^3 ;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "abs( \" );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Pi ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "v:= sin( Pi / 4 ) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "w:= v^2 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "tan( -Pi / 2 ) ; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "3 / ( 5 - sqrt( number \+ ) ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Now enter some commands of your own! To produce the input prompt " }{TEXT 256 1 ">" }{TEXT -1 11 " use the " } {TEXT 257 2 "[>" }{TEXT -1 253 " button in the Menu Bar. Be generous with the space bar to make your commands easy to read, and to edit (m odify after the fact). Go back to the tangent calculation above (remem ber how to reposition the cursor!) and change it to compute the tangen t of " }{XPPEDIT 18 0 "Pi / 3" "*&%#PiG\"\"\"\"\"$!\"\"" }{TEXT -1 1 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Next we define some functions for later use." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f := sin( 2 * x ) ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g := 4 * x^2 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h:= 0.25 * cos ( 8 * x ) ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "p:= f * g ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "q:= f * h ;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "s:= f + h ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Plotting" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 501 "Graphs of functions are produced \+ by the plot command. In its simplest form, plot needs to know the func tion to be plotted and the range of values for the independent variabl e. Note that a..b is Maple's way of describing the interval [a,b]. Obs erve that I have placed signed titles on some of these graphs. When yo u actually print plots to turn in with your homework, they MUST have a title and signature [by your initials or last name]. Again, try to pr edict the output before tapping the return key! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "plot( 3 * t - 2 , t = -3 .. 10 ) ; # WAIT F OR THE GRAPH TO APPEAR!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot( f , x = -Pi .. 2 * Pi ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot( p , x = -6 .. 8 , title = ` f * g [by DM] ` ); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 512 "These plots are nice, but what information do they \+ convey? Let's concentrate on the plot of p, that is f*g. Position the cursor on a point on the graph and click the left button. The numbers that appear on the upper-left corner are the coordinates of the curre nt location of the cursor. Use this technique to identify the global m aximum and minimum values of f*g on the interval [-6, 8], and the x-va lues at which these are found. Where do other (local) minima and maxim a occur? Can you guess the exact values? " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 82 "plot(2 * u^3 + 4 * u - 5 , u = -10 .. 7 , title = ` cubic function [by DM] ` ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 301 "Where does the cubic \+ function cross the u-axis? Maybe it would be helpful to cut down the p lotting interval from [-10, 7] to [-1, 3], or even narrower, say to [0 , 1.5]. Try it. Can you find the u-intercept to 2-decimal point accura cy by this process? It is a powerful method, which we call ZOOMING IN. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot( s , x = 0 .. 3 * Pi );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot( q , x = -1. 2 .. 1.2 ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Can you explain why the graphs of s and q look the way they do?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Housecleaning" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 293 "As you scroll up and down you may find that ol d plots take time to be redrawn and aren't really needed anyhow. If yo u click on a plot you will box it (and for printing purposes this box \+ can be resized by dragging on the sides or corners). To remove it hold down the shift key and press delete." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 38 "Graphing S everal Functions in One Plot" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot( \{ p , g , -g \} , x= -6 .. 8 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Can you \+ identify the three different plots?" }}{PARA 0 "" 0 "" {TEXT -1 24 "Wh at about the next one?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "p lot( \{ f , h , s \}, x=0 .. 3*Pi );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Can you explain the little bumps that appear inside the large d ips in the graph of s?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Plotting A Discontinuous Func tion" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "The tangent function is we ll-known to all of us. In particular, we know that the graph of " } {XPPEDIT 18 0 "y=tan(x)" "/%\"yG-%$tanG6#%\"xG" }{TEXT -1 49 " has ver tical asymptotes at all odd multiples of " }{XPPEDIT 18 0 "Pi/2" "*&%# PiG\"\"\"\"\"#!\"\"" }{TEXT -1 36 ". Let's see how Maple handles this. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := tan(x);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Note: This definition completely r eplaces the previous definition of f." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot( f , x = -Pi .. Pi );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Is this what \+ you expected to see?" }}{PARA 0 "" 0 "" {TEXT -1 34 "Why does the grap h look like this?" }}{PARA 0 "" 0 "" {TEXT -1 55 "What can be done to \+ improve the appearance of the plot?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "The key is t o restrict the vertical range of the plot and tell Maple that the func tion is discontinuous." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "p lot( f, x = -Pi .. Pi , -10 .. 10 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot( f, x = -Pi .. Pi , -10 .. 10 , discont=true ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 64 "plot ( ( 1 - 0.4*t^3) / ( 1 - t^2 ) , t = -3 \+ .. 5 , -10 .. 10 ," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 " discon t = true, title = `vertical asymptotes [by DM]` ) ; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "T his technique is very useful for any function that has vertical asympt otes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Congratulations" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 471 "You have just completed your first Maple worksheet. If you wish to save it select File in the menu bar, and then either Save (which will destroy the original version of day1.mws) or Save As... ( which will leave day1.mws untouched, and will request a new name for t his modified version). Worksheet names should always end with .mws; al so unless you really need the output it is usually a good idea to remo ve it before saving -- to do this, select Edit, then Remove Output." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }