{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 "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 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 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 271 "" 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 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 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 1 " -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 " Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Out put" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 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 "Normal " -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 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 "Maple Plot" -1 257 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 "Author" -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 8 8 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "Getting Started With Mapl e" }}{PARA 258 "" 0 "" {TEXT -1 650 "Maple is what is known as a \"com puter algebra system\" often abbreviated \"CAS\". The difference betw een a CAS and a typical calulator (even graphing calculators) will be \+ expanded upon later. Simply put however, a computer algebra system do es \"symbolic\" manipulations. Ie. it can perform operations on expr essions containing variables that have not been given a numerical valu e. In addition, Maple has a built in word processor that allows you t o write text, including mathematical notation, in the same document co ntaining mathematical input and output. The Maple Worksheet combines t hese two features. Click on the \"+\" sign to open the section." }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 49 "The Maple Worksheet - Text and Ex ecutable Groups:" }}{EXCHG {PARA 258 "" 0 "" {TEXT -1 264 "The file yo u are reading is called a Maple Worksheet. It is seperated into text and executable \"groups\". Each group is delineated by the square br acket to the left of this paragraph. You can choose between text grou ps and executable groups by clicking on the \"" }{TEXT 262 1 "T" } {TEXT -1 10 "\" or the \"" }{TEXT 263 2 "[>" }{TEXT -1 1 "\"" }{TEXT 265 2 " " }{TEXT -1 207 "located on the tool bar (the yellow boxes). \+ The paragraph you are reading is a \"text\" group. If you want Mapl e to perform some type of operation, you can switch to an executable g roup by clicking on the \"" }{TEXT 264 2 "[>" }{TEXT -1 87 "\" from th e tool bar. Then you can type in a command for Maple to execute. For \+ example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3 * 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 155 "After you execute this command, the result is displayed centered \+ in blue (in this example, \"15\" is the Maple output) and Maple wil gi ve you an executable\" " }{TEXT 260 2 "[>" }{TEXT -1 91 "\" prompt for the next command. If you wish instead to put in some text, just click on the \"" }{TEXT 261 1 "T" }{TEXT -1 286 "\" from the tool bar and t he executable prompt goes away.. then you are, by default, in a text g roup. Note, the semicolon after each command is necessary. This lets Maple know you are done entering a command. This may be replaced by a colon and the output is supressed. For example: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3 * 5:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "If you do not end the statement with a colon or semicolon, you \+ will get an error message:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "3 * 5" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, premature end of inp ut\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 348 "Get used to this ... you will probably see it often. If this happens, or some other error mes sage, you can edit the line by left clicking the mouse on that line, o r moving up to it by using the arrows on your keyboard. Make the nece ssary changes and then re-execute the command by hitting \"enter\" whi le the cursor is anywhere on the command line " }{TEXT 266 29 "before \+ the colon or semicolon" }{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "# end of section" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "Basic Commands" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 511 "If you a re reading this from a downloaded Maple worksheet you must hit \"enter \" somewhere on each command line (in red) before the colon or semicol on. This is called \"executing\" the command. If you don't execute ea ch command, the values (or expressions) assigned to variables will not be made and this will lead to problems. I generally start each sessi on with the command \"restart\". This clears the assignments made to a ny variables and allows you to \"start from scratch\" without opening \+ a \"new\" worksheet. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r estart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Notice, there is no ou tput from this command. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 267 34 "Assigning a value to a variable. " }}{PARA 0 "" 0 "" {TEXT -1 182 "You must use \"colon equals (:=)\" to assign a value to a variable. The \"=\" sign alone is a test character and returns a v alue of true or false. Below, \"a\" is assigned the value 10." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a := 10;" }{TEXT -1 0 "" } {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "and the equal sign results in the \+ rather strange statement:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a = 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"#5\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "This can be tested as a \"true\" or \"fal se\" by the command \"evalb\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalb(a = 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Despite the \"assignment\" a = 3, \+ the value is still the one assigned with the \":=\". Notice:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 268 22 "Calculator Operations:" }{TEXT -1 59 " Create a new variable \+ \"b\" and assign it the value 132 by:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "b := 132;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"$ K\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 270 41 "Multiplication must use t he \" * \" symbol:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a * b; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%?8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "You will probably forget this. Below is what happens if y ou do. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a b;" }}{PARA 8 " " 1 "" {TEXT -1 31 "Error, missing operator or `;`\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Division is as you would expect:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a/b;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"#m" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Notice, Maple simplifies but does give a decimal expansion. In order to do this, type " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf (a/b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+wvvvv!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "The above command evaluates 5/66 as a fl oating point number with 10 significant digits. evalf(5/66,n) gives th e result with n significant digits. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(5/66,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" $e(!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 271 7 "Notice:" }{TEXT -1 81 " Preceding zeros do not count as significant digits and evalf rounds \+ the result. " }{TEXT 269 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 272 18 "Stored Functions: " }{TEXT -1 211 "Maple has many funct ions stored in its memory. The list is long and we will investigate t hem as needed. Here we only look at the simple trig and exponential fu nction. Trig functions are as you would expect and " }{XPPEDIT 18 0 "P i;" "6#%#PiG" }{TEXT -1 17 " is denoted Pi. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(Pi/" }{TEXT -1 0 "" }{MPLTEXT 1 0 3 "3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"\"$\"\"\"#F)\"\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Maple will give you an exact valu e for trig expressions. If it cannot, it will reiterate your input: \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "cos(Pi/13);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#,$%#PiG#\"\"\"\"#8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "If you want a decimal approximation to th is number, use evalf:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ev alf(cos(Pi/13));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u\"=%4(*!#5" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "The exponential function " } {XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }{TEXT -1 81 "is executed b y exp(x). Therefore, you can get Maple to evaluate the number e by:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+G=G=F!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 273 20 "Defining a function:" }{TEXT -1 88 " Thi s is rather odd notation but you can think of it as \"f takes x and as signs it to\". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f := x - > (3*x^2 + 2*x + 5);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arro wGF(,(*$)9$\"\"#\"\"\"\"\"$*&F0F1F/F1F1\"\"&F1F(F(F(" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }{TEXT 258 227 "Do not forget the * for deno ting multiplication. 3 x does not mean \"3 times x\". You must use 3 \+ * x. Also, do not forget the \":\" in front of the \"=\" and of cours e \"->\" created by typing in the \"-\" followed by the \" >\" symbol \+ ." }{TEXT -1 53 " You can now evaluate f(x) at x = 3 with the command: " }{TEXT 259 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3); " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#Q" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 22 "Plotting \+ a function. " }{TEXT -1 201 "You can plot a function with the \"plot \" command that has the form: plot(f(x), range, domain, etc.). Where \+ the \"etc.\" may be a range, a color designation or many other options we will discuss later. " }{TEXT 274 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 79 "plot(f(x),x=-5..5,color=green,linestyle=SOLID,thick ness=4,labels=[\"x\",\"f(x)\"]);" }}{PARA 13 "" 1 "" {GLPLOT2D 373 373 373 {PLOTDATA 2 "6(-%'CURVESG6#7S7$$!\"&\"\"!$\"#qF*7$$!3YLLLe%G?y %!#<$\"3*pHE7;LRS'!#;7$$!3OmmT&esBf%F0$\"3YLE!>F\"\\3fF37$$!3ALL$3s%3z VF0$\"3_=T]`z4x`F37$$!3_LL$e/$QkTF0$\"3!pcglB\\(p[F37$$!3ommT5=q]RF0$ \"3CDbOwIF#R%F37$$!3ILL3_>f_PF0$\"3-9bBcFX#F37$$!33LL$e4OZr#F0$\"3eb%R=S!*z ;#F37$$!3u*****\\n\\!*\\#F0$\"3S\"GN%[[wt=F37$$!3%)*****\\ixCG#F0$\"3q \"p(e2dT1;F37$$!3#******\\KqP2#F0$\"3w\"=bK%HSv8F37$$!39LL3-TC%)=F0$\" 3K\"3a/$RE)=\"F37$$!3[mmm\"4z)e;F0$\"3'>9t*Q8)y$**F07$$!3Mmmmm`'zY\"F0 $\"3om]')>i$)G&)F07$$!3#****\\(=t)eC\"F0$\"3;#>mb*4$\\;(F07$$!3!ommmh5 $\\5F0$\"343[Txq`/iF07$$!3S$***\\(=[jL)!#=$\"3$R.(f&RrvT&F07$$!3)f*** \\iXg#G'F[r$\"3NtB;!p7w#\\F07$$!3ndmmT&Q(RTF[r$\"35![nuMvho%F07$$!3%\\ mmTg=><#F[r$\"36D/'=>Lrq%F07$$!3vDMLLe*e$\\!#?$\"35mj`(H,-*\\F07$$\"3! =nm\"zRQb@F[r$\"3]&yi()>Z/d&F07$$\"3_,+](=>Y2%F[r$\"3r&H%>$[**HJ'F07$$ \"3summ\"zXu9'F[r$\"3_Wx<^=AjtF07$$\"3#4+++]y))G)F[r$\"3+oGj.4%*=()F07 $$\"3H++]i_QQ5F0$\"3WeJ^Q-:J5F37$$\"3b++D\"y%3T7F0$\"3j3^_'Q/.@\"F37$$ \"3+++]P![hY\"F0$\"3RI&fyi1\"Q9F37$$\"3iKLL$Qx$o;F0$\"3))>@j//so;F37$$ \"3Y+++v.I%)=F0$\"3fUv'fWO?%>F37$$\"3?mm\"zpe*z?F0$\"3S\"4&4&>gQ@#F37$ $\"3;,++D\\'QH#F0$\"3DyNCtyJPDF37$$\"3%HL$e9S8&\\#F0$\"3!)))e8G\\tmGF3 7$$\"3s++D1#=bq#F0$\"3(p1b0F_qB$F37$$\"3\"HLL$3s?6HF0$\"3'RDAYmzZi$F37 $$\"3a***\\7`Wl7$F0$\"3C%y;!=J*y0%F37$$\"3enmmm*RRL$F0$\"3[NXt.ZL,XF37 $$\"3%zmmTvJga$F0$\"3gM3I6(3:)\\F37$$\"3]MLe9tOcPF0$\"39rw`$3iV[&F37$$ \"31,++]Qk\\RF0$\"3]\\GbKZ$)pfF37$$\"3![LL3dg6<%F0$\"3[o!pkE1Qb'F37$$ \"3%ymmmw(GpVF0$\"3>KirH-1,rF37$$\"3C++D\"oK0e%F0$\"3>%z\\%H/\\5xF37$$ \"35,+v=5s#y%F0$\"3h9zq1.()=$)F37$$\"\"&F*$\"#!*F*-%*THICKNESSG6#\"\"% -%'COLOURG6&%$RGBG$F*F*$\"*++++\"!\")Fc[l-%*LINESTYLEG6#\"\"\"-%+AXESL ABELSG6$Q\"x6\"Q%f(x)F_\\l-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 4 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 270 "You should label the axes in all graphs. If you' re only plotting one function, the \"color\" and \"linestyle\" are rat her irrelevant. However, if you are printing up a graph, the thicknes s command is useful as the default thickness may be hard to see on a p rinted document." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 276 29 "Plotting more than one curve." }{TEXT -1 165 " More than one funct ion may be plotted on the same graph by listing them, and their featur es, in square brackets. For example, we introduce another function g( x) = " }{XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }{TEXT -1 4 " by " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "g := x -> exp(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG%$expG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "plot([f(x),g(x)],x=-5..5,color=[red,blue],lines tyle=[SOLID,DASH],thickness=[3,4],labels=[\"x\",\"f-solid,red, g-dashe d,blue\"]);" }}{PARA 13 "" 1 "" {GLPLOT2D 373 373 373 {PLOTDATA 2 "6&- %'CURVESG6&7S7$$!\"&\"\"!$\"#qF*7$$!3YLLLe%G?y%!#<$\"3*pHE7;LRS'!#;7$$ !3OmmT&esBf%F0$\"3YLE!>F\"\\3fF37$$!3ALL$3s%3zVF0$\"3_=T]`z4x`F37$$!3_ LL$e/$QkTF0$\"3!pcglB\\(p[F37$$!3ommT5=q]RF0$\"3CDbOwIF#R%F37$$!3ILL3_ >f_PF0$\"3-9bBcFX#F37$$!33LL$e4OZr#F0$\"3eb%R=S!*z;#F37$$!3u*****\\n\\!*\\# F0$\"3S\"GN%[[wt=F37$$!3%)*****\\ixCG#F0$\"3q\"p(e2dT1;F37$$!3#****** \\KqP2#F0$\"3w\"=bK%HSv8F37$$!39LL3-TC%)=F0$\"3K\"3a/$RE)=\"F37$$!3[mm m\"4z)e;F0$\"3'>9t*Q8)y$**F07$$!3Mmmmm`'zY\"F0$\"3om]')>i$)G&)F07$$!3# ****\\(=t)eC\"F0$\"3;#>mb*4$\\;(F07$$!3!ommmh5$\\5F0$\"343[Txq`/iF07$$ !3S$***\\(=[jL)!#=$\"3$R.(f&RrvT&F07$$!3)f***\\iXg#G'F[r$\"3NtB;!p7w# \\F07$$!3ndmmT&Q(RTF[r$\"35![nuMvho%F07$$!3%\\mmTg=><#F[r$\"36D/'=>Lrq %F07$$!3vDMLLe*e$\\!#?$\"35mj`(H,-*\\F07$$\"3!=nm\"zRQb@F[r$\"3]&yi()> Z/d&F07$$\"3_,+](=>Y2%F[r$\"3r&H%>$[**HJ'F07$$\"3summ\"zXu9'F[r$\"3_Wx <^=AjtF07$$\"3#4+++]y))G)F[r$\"3+oGj.4%*=()F07$$\"3H++]i_QQ5F0$\"3WeJ^ Q-:J5F37$$\"3b++D\"y%3T7F0$\"3j3^_'Q/.@\"F37$$\"3+++]P![hY\"F0$\"3RI&f yi1\"Q9F37$$\"3iKLL$Qx$o;F0$\"3))>@j//so;F37$$\"3Y+++v.I%)=F0$\"3fUv'f WO?%>F37$$\"3?mm\"zpe*z?F0$\"3S\"4&4&>gQ@#F37$$\"3;,++D\\'QH#F0$\"3DyN CtyJPDF37$$\"3%HL$e9S8&\\#F0$\"3!)))e8G\\tmGF37$$\"3s++D1#=bq#F0$\"3(p 1b0F_qB$F37$$\"3\"HLL$3s?6HF0$\"3'RDAYmzZi$F37$$\"3a***\\7`Wl7$F0$\"3C %y;!=J*y0%F37$$\"3enmmm*RRL$F0$\"3[NXt.ZL,XF37$$\"3%zmmTvJga$F0$\"3gM3 I6(3:)\\F37$$\"3]MLe9tOcPF0$\"39rw`$3iV[&F37$$\"31,++]Qk\\RF0$\"3]\\Gb KZ$)pfF37$$\"3![LL3dg6<%F0$\"3[o!pkE1Qb'F37$$\"3%ymmmw(GpVF0$\"3>KirH- 1,rF37$$\"3C++D\"oK0e%F0$\"3>%z\\%H/\\5xF37$$\"35,+v=5s#y%F0$\"3h9zq1. 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x$\"3cT[bUVanMF37$Fix$\"3+C#e(*3p#zUF37$F^y$\"3#GlNZL(o\">&F37$Fcy$\"3 !\\&pQd-1zkF37$$\"3K,+voTAqUF0$\"3QlZ?Lqw`rF37$Fhy$\"33&G+MUN()*yF37$$ \"3/M$eRA5\\Z%F0$\"35[S=\"*=ny()F37$F]z$\"3+IJP8_jc(*F37$$\"3m+++]oi\" o%F0$\"3GVn05aXz5!#:7$Fbz$\"3SVfNl()G%>\"F[fl7$$\"3Q+D1k2/P[F0$\"3sng% G_c4E\"F[fl7$$\"3a+]P40O\"*[F0$\"3NpiQ " 0 "" {MPLTEXT 1 0 18 "A := (l,w) -> l*w;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6$%\"lG%\"wG6\"6$%)operatorG %&arrowGF)*&9$\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "A(4,12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#[" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "We will not be doing much of this but its cool to see how Maple plots a function of two variables" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "plot3d(A(x,y),x=0..3,y=0..3,axes = \+ boxed, labels = [\"length\",\"width\",\"area\"]);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%%GRIDG6%;$\"\"!F($\"\"$F(F&X,%) 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0000000000004010800000000000401200000000000040138000000000004015000000 000000401680000000000040180000000000004019800000000000401B000000000000 401C800000000000401E000000000000401F8000000000004020800000000000402140 00000000004022000000000000-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6%Q'lengt hF.Q&widthF.Q%areaF." 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Place your cursor in the box containing the graph. left click and drag. Th is rotates the image. I think this is cool. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 32 "Clearing Variables and comments." }{TEXT -1 95 " To c lear the value, or expression, assigned to a variable, you must use o ne of the following." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a := 'a';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "unassign('f');" }}{PARA 0 "" 0 "" {TEXT -1 60 "The latter does not confirm your command but \"f\" is cleared\"" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"fG6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "A # sign may be used for comments and everything after it is ignored by Maple:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "3*a + b; # H i, How are you?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"aG\"\"$\"$K\" \"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Notice that variable " }{TEXT 256 1 "a" }{TEXT -1 22 " has been cleared but " }{TEXT 257 1 "b " }{TEXT -1 27 " still has a value of 132. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "# end of section" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 41 "The \"Algebra\" in Computer Algebra Systems" }}{PARA 0 " " 0 "" {TEXT -1 192 "Here you will see what makes a computer algebra s ystem so special. There are many features other than those demonstrat ed here but you should get a good idea what Maple can, and cannot, do. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "restart; # this clea rs our previous variables." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 279 18 "Solving Equations:" }{TEXT -1 51 " A simple linear equa tion can be solved for x by:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(3*x + 5 = 7,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"# \"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 445 "Here you first type in \+ the equation, and then the variable you want to solve for. Hopefully, \+ you could have done this by hand. Furthermore, your calculator probabl y could do the same thing. So .. this is not so special. However, su ppose we have a line described by the equations \"a x + b y = c\", whe re no numercal values are yet assigned to a, b or c. We can find the y-intercept by solving the equation for y when x is set equal to zero . " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "yint := solve(a*0 + b*y = c,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%yintG*&%\"cG\"\"\"% \"bG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "You can also solve \+ the same linear equation for the x intercept by solving for x when y i s set equal to zero. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "xi nt := solve(a*x + b*0 = c,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xi ntG*&%\"cG\"\"\"%\"aG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Map le can solve more difficult equations such as " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "solve(cos(x) = sin(x), x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$%#PiG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Not bad, but Maple doesn't let you know that you can add any in teger multple of " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 201 " to t his solution to obtain another solution. Still, its a nice starting p oint. It is not hard to come up with an equation that Maple cannot so lve algebraically. Notice from the graph below that " }{XPPEDIT 18 0 "x+cos(x)^2 = exp(x);" "6#/,&%\"xG\"\"\"*$-%$cosG6#F%\"\"#F&-%$ex pG6#F%" }{TEXT -1 8 " at " }{XPPEDIT 18 0 "x = 0;" "6#/%\"xG\"\"! " }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot([ x + (cos(x))^2, exp(x)],x=-1..1); " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"\"\"\"!$!3k5dt#=M23(!#=7$$! 3ommm;p0k&*F-$!3UsoV0v)4C'F-7$$!3wKL$37$$!3[++](y$pZ iF-$\"3j2N#)oT16LFV7$$!33LLL$yaE\"eF-$\"3'>[Ai`MC<\"F-7$$!3hmmm\">s%Ha F-$\"3%)ooD5c8,>F-7$$!3Q+++]$*4)*\\F-$\"3zZo%fK6]q#F-7$$!39+++]_&\\c%F -$\"3%Qq\\Ac_>\\$F-7$$!31+++]1aZTF-$\"3_&o3Od_'GUF-7$$!3umm;/#)[oPF-$ \"3_mxD#))Gt([F-7$$!3hLLL$=exJ$F-$\"3P$pfHC!H@cF-7$$!3*RLLLtIf$HF-$\"3 om*[az$eEiF-7$$!3]++]PYx\"\\#F-$\"3\\1rf\"ov+!pF-7$$!3EMLLL7i)4#F-$\"3 ajP;,bQnuF-7$$!3c****\\P'psm\"F-$\"3C=!f3xozJ#o47Fgs7$$\"3ElmmmZvOLF-$\"3]=%oRW2kA\" Fgs7$$\"3i******\\2goPF-$\"3>SGf\"3M9C\"Fgs7$$\"3UKL$eR<*fTF-$\"3sMid? rp_7Fgs7$$\"3m******\\)Hxe%F-$\"3-Y?Ol$eEE\"Fgs7$$\"3ckm;H!o-*\\F-$\"3 !*\\[rgj**p7Fgs7$$\"3y)***\\7k.6aF-$\"3e*y@])Qzv7Fgs7$$\"3#emmmT9C#eF- $\"3m.=EYU&)z7Fgs7$$\"33****\\i!*3`iF-$\"3)G=(45pn#G\"Fgs7$$\"3%QLLL$* zym'F-$\"35ru`a))G%G\"Fgs7$$\"3wKLL3N1#4(F-$\"3s^N[LO5&G\"Fgs7$$\"3Nmm ;HYt7vF-$\"3uZQ`x;P&G\"Fgs7$$\"3Y*******p(G**yF-$\"3?6_RD#)R&G\"Fgs7$$ \"3]mmmT6KU$)F-$\"3?ROPkdZ&G\"Fgs7$$\"3fKLLLbdQ()F-$\"39e$R'3*eeG\"Fgs 7$$\"3[++]i`1h\"*F-$\"3)zS3^#=)oG\"Fgs7$$\"3W++]P?Wl&*F-$\"3!>'4uh1s)G \"Fgs7$$\"\"\"F*$\"3%*Gks\"eE>H\"Fgs-%'COLOURG6&%$RGBG$\"#5F)$F*F*Fa[l -F$6$7S7$F($\"3MBWr6WzyOF-7$F/$\"3.W^QtfrUQF-7$F4$\"3[$*)f+Ru7*RF-7$F9 $\"3sbu^dg@lTF-7$F>$\"3o&GlMXnzM%F-7$FC$\"3Pc)=:(4\"y`%F-7$FH$\"3G4;0f u@@ZF-7$FM$\"3tE.r.&R*=\\F-7$FR$\"30z!*=&=Q@8&F-7$FX$\"3+m09a)[QN&F-7$ Fgn$\"3%*o7XaF!>f&F-7$F\\o$\"3R/uvRHL5eF-7$Fao$\"3Eh`=4&fk1'F-7$Ffo$\" 3en)*)HW)*\\L'F-7$F[p$\"3QSdj9q-0mF-7$F`p$\"3Oc1T#y(>goF-7$Fep$\"3;7<* Q)=[wrF-7$Fjp$\"3)=y\\.E)zbuF-7$F_q$\"33wFu%Q;Wz(F-7$Fdq$\"3v7-HV,'p5) F-7$Fiq$\"3k,F]goIk%)F-7$F^r$\"3//[k;i@>))F-7$Fcr$\"3(RvD]\\+a?*F-7$Fh r$\"3Kh#G[g:\\d*F-7$F]s$\"3i$)QMzI8!***F-7$Fcs$\"32Z0q6.0W5Fgs7$Fis$\" 3cs^ka\\!\\3\"Fgs7$F^t$\"3;(zM@lE38\"Fgs7$Fct$\"3W$e]g`5.=\"Fgs7$Fht$ \"3TE;`;c\"3B\"Fgs7$F]u$\"3+&y'4$)zt\"G\"Fgs7$Fbu$\"3H'>'[,1vS8Fgs7$Fg u$\"3k*>pi+!4'R\"Fgs7$F\\v$\"3oHAQE.qd9Fgs7$Fav$\"3]!RtqMte^\"Fgs7$Ffv $\"3wD+V%\\J@e\"Fgs7$F[w$\"31]tZ?v6Z;Fgs7$F`w$\"3'Qf'fjFgs7$Fdx$\"3 PvSfBwPK?Fgs7$Fix$\"3[J]$\\l(p>@Fgs7$F^y$\"3,i!=R[RK?#Fgs7$Fcy$\"3J=Ad $*[/.BFgs7$Fhy$\"3Q`]xri8'R#Fgs7$F]z$\"3qVqM`&R&*\\#Fgs7$Fbz$\"3`rQsfl o-EFgs7$Fgz$\"34X!f%G=G=FFgs-F\\[l6&F^[lFa[lF_[lFa[l-%+AXESLABELSG6$Q \"x6\"Q!F^el-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "But Maple has a hard time finding this solution algebraically. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(x + (cos(x))^2 = exp(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootO fG6#,(%#_ZG\"\"\"*$)-%$cosG6#F'\"\"#F(F(-%$expGF-!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Does this equal zero. Its hard to say. L ets try evaluating it as a floating point number: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$\"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 313 " Notice, the % symb ol denotes the last Maple output, and it turns out that the \"RootOf . ...\" is equal to zero. However, what is hidden in this sequence of co mmands is the fact that Maple did not find this solution algebraically . It actually used a numerical routine to find where these two curves intersect. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 10 "Simplify. " }{TEXT -1 130 "Maple can take the pain out of simplifying some express ions. For example Maple knows the most common identity from trigonome try: " }{XPPEDIT 18 0 "cos^2*x+sin^2*x = 1;" "6#/,&*&)%$cosG\"\"#\"\" \"%\"xGF)F)*&)%$sinGF(F)F*F)F)F)" }{TEXT -1 5 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify((cos(x))^2 + (sin(x))^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 186 "But, you don't have to look very far to find an expressi on that can be simplified easily by hand but stumps Maple. For exampl e, the laws of logarithms shows that the expression given by" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "expression := ln(exp(x)) - l n(exp(-x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+expressionG,&-%#lnG6 #-%$expG6#%\"xG\"\"\"-F'6#-F*6#,$F,!\"\"F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "equals 2 x. Confirm this. But when Maple is asked to si mplify this expression by" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "simplify(expression);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6 #-%$expG6#%\"xG\"\"\"-F%6#-F(6#,$F*!\"\"F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "It just returns the original expression. Lesson: Maple \+ can't solve all of your simplification needs. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 281 18 "Expand and Factor:" }{TEXT -1 115 " \+ Maple can expand and factor some polynomial expressions. For example , you can have Maple multiply monomials by " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "expand((x-2) * (x-2) * (3 - x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"xG\"\"#\"\"\"\"\"(*$)F&\"\"$F(!\"\"*&\"#;F (F&F(F-\"#7F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Maple can then f actor this cubic polynomial. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&%\"xG\"\"\" \"\"$!\"\"F'),&F&F'\"\"#F)F,F'F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 "That's pretty nice because factoring anything greater than quadra tic polynomials by hand can be very time consuming. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "# end of section" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Assignment " }}{PARA 0 "" 0 "" {TEXT -1 141 "This is a very simple assignment that lets me know you have an id ea of how to use Maple as a mathematical tool and a word processing de vice. " }}{EXCHG {PARA 0 "" 0 "" {TEXT 282 6 "First." }{TEXT -1 297 " \+ Open a new worksheet by clicking on \"File\" from the menu bar and ch oosing new. Start by clicking on \"T\" from the tool bar and type you r name and section. Create an expression or equation that would be d ifficult to produce on a typical word processor. This can best be done by clicking on the " }{XPPEDIT 18 0 "Sigma;" "6#%&SigmaG" }{TEXT -1 201 " button from the tool bar and typing in Maple code for the expres sion you want to create. For example, if you type in the following: \+ \"exp(x^2) * cos(Pi) = - exp(x^2)\" and hit enter, the expression \" \+ " }{XPPEDIT 18 0 "exp(x^2)*cos(Pi);" "6#*&-%$expG6#*$%\"xG\"\"#\"\"\"- %$cosG6#%#PiGF*" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "-exp(x^2);" "6#,$- %$expG6#*$%\"xG\"\"#!\"\"" }{TEXT -1 51 " \" is printed at the cursor \+ location. To exit the \"" }{XPPEDIT 18 0 "Sigma;" "6#%&SigmaG" }{TEXT -1 197 "\" mode, click on the \"T\" from the menu bar. You can also \+ do this sort of thing by cutting and pasting Maple output, or using th e palettes found in \"View/Palettes\" from the menu bar. However the \+ " }{XPPEDIT 18 0 "Sigma;" "6#%&SigmaG" }{TEXT -1 21 " button works bes t. " }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 283 8 "Second. " }{TEXT -1 45 " P lot the functions f(x) = cos(x) and g(x) = " }{XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }{TEXT -1 36 " on the same graph over the domain [ " }{XPPEDIT 18 0 "-Pi,Pi;" "6$,$%#PiG!\"\"F$" }{TEXT -1 2 " ]" }{TEXT -1 308 ". Make sure that when printed up, these two curves are differ entiated by color (if you have a color printer) or by linestyle = \"SO LID, DASH, DOT, or DASHDOT\" and that the thickness is large enough to be easily read. Furthermore, label the x and y axes using the \"labe l\" command and give the graph a title. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 284 7 "Third. " }{TEXT -1 176 " Print it up and h and it in. This should be one page only. If your graph turns out to b e too big, you can adjust the size by clicking on the graph and shrink ing the borders. " }}}}}{MARK "4" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }