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0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Bullet Item" -1 15 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 3 3 1 0 1 0 2 2 15 2 }{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 "Author" -1 19 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 8 8 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 12 "Maple Basics" }}{PARA 19 "" 0 "" {TEXT -1 14 "Brian E. Blank" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 38 "Click o n a button to open the section." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 265 5 "MAPLE" }{TEXT -1 17 ", the Calculator" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 13 "All input to " }{TEXT 268 5 "MAPLE" }{TEXT -1 16 " is t yped at a " }{TEXT 267 6 "prompt" }{TEXT -1 4 ". A " }{TEXT 381 5 "MA PLE" }{TEXT -1 30 " prompt typically looks like " }{TEXT 269 2 "[>" } {TEXT -1 6 ".\n\n\nA " }{TEXT 382 5 "MAPLE" }{TEXT -1 50 " prompt may \+ be inserted where desired by means of " }}{PARA 15 "" 0 "" {TEXT -1 4 "The " }{TEXT 270 6 "Insert" }{TEXT -1 5 " menu" }}{PARA 15 "" 0 "" {TEXT -1 20 "An icon on a toolbar" }}{PARA 15 "" 0 "" {TEXT -1 53 "A k eyboard shortcut (such as Ctrl + K or Ctrl + J in " }{TEXT 271 7 "Wind ows" }{TEXT -1 3 "). " }}{PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }}{PARA 0 " " 0 "" {TEXT 266 5 "MAPLE" }{TEXT -1 141 " can be used as a calculator , but not a traditional one that is based on decimalizations of number s. A traditional calculator will return " }{XPPEDIT 19 1 ".625;" "6 #-%&FloatG6$\"$D'!\"$" }{TEXT -1 20 " as the answer to " }{XPPEDIT 19 1 "5/8;" "6#*&\"\"&\"\"\"\"\")!\"\"" }{TEXT -1 18 ". Contrarily, " }{TEXT 272 5 "MAPLE" }{TEXT -1 25 " will leave the input " } {TEXT 273 3 "5/8" }{TEXT -1 49 " alone (unless a decimalization is r equested):\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "5/8;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 274 5 "MAPLE" }{TEXT -1 52 " does perform certain simplific ations on its own: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "10/16;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "A traditional calculator will return " }{XPPEDIT 19 1 "1.225;" "6# -%&FloatG6$\"%D7!\"$" }{TEXT -1 20 " as the answer to " }{TEXT 275 9 "5/8 + 3/5" }{TEXT -1 32 " . Unless otherwise requested, " }{TEXT 383 5 "MAPLE" }{TEXT -1 43 " performs rational arithmetic. That is, \+ " }{TEXT 276 5 "MAPLE" }{TEXT -1 71 " will sum the two fractions and return the answer as another fraction:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "5/8 + 3/5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#\\ \"#S" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 3 "In " }{TEXT 277 5 "MAPLE" }{TEXT -1 89 " you can obtain the decimalization of any real number by calling \+ for it by means of the " }{HYPERLNK 17 "floating point evaluation" 2 " evalf" "" }{TEXT -1 12 " command, " }{TEXT 278 5 "evalf" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalf( 5/8 + 3/5 );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++D7!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 279 5 "MAPLE" }{TEXT -1 125 " can calc ulate more decimal places than a traditional calculator. Simply specif y the desired number as a second argument of " }{TEXT 280 5 "evalf" } {TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalf(sqrt(2 ), 2000);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#$\"[hr,OY-'[yv5Zk^ena_HL[ L&eMn:h'3P$*3;spj46t?HpOx\\U!\\n=@_shdyM2))=#f,+'>VPyYZOR?&=1L)zpJ5W'>Qcv#\\uDmkQXR*)Ga'4 Cl4EX$)Gev/*QD\\&[\"*)o@&H'\\z%pNZMXGKR*)>wd_$em*>Dm\\xpyj&G#)GnQ&*)*) *H$)*o1u7B(R^X>*zQx@E9o`xx.%>U*f\\FyhjLEg)yD)f@lz'zlyXO%)R LB`c!4lUqS?9=Bs9=&3dM3S'[$f\"))4a<*)p_i<@l#**fRe:r'3AiUF[hAjQsjMfD%*)os\"e;Ro66<5ZJpG=4t2rLg.e5y9`GU.['=.Sqe[f+,j#3d\"okC)Q6.!=fE4PWR *))Re9_mWe&3-gAdE#\\Ze2i,)ee,Za[E-s`wnpqlbT([&eVr2sCo9ggo&G/UL=U:x\\\\ 7'[E4&)GNsB()*o&=c,8Iromf6JYy0e@'=p$H\\oI#yCakJ!zFSaI]\"[+*pq***oQgr%) )\\3MguVN6q&=`P.Avb$)H<'*fxG]dua]R_$e_h?1kH)3=LYlR`so*)zS^_*zi.EwR3X@V r3V[I#HBb4')>*)3k=u^GZ,iofMXFqfgr*f&4,Zr01#y_6]]**zbFf0v#fmAKTJe$**4( \\@Tk7st]e0O[#\\-(H74BYQ,NFdTwKMvQ])Qq5i%yCt!*ztzm" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "Any object in " }{TEXT 281 5 "MAPLE" }{TEXT -1 49 " can b e assigned a name for easy reference. The " }{HYPERLNK 17 "assignment operator" 2 "assignment" "" }{TEXT -1 120 " is a two character toke n consisting of a colon followed immediately, with no space in between , by an equality sign ( " }{TEXT 282 2 ":=" }{TEXT -1 3 " )." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A := 5/8; B := 3/5; A + B;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG#\"\"&\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG#\"\"$\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6## \"#\\\"#S" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 131 "Notice that, at a prompt, more than one command can be issued. Multiple commands are executed seque ntially from left to right. \n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "s := 0; s := s + 1; s := s + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"sG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 35 "\n\nEach command is terminated by a " } {HYPERLNK 17 "statement separator" 2 "separator" "" }{TEXT -1 26 ", n amely a semicolon ( " }{TEXT 284 1 ";" }{TEXT -1 6 " ) if " }{TEXT 283 5 "MAPLE" }{TEXT -1 40 "'s response is to be seen or a colon ( " }{TEXT 286 1 ":" }{TEXT -1 6 ") if " }{TEXT 285 5 "MAPLE" }{TEXT -1 37 "'s response is to be suppressed. \n\n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "s := 0: s := s + 1: s := s + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 79 "\n\nThe entire group of commands appearing after the single prompt is called an " }{HYPERLNK 17 "execution group" 2 "executiongroups,overv iew" "" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 287 5 "MAPLE" }{TEXT -1 6 " is " }{TEXT 288 14 "case-sensitive" }{TEXT -1 17 ". For example, \+ " }{TEXT 289 2 "pi" }{TEXT -1 7 " and " }{TEXT 290 2 "Pi" }{TEXT -1 58 " are not the same thing. The first of these two tokens, " } {TEXT 291 2 "pi" }{TEXT -1 110 ", is a Greek letter that can be used a s a name, if desired. It has no initially known meaning \n\n\nThe seco nd, " }{TEXT 292 2 "Pi" }{TEXT -1 60 ", is the famous ratio that has \+ to do with circles. It is an " }{HYPERLNK 17 "initially known name" 2 "ininames" "" }{TEXT -1 3 " : " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "pi; \nevalf(pi); \n\n\nPi; \nevalf(Pi); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pi := 7 .2; pi + 2.8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#piG$\"#s!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$+\"!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Pi + 2.8; Pi := 7.2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%#PiG\"\"\"$\"#G!\"\"F% " }}{PARA 8 "" 1 "" {TEXT -1 55 "Error, attempting to assign to `Pi` w hich is protected\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 193 "Sometimes it is desira ble to restore a name to its original unassigned state. One does this \+ by assigning the literal value of the name back to the name. The liter al value is obtained by using " }{HYPERLNK 17 "single quotes" 2 "quot es" "" }{TEXT -1 13 " as follows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pi; \npi := 'pi'; \npi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#s! \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#piGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 384 7 "MAPLE's" }{TEXT -1 265 " memory is long. Often a user forgets that a value has been assi gned to a variable. When this happens, surprising results may ensue an d it is often difficult to pin down the problem. For this reason and m any others, it is often desirable to remove everything from " }{TEXT 385 7 "MAPLE's" }{TEXT -1 26 " memory. To do that, you " }{HYPERLNK 17 "restart" 2 "restart" "" }{TEXT -1 25 " the session as follows:" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 293 5 "MAPLE" }{TEXT -1 27 ", the Follower o f Commands" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 299 5 "MAPLE" }{TEXT -1 61 " commands \+ have the form\n\n " }{TEXT 294 49 " nameOfCommand(comma-separatedSequenceOfArguments)" }{TEXT -1 30 " \n\n followed by a semi-colon ( " }{TEXT 295 1 ";" }{TEXT -1 68 " ), if the result of the command is to be displayed, or a colon ( " }{TEXT 296 1 ":" }{TEXT -1 131 " ), if the display of the result of the comma nd is to be suppressed.\n\nExecution of a command is accomplished by p lacing the cursor " }{TEXT 298 8 "anywhere" }{TEXT -1 39 " on the prom pt line and pressing the " }{TEXT 297 5 "Enter" }{TEXT -1 35 " key. In more recent releases of " }{TEXT 392 5 "MAPLE" }{TEXT -1 103 ", r ight-clicking on axecution group will bring up an appropriate menu of \+ actions, including \"execute.\"\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 80 "The array of available commands is vast! \+ Here are some that are frequently used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "expand( (a+b)^5 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,.*$)%\"aG\"\"&\"\"\"F(*(F'F()F&\"\"%F(%\"bGF(F(*(\"#5F()F&\"\"$F()F, \"\"#F(F(*(F.F()F&F2F()F,F0F(F(*(F'F(F&F()F,F+F(F(*$)F,F'F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "expand( cos(3*theta) );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\")-%$cosG6#%&thetaG\"\"$ F&F&*&F,F&F(F&!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor( x^2-y^2 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yG!\"\"F&,&F%F&F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "poly := x^4+16/3*x^3-73*x^2-108*x+308/3;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%polyG,,*$)%\"xG\"\"%\"\"\"F**(\"#;F *\"\"$!\"\"F(F-F**&\"#tF*)F(\"\"#F*F.*&\"$3\"F*F(F*F.#\"$3$F-F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "factor( poly );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"$!\"\",&%\"xG\"\"\"\"#6F)F),&F(F)\"\"(F &F),&*&F%F)F(F)F)\"\"#F&F),&F(F)F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ifactor( 111111111111 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*0-%!G6#\"\"$\"\"\"-F%6#\"\"(F(-F%6#\"#6F(-F%6#\"#8F(-F %6#\"#PF(-F%6#\"$,\"F(-F%6#\"%,**F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify( (a^b)^3 );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#)%\"aG,$*&\"\"$\"\"\"%\"bGF(F(" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "Sometimes the choice of \"simplification\" is \+ not obvious. For example, we know that the expression " }{XPPEDIT 19 1 "cos(A)*cos(B)-sin(A)*sin(B);" "6#,&*&-%$cosG6#%\"AG\"\"\"-F&6#% \"BGF)F)*&-%$sinG6#F(F)-F/6#F,F)!\"\"" }{TEXT -1 17 " is equal to \+ " }{XPPEDIT 19 1 "cos(A+B);" "6#-%$cosG6#,&%\"AG\"\"\"%\"BGF(" }{TEXT -1 380 ". The latter looks to be simpler, but is it really a simplifi cation? In fact, the angles of the trigonometric functions in the firs t expression are monomials, while the angle of the second expression i s a binomial. In going from the first to the second expression, a gai n in simplicity in one aspect of the expression is counteracted by a l oss of simplicity in another aspect. " }{TEXT 300 5 "MAPLE" }{TEXT -1 40 " does not carry out the simplification: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "simplify( co s(A)*cos(B)-sin(A)*sin(B));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$ cosG6#%\"AG\"\"\"-F&6#%\"BGF)F)*&-%$sinGF'F)-F/F+F)!\"\"" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 11 "However, " }{TEXT 301 5 "MAPLE" }{TEXT -1 104 " does \+ know the trigonometric identity in question and will apply it if comma nded in the appropriate way:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "co mbine( cos(A)*cos(B)-sin(A)*sin(B) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#,&%\"AG\"\"\"%\"BGF(" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "There is an equation data-type in " }{TEXT 319 5 "MAPLE" }{TEXT -1 38 ". It uses the standard equality sign. " } {TEXT 320 46 "Do not confuse an equation with an assignment." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A := 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A := 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG\"\"# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "A = 3; A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 56 "An equation is an equation whether it is always true ( " }{XPPEDIT 19 1 "1 = 1;" "6#/\"\"\"F$" }{TEXT -1 22 " ), sometimes true ( " }{XPPEDIT 19 1 "x = sqrt(x^2);" "6#/%\"xG- %%sqrtG6#*$F$\"\"#" }{TEXT -1 20 " ), or never true ( " }{XPPEDIT 19 1 "2 = 3;" "6#/\"\"#\"\"$" }{TEXT -1 16 " ). \nThere is a " }{TEXT 321 6 "MAPLE " }{TEXT -1 49 " command for testing the validity of an e quation:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "value(A); # A reminde r of the value of A\ntype(A = 3, equation); \ntesteq(A = 3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "eqn := 8*sin(t)*cos(t)^3-4*sin(t)*c os(t) = sin(4*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,&*(\"\") \"\"\"-%$sinG6#%\"tGF))-%$cosGF,\"\"$F)F)*(\"\"%F)F*F)F/F)!\"\"-F+6#,$ *&F3F)F-F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "testeq( eqn );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "The solve commands are often useful." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "solve( x^3 + 4*x^2 + 4*x + 3 = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%!\"$,&#\"\"\"\"\"#!\"\"*&^##F&F'F&\"\"$F+F&,&#F&F' F(*&^##F(F'F&F,F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "solv e( \{x^2 + y^2 = 10, 3*x + y = 0\}, \{x,y\} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG\"\"\"/%\"yG!\"$<$/F(\"\"$/F%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "fsolve( x^5 + 4*x + 3 = 0, x); #fl oating point solution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+e\"\\61(!# 5" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 303 5 "MAPLE" }{TEXT -1 3 ", " }{TEXT 304 27 "the Distinguisher Between a" }{TEXT 305 9 " Fun ction" }{TEXT 306 7 " and an" }{TEXT 307 11 " Expression" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "In mathematics a \+ " }{TEXT 259 9 " function" }{TEXT -1 139 " is an input-output machine : you put in some input and you get a specific output value as a resul t. The input comes from a set called the " }{TEXT 260 6 "domain" } {TEXT -1 57 " of the function. The output is usually determined by an \+ " }{TEXT 258 10 "expression" }{TEXT -1 25 " that involves the input." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "In " } {TEXT 261 5 "MAPLE" }{TEXT -1 61 " the input-to-output nature of a fun ction is captured by the " }{HYPERLNK 17 "arrow notation" 2 "->" "" } {TEXT -1 158 " for a \"functional opearator\". The arrow notation i s a two character token made up of a dash followed by a right angle br acket, with no space in between: " }{TEXT 262 2 "->" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "x -> x^3 + 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arro wGF&,&*$)9$\"\"$\"\"\"F/\"\"#F/F&F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 43 "Technical Aside for Computer \+ Science Majors" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "The object " }{XPPEDIT 19 1 "proc (x) options operator, arrow; x^3+2 end proc;" "6#f*6#%\"xG7 \"6$%)operatorG%&arrowG6\",&*$F%\"\"$\"\"\"\"\"#F.F*F*F*" }{TEXT -1 9 " has a " }{HYPERLNK 17 "data type" 2 "type" "" }{TEXT -1 7 " in \+ " }{TEXT 308 5 "MAPLE" }{TEXT -1 34 ". It can be viewed either as a " }{HYPERLNK 17 "functional operator" 2 "type,operator" "" }{TEXT -1 7 " or a " }{HYPERLNK 17 "procedure" 2 "type,procedure" "" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "type( x -> x^3 + 2 , opera tor ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "whattype( \+ x -> x^3 + 2 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*procedureG" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "When " }{TEXT 309 5 "MAPLE" }{TEXT -1 221 " is used as a programming language, fun ctions are not prototyped. That allows for great flexibility, but it \+ also requires programmers to do lots of type checking to ensure that t he function works in the expected way. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "Note that it is the transformation " }{XPPEDIT 19 1 "proc (x) options operato r, arrow; x^3+2 end proc;" "6#f*6#%\"xG7\"6$%)operatorG%&arrowG6\",&*$ F%\"\"$\"\"\"\"\"#F.F*F*F*" }{TEXT -1 18 " of the input " } {XPPEDIT 19 1 "x;" "6#%\"xG" }{TEXT -1 19 " to the output " } {XPPEDIT 19 1 "x^3+2;" "6#,&*$%\"xG\"\"$\"\"\"\"\"#F'" }{TEXT -1 60 " \+ that is the function.\nTo the right of the arrow we find " } {XPPEDIT 19 1 "x^3+2;" "6#,&*$%\"xG\"\"$\"\"\"\"\"#F'" }{TEXT -1 22 ". This obect is an " }{TEXT 310 10 "expression" }{TEXT -1 17 ", not \+ a function." }}{PARA 0 "" 0 "" {TEXT -1 2 "\n\n" }}{PARA 0 "" 0 "" {TEXT -1 61 "We usually assign a name to a function for ease of refere nce:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f := x -> x^3 + 2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&*$)9$\"\"$\"\"\"F1\"\"#F1F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 23 "The cast of characters:" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 19 1 "x^3+2;" "6#,&*$%\"xG\"\"$\"\"\"\"\"#F' " }{TEXT -1 28 " : An expression" }}{PARA 15 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 19 1 "proc (x) options operator, arrow; x^3+ 2 end proc;" "6#f*6#%\"xG7\"6$%)operatorG%&arrowG6\",&*$F%\"\"$\"\"\" \"\"#F.F*F*F*" }{TEXT -1 49 " : The function that returns the expr ession " }{XPPEDIT 19 1 "x^3+2;" "6#,&*$%\"xG\"\"$\"\"\"\"\"#F'" } {TEXT -1 23 " when the input is " }{XPPEDIT 19 1 "x;" "6#%\"xG" } {TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 19 1 "f;" "6#%\"fG" }{TEXT -1 50 " : The name of the funct ion " }{XPPEDIT 19 1 "proc (x) options operator, arrow; x^3+2 end proc ;" "6#f*6#%\"xG7\"6$%)operatorG%&arrowG6\",&*$F%\"\"$\"\"\"\"\"#F.F*F* F*" }{TEXT -1 3 " " }}{PARA 15 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 19 1 "f(x);" "6#-%\"fG6#%\"xG" }{TEXT -1 38 " : The exp ression " }{XPPEDIT 19 1 "x^3+2;" "6#,&*$%\"xG\"\"$\"\"\"\"\"#F'" } {TEXT -1 26 " that the function named " }{XPPEDIT 19 1 "f;" "6#%\"fG " }{TEXT -1 29 " outputs when the input is " }{XPPEDIT 19 1 "x;" "6# %\"xG" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"uG\"\"$\"\"\"F(\"\"#F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%#PiG\"\"$\"\"\"F(\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$F\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 56 "A function of two variables is created in a similar way:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := (x,y) - > x^2 - y^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6 \"6$%)operatorG%&arrowGF),&*$)9$\"\"#\"\"\"F2*$)9%\"\"$F2!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f(x,y);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(*$)%\"yG\"\"$F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f(2,y); f(2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"%\"\"\"*$)%\"yG\"\"$F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"%\"\"\"*$)%\"xG\"\"$F%!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(x,2); f(y,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(\"\")!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*$)%\"yG\"\"#\"\"\"F(\"\")!\"\"" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 302 5 "MAPLE" }{TEXT -1 21 ", the Calculus Do-er" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 " The " }{TEXT 311 5 "MAPLE" }{TEXT -1 10 " commands " }{HYPERLNK 17 "li mit" 2 "limit" "" }{TEXT -1 4 ", " }{HYPERLNK 17 "D" 2 "D" "" } {TEXT -1 4 ", " }{URLLINK 17 "diff" 4 "" "" }{TEXT -1 9 ", and " }{HYPERLNK 17 "int" 2 "int" "" }{TEXT -1 9 " , and " }{HYPERLNK 17 " series" 2 "series" "" }{TEXT -1 42 " implement the main calculus oper ations. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "expr := sin(3*x)^2/(1-cos(5*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG*&-%$sinG6#,$*&\"\"$\"\"\"%\"xGF,F,\"\"#,&F,F,- %$cosG6#,$*&\"\"&F,F-F,F,!\"\"F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "limit(expr, x = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6##\"#=\"#D" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Notice that there are two differentiation commands, " }{HYPERLNK 17 "D" 2 "D" "" }{TEXT -1 8 " and " }{URLLINK 17 "diff" 4 "" "" } {TEXT -1 84 " . The first takes a function as its argument. It return s a function as its output." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f \+ := x -> x^3 + 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\" 6$%)operatorG%&arrowGF(,&*$)9$\"\"$\"\"\"F1\"\"#F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arrowGF&,$*&\"\"$\"\"\")9$\"\"#F-F-F& F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(f)(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$\"\"\")%\"xG\"\"#F&F&" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 166 "The second takes an ex pression as its first argument and information about the type of diffe rentiation as its second argument.\nIt returns an expression as its ou tput." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff( f(x), x ); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$\"\"\")%\"xG\"\"#F&F&" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 93 "Higher derivatives can be obtained as well, but without shortcuts, the input becomes tedious:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "D( D(f) ); D( D( D(f) ) );" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#f*6#%\"xG6\"6$%)operatorG%&arrowGF&,$*&\"\"'\"\"\"9$F -F-F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "diff( diff( f(x), x ) , x);\ndiff( diff( di ff( f(x), x ) , x), x ); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"' \"\"\"%\"xGF&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "The shortcuts for \+ higher derivatives use " }{TEXT 386 5 "MAPLE" }{TEXT -1 40 "'s composi tion and repetition operators:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "(D@@2)(f); (D@@3)(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\" xG6\"6$%)operatorG%&arrowGF&,$*&\"\"'\"\"\"9$F-F-F&F&F&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "diff( f(x), x$2 ); diff( f(x), x$3 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"'\"\"\"%\"xGF&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Depending on its second argumen t, " }{TEXT 387 5 "MAPLE" }{TEXT -1 4 "'s " }{HYPERLNK 17 "integratio n" 2 "int" "" }{TEXT -1 61 " command performs both definite and indef inite integrations:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(1/(1+x^4),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\")F&*&\"\"##F&F)-%#lnG6#*&,(*$)%\"xGF)F&F &*&F2F&F)F*F&F&F&F&,(F0F&F3!\"\"F&F&F5F&F&F&*&#F&\"\"%F&*&F)F*-%'arcta nG6#,&F3F&F&F&F&F&F&*&F7F&*&F)F*-F;6#,&F3F&F&F5F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(1/(1+x),x=0..2);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%#lnG6#\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 55 "Sometimes the inert forms of these comman ds are useful:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "V := Int(1/( 1+x^2),x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%$Int G6$*&\"\"\"F),&*$)%\"xG\"\"#F)F)F)F)!\"\"/F-;\"\"!%)infinityG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(V);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&\"\"#!\"\"%#PiG\"\"\"F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "V := Int(D(F )(x),x=a..b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%$IntG6$--%\"D G6#%\"FG6#%\"xG/F.;%\"aG%\"bG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%\"FG6#%\"bG\"\" \"-F%6#%\"aG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "V := D iff(Int(g(x),x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%%DiffG6 $-%$IntG6$-%\"gG6#%\"xGF.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"gG6#%\"xG" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "Another basic c alculus construction is the Taylor polynomial of a function:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "series(sin(x),x=0,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-%\"xG\"\"\"F%#!\"\"\"\"'\"\"$#F%\"$?\"\"\"&#F '\"%S]\"\"(-%\"OG6#F%\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "series(sin(x),x=Pi/4,10);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+9,&% \"xG\"\"\"*&\"\"%!\"\"%#PiGF&F),$*&\"\"#F)F-#F&F-F&\"\"!F+F&,$*&F(F)F- F.F)F-,$*&\"#7F)F-F.F)\"\"$,$*&\"#[F)F-F.F&F(,$*&\"$S#F)F-F.F&\"\"&,$* &\"%S9F)F-F.F)\"\"',$*&\"&!35F)F-F.F)\"\"(,$*&\"&S1)F)F-F.F&\"\"),$*& \"'gdsF)F-F.F&\"\"*-%\"OG6#F&\"#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f := 'f':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "series(f(x) ,x=c,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-,&%\"xG\"\"\"%\"cG!\"\"- %\"fG6#F'\"\"!--%\"DG6#F*F+F&,$*&#F&\"\"#F&---%#@@G6$F/F4F0F+F&F&F4,$* &#F&\"\"'F&---F86$F/\"\"$F0F+F&F&FB-%\"OG6#F&\"\"%" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 312 5 "MAPLE" }{TEXT -1 15 ", the Repeater" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "The resul t of the last " }{TEXT 314 5 "MAPLE" }{TEXT -1 10 " command (" }{TEXT 318 18 "in time, not space" }{TEXT -1 25 ") can be obtained by the " } {HYPERLNK 17 "ditto operator" 2 "ditto" "" }{TEXT -1 19 ". Beginning \+ with " }{TEXT 315 16 "MAPLEV release 5" }{TEXT -1 23 " the per cent s ign ( " }{TEXT 316 1 "%" }{TEXT -1 75 " ) has been used for this op erator. In prior releases the double quote ( " }{TEXT 317 1 "\"" } {TEXT -1 12 " ) was used." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(F (x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$-%\"FG6#%\"xGF)" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "diff(%, x);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%\"FG6#%\"xG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 30 "You can check what release of " }{TEXT 313 5 "MAPLE" }{TEXT -1 26 " you are using as follows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "interfa ce(version);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%[pMaple~Worksheet~Int erface,~Maple~8.00,~IBM~INTEL~NT,~Mar~19~2002~Build~ID~109153G" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 156 "The ditto operator is convenient if you work s equentially in space. But if you jump around a worksheet then usage of the ditto operator can lead to errors. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "There are also double and triple d itto operators:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "a; \n%+%; \n%+%%; \n%+%%+%%%; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"# \"\"\"%\"aGF&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$\"\"\"%\"a GF&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"'\"\"\"%\"aGF&F&" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" } {TEXT 396 5 "Note:" }{TEXT -1 22 " In releases prior to " }{TEXT 393 9 "MAPLEV R5" }{TEXT -1 31 " , the double-quote character " }{TEXT 395 1 "\"" }{TEXT -1 23 " was used instead of " }{TEXT 394 1 "%" } {TEXT -1 3 ".\n\n" }}{PARA 0 "" 0 "" {TEXT -1 86 "The notion of loopin g (as well as branching) is central to all programming languages. " } {TEXT 388 5 "MAPLE" }{TEXT -1 17 " has the usual " }{HYPERLNK 17 "fo r...while...do" 2 "do" "" }{TEXT -1 96 " constructions. Here we use a do-loop to generate the sequence of the first 10 perfect squares:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "for j from 1 to 10 do\nj^2; \nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\\" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" $+\"" }}}{PARA 0 "" 0 "" {TEXT -1 62 "\nIt is sometimes important to k now that the do-loop index is " }{TEXT 390 3 "not" }{TEXT -1 106 " l ocal. That is, after the do-loop is over, the index variable retains i ts last value. Because of the way" }{TEXT 391 6 " MAPLE" }{TEXT -1 121 " implements loops, that might be the first value assigned to the \+ index variable for which the loop does not continue. \n\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "j;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#6" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "There are several ways to " }{HYPERLNK 17 "break" 2 "break" "" } {TEXT -1 345 " out of loops. Here is a small loop to illustrate. By w ay of background, notice that there are many perfect squares that are \+ immediate predecessors of primes. For example, 1, 4, 16, 36, 100, 196 , 256, 400, 576, 676, 1296 are the first eleven perfect squares with \+ this property. What is the first seven digit perfect square with this \+ property?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "for j from 10^3 to i nfinity by 2 do\n if isprime(j^2+1) then print(j^2); \n break; \n end if;\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(;!35 " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 400 5 "Note :" }{TEXT -1 22 " In releases prior to " }{TEXT 397 9 "MAPLEV R7" } {TEXT -1 13 " , the word " }{TEXT 402 2 "fi" }{TEXT -1 23 " was used instead of " }{TEXT 403 7 " end if" }{TEXT -1 20 " and \nthe wor d " }{TEXT 404 2 "od" }{TEXT -1 23 " was used instead of " }{TEXT 405 7 " end do" }{TEXT -1 94 ". The older words continue to work in n ewer versions. \n\n\nSome specialized commands such as " }{HYPERLNK 17 "seq" 2 "seq" "" }{TEXT -1 6 " and " }{HYPERLNK 17 "sum" 2 "sum" " " }{TEXT -1 32 " have do-loops built into them:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "seq(j^2,j=1..20); #The first 20 perfect squares" } }{PARA 11 "" 1 "" {XPPMATH 20 "66\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\\"#k \"#\")\"$+\"\"$@\"\"$W\"\"$p\"\"$'>\"$D#\"$c#\"$*G\"$C$\"$h$\"$+%" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "Note that the index variable of the sequence command " }{TEXT 389 2 "is" } {TEXT -1 9 " local: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "j;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"%/5" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 50 "If we wanted the sum of the first twe nty squares:\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "sum(k^2,k =1..20); \n#A summation index should not have a value already assigned to it, so another letter has been chosen" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%qG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "As with the sequence command, the index of the summat ion command is local:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "k;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"k G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Whe re appropriate, the summation command also computes infinite sums:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "sum(1/k^2,k=1..infinity); #N o need for another index variable" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, $*&\"\"'!\"\"%#PiG\"\"#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 326 5 "MAPLE" }{TEXT -1 16 ", the Organizer" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 94 "Many commands, particularly those that are of a \"speci alized\" nature, are grouped together in " }{HYPERLNK 17 "packages" 2 "index,package" "" }{TEXT -1 34 " . Packages are included with the " } {TEXT 328 5 "MAPLE" }{TEXT -1 57 " distribution but are not automatica lly \"loaded\" when a " }{TEXT 327 5 "MAPLE" }{TEXT -1 18 " session \+ starts. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 106 "A command that belongs to a package requires a reference to that \+ package when it is called. The syntax is" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 331 59 "[> packageName[c ommandName](comma_separated_argument_list);" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 54 "For example, data about the e lement Gold is stored in " }{TEXT 332 5 "MAPLE" }{TEXT -1 41 ". That d ata is retrieved by the command " }{HYPERLNK 17 "GetElement" 2 "GetEl ement" "" }{TEXT -1 9 " in the " }{HYPERLNK 17 "ScientificConstants" 2 "ScientificConstants" "" }{TEXT -1 11 " package." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "GetElement(Au);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+GetElementG6#%#AuG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ScientificConstants[GetElement](Au);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6-\"#z/%'symbolG%#AuG/%%nameG%%goldG/%&namesG<#F)/%2electronegativity G7%/%&valueG$\"$a#!\"#/%,uncertaintyG%*undefinedG/%&unitsG\"\"\"/%(den sityG7%/F1$\"$$>!\"\"F5/F9*&%\"gGF:%#cmG!\"$/%1ionizationenergyG7%/F1$ \"&bA*!\"%F5/F9%#eVG/%1electronaffinityG7%/F1$\"'j3B!\"&/F6$\"\"$FVFN/ %-meltingpointG7%/F1$\"'LP8F4F5/F9%\"KG/%-boilingpointG7%/F1$\"%HJ\"\" !F5Fjn/%-atomicweightG7%/F1$\")bmp>FV/F6$\"\"#FV/F9%\"uG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "GetElement(Hg); #The package has b een referenced but not loaded" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+Ge tElementG6#%#HgG" }}}{PARA 0 "" 0 "" {TEXT -1 72 "\n\nIn practice it i s easier to just load the entire package by using the " }{HYPERLNK 17 "with" 2 "with" "" }{TEXT -1 11 " command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "For example, data about the ele ment Gold is stored in " }{TEXT 329 5 "MAPLE" }{TEXT -1 41 ". That dat a is retrieved by the command " }{HYPERLNK 17 "GetElement" 2 "GetElem ent" "" }{TEXT -1 9 " in the " }{HYPERLNK 17 "ScientificConstants" 2 "ScientificConstants" "" }{TEXT -1 11 " package." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(Scienti ficConstants):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "GetElemen t( Hg );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6,\"#!)/%'symbolG%#HgG/%%nam eG%(mercuryG/%&namesG<#F)/%2electronegativityG7%/%&valueG\"\"#/%,uncer taintyG%*undefinedG/%&unitsG\"\"\"/%(densityG7%/F1$\"'O`8!\"%F3/F7*&% \"gGF8%#cmG!\"$/%1ionizationenergyG7%/F1$\"'vV5F?F3/F7%#eVG/%-meltingp ointG7%/F1$\"&KM#!\"#F3/F7%\"KG/%-boilingpointG7%/F1$\"&))H'FSF3FT/%-a tomicweightG7%/F1$\"&f+#FS/F4$F2FS/F7%\"uG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 324 5 "When " }{TEXT -1 1 " " }{TEXT 322 5 "MAPLE" }{TEXT -1 2 " " }{TEXT 323 95 "unexpectedly echoes your input then it is often the case that you spelled a command incorrectl y" }}{PARA 0 "" 0 "" {TEXT 333 19 "(including case). \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "getElement(Hg);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%+getElementG6#%#HgG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 330 142 "\nIt might be the case, however, t hat you are calling a command in a package without having first loaded the package, as in our first call to " }{TEXT 334 10 "GetElement" } {TEXT 335 8 " above.\n" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 325 64 "Do not forget to reload any needed p ackages following a restart!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "GetElement( Hg );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+GetElementG6#%#HgG" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 336 5 "MAPLE" }{TEXT -1 14 ", the Plotter" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "In this section we \+ sketch the rudiments of plane-curve plotting. To plot the graph of an \+ expression " }{XPPEDIT 19 1 "A;" "6#%\"AG" }{TEXT -1 53 " that depe nds on one (and only one) variable, say " }{XPPEDIT 19 1 "u;" "6#%\"u G" }{TEXT -1 6 ", for " }{XPPEDIT 19 1 "u;" "6#%\"uG" }{TEXT -1 10 " b etween " }{XPPEDIT 19 1 "a;" "6#%\"aG" }{TEXT -1 7 " and " } {XPPEDIT 19 1 "b;" "6#%\"bG" }{TEXT -1 18 ", we make the call" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 337 1 "[" } {TEXT 339 1 ">" }{TEXT 338 21 " plot(A, u = a .. b);" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "For example," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A := \+ (1+2*x^3)/(1+x^4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&,&\"\"\" F'*&\"\"#F')%\"xG\"\"$F'F'F',&F'F'*$)F+\"\"%F'F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot( A, x = -2..3);" }}{PARA 13 " " 1 "" {GLPLOT2D 374 374 374 {PLOTDATA 2 "6%-%'CURVESG6$7_o7$$!\"#\"\" !$!3i0Zw6%HN#))!#=7$$!3smm;HU,\"*=!#<$!3!f6%)>&Q#R3*F-7$$!3SL$3FH'='z \"F1$!3M92q$3IAG*F-7$$!3gmmTgBa*o\"F1$!3K-2deC^]%*F-7$$!3amm\"H_\">#e \"F1$!3KNu)3T+]_*F-7$$!30+D197xG:F1$!331F_F!30^*F-7$$!3ML$3_!4Nv9F1$!3 Y`k@^'42X*F-7$$!3))**\\iSM#eU\"F1$!3%f%[<@k2Y$*F-7$$!3km;/wfHw8F1$!3I; U\"\\qpZ=*F-7$$!3_L$3_:8]K\"F1$!3mhH+z3=Z*)F-7$$!3;+]PM.tt7F1$!3yLJ8;y nD')F-7$$!3em;/,oln6F1$!3h\"=#*[q7$RwF-7$$!3%)**\\(oWB>1\"F1$!3qV!QG+p 49'F-7$$!3eJLLepjJ&*F-$!3C%=T\\B?(4SF-7$$!3])**\\(=(eE0*F-$!35,4'>U.R* GF-7$$!3Ulm;z/ot&)F-$!3Oxf*[_v4p\"F-7$$!33KL3FWYM!)F-$!3_!z(z#>nAj#!#> 7$$!3u)****\\P[_\\(F-$\"3S()zFd#[)*>\"F-7$$!3)*)*****\\#=Q&pF-$\"3O+x$ *owCaEF-7$$!3A*****\\7)Q7kF-$\"3TB\\I\"RRI/%F-7$$!3Q*****\\()>1*eF-$\" 3g=7!eOYmF&F-7$$!3e*****\\i^)o`F-$\"31BrHn]@vjF-7$$!3vlmT50A@WF-$\"3Qq vBwG8nzF-7$$!3OKLLeaR%H$F-$\"3mV5;eL#o<*F-7$$!3+KL$e96r\"GF-$\"3=A,mIC 2$\\*F-7$$!3kJLLLo#)RBF-$\"3x&[cFo!o9(*F-7$$!3gl;a8!y)yUU4\"F17$$\"3)GLL3_?`(\\F-$\"3g%[uX TdV<\"F17$$\"3!fL$e*)>pxgF-$\"3)y2$Hj%H]F\"F17$$\"3w++v$f4t.(F-$\"3e(e >z#)*yi8F17$$\"3OPL$e*Gst!)F-$\"3tzAb]M\\S9F17$$\"3\"*om\"H2\"34')F-$ \"33iAhBP7p9F17$$\"3Y+++]#RW9*F-$\"3wt@*Qy.&)[\"F17$$\"3s+]i:5J1%*F-$ \"3sv67u!GX\\\"F17$$\"3'4+]7y#=o'*F-$\"3].cp)=9$)\\\"F17$$\"3A,](oaa+$ **F-$\"3yRBbwi#**\\\"F17$$\"3:++DJE>>5F1$\"3uw!oCwa%*\\\"F17$$\"3A+v$4 ^n)p5F1$\"3KQt#\\#[0$\\\"F17$$\"3F+]i!RU07\"F1$\"3?@lH>&R-[\"F17$$\"39 +vo/#3o<\"F1$\"3%[!y**3(z(f9F17$$\"3+++v=S2L7F1$\"3pK?%GciTV\"F17$$\"3 Jmmm\"p)=M8F1$\"35T\")e?]Kz8F17$$\"3B++](=]@W\"F1$\"3a6*\\,!Q=98F17$$ \"35L$e*[$z*R:F1$\"3O1=c[Ni`7F17$$\"3e++]iC$pk\"F1$\"3!*Hu@$RE()=\"F17 $$\"3[m;H2qcZ1YI6F17$$\"3O+]7.\"fF&=F1$\"3okr%GZaK2\"F17$ $\"3Ymm;/Ogb>F1$\"3/=wG$H\\7-\"F17$$\"3w**\\ilAFj?F1$\"3X\"=!o:lP4(*F- 7$$\"3yLLL$)*pp;#F1$\"3ct_/x_!HE*F-7$$\"3)RL$3xe,tAF1$\"3Lu.kgSDU))F-7 $$\"3Cn;HdO=yBF1$\"3O.\\hbg)zX)F-7$$\"3a+++D>#[Z#F1$\"3Z!)HH" } {TEXT -1 1 " " }{TEXT 341 1 " " }{TEXT 342 39 "plot( f(t), t = a .. b, color = coral);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "or" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 347 1 "[" }{TEXT 348 1 ">" } {TEXT -1 1 " " }{TEXT 345 1 " " }{TEXT 346 39 "plot( f(t), t = a .. b, color = CORAL);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 " (In general, " }{TEXT 349 5 "MAPLE" }{TEXT -1 131 " is case sensitive. To avoid breaking leg acy code, a few specific strings may be entered in either lower case or in upper case.) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "You can also mix red, g reen, and blue (RGB) in whatever combination you wish:" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 352 1 "[" }{TEXT 353 1 "> " }{TEXT -1 1 " " }{TEXT 350 1 " " }{TEXT 351 50 "plot( f(t), t = a .. b, color = COLOR(RGB,r,g,b));" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 6 "where " }{TEXT 354 5 "r,g,b" }{TEXT -1 37 " are decimal numbers between 0 and 1." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "plot(sin(Pi*cos(x)), x = 0.. 2*Pi, thickness=2, color = COLOR(RGB,.2,.4,.8), tickmarks=[6,3]);" }} {PARA 13 "" 1 "" {GLPLOT2D 374 374 374 {PLOTDATA 2 "6(-%'CURVESG6#7gs7 $$\"\"!F)$\"3Z_t9*zYYA\"!#L7$$\"3eET6j*))QU$!#>$\"3#=&ephgET=!#?7$$\"3 ;`#Gi#zxZoF0$\"3qJ!>AdVGO(F37$$\"3\"zBM*)omr-\"!#=$\"3]v!QH**pdl\"F07$ $\"3i]cC&eb&p8F<$\"3LcqU4&)GTHF07$$\"3q5)>63x`'>F<$\"3xx>;cQLWgF07$$\" 3YqR*pd)>hDF<$\"3=1:3+#))H-\"F<7$$\"3Zs[E^dK,RF<$\"3Ud7649xQBF<7$$\"3+ 9+\"[&4$ed%F<$\"3%\\#QJom+wJF<7$$\"3ab^NehL]_F<$\"3v%HYR#)[j5%F<7$$\"3 Ls#3kbN;#fF<$\"3Y]Dz%zxv4&F<7$$\"35*QhW&\\$Hf'F<$\"3Jl9hO+^=hF<7$$\"3] :5wGaJ:sF<$\"3IEQ)>%fQ`qF<7$$\"3zS11.fpPyF<$\"34!QeB/&)\\$zF<7$$\"3#e! 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One of these is " }{HYPERLNK 17 "display" 2 " plots[display]" "" }{TEXT -1 58 ", which is used to simultaneously dis play different plots." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "The equation of the tangent to the spiral (defined abo ve) at the point corresponding to " }{XPPEDIT 19 1 "t = 3;" "6#/%\"tG \"\"$" }{TEXT -1 7 " is \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "tangentLineEquation := y = D(g)(3)/D(f)(3)*(x-f(3))+g(3); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%4tangentLineEquationG/%\"yG,&*(,&*&# \"\"\"\"\"$F,-%$sinG6#F-F,F,*&-%#lnGF0F,-%$cosGF0F,F,F,,&*&F+F,F4F,F,* &F2F,F.F,!\"\"F9,&%\"xGF,F1F9F,F,F8F," }}}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "spiralPlot := plot([f(t),g(t), t = 1 .. 16], thickne ss = 2, color = sienna, numpoints = 1000 ): #We name but suppress the \+ plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "tangentLinePlot := plot( rhs(tangentLineEquation), x=-2.8..2.8, color=COLOR(RGB,.7,.7,.7 )): #We name but suppress the plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "plots[display](spiralPlot,tangentLinePlot, view=[-2.8 ..2.8,-2.5..3.2]);" }}{PARA 13 "" 1 "" {GLPLOT2D 374 374 374 {PLOTDATA 2 "6&-%'CURVESG6%7din7$$\"\"!F)F(7$$\"3mk*p&Q&)*[@)!#?$\"3&) [\\!oi9ZK\"!#>7$$\"3!>*pVqV@#\\\"F0$\"3?e$f7x09[#F07$$\"3y&=>/l#=)>#F0 $\"3!egqY&)Rfy$F07$$\"3Y+xTlw\"y&GF0$\"3m$ePH5[A5&F07$$\"3uuk*\\.tTY$F 0$\"3#)4\"=!*p_XT'F07$$\"3'=K!fxmA#)RF0$\"3bLSsfQ\\KwF07$$\"3qJgq)[uWZ %F0$\"3ovM0Ld:%*))F07$$\"30)>:*oJ)o$\\F0$\"3\\w9d%>z)>5!#=7$$\"3%[pFPv \"=^`F0$\"3KlOF=!G)\\6FT7$$\"3O=vN&R-%HdF0$\"3UW\"\\vd8LG\"FT7$$\"3^b: gfDyAgF0$\"3^\\L=*3o1S\"FT7$$\"3[Z*)>f>24jF0$\"3PR``'ohC`\"FT7$$\"3YId &\\6g-b'F0$\"3[g\"4$>$yVm\"FT7$$\"3&4#[['[$RRnF0$\"3I'))e$fO.\"z\"FT7$ $\"3IGP6:\")zuoF0$\"3I[eJp')e0>FT7$$\"3m^'p'prO\"*pF0$\"3h\"4h)y8;T?FT 7$$\"3='3l?lEG0(F0$\"3;,L2n6Sb@FT7$$\"3e46s$3p=3(F0$\"35a`T'*[^(G#FT7$ $\"3w`O.(*e)*pqF0$\"3aS9?N=q.CFT7$$\"3U5)p]W'*o,(F0$\"3Ln5miCHIDFT7$$ \"3-;[5+,#z#pF0$\"3u4#e$GE\"*\\EFT7$$\"3!o&='**Q\"p&z'F0$\"3YZh%)=eptF FT7$$\"3a))fs^cKRmF0$\"3Y;\"*yQ_Q')GFT7$$\"3+^RU)*4qLkF0$\"3xt?mG-#o+$ FT7$$\"3%ojW\"\\F4!='F0$\"3w-s;:\\iIJFT7$$\"3Xs$oN1:m#fF0$\"3TkhTZ'psB $FT7$$\"3\\?06\"3k\">cF0$\"39\"G*=PU@^LFT7$$\"3AD!pU6\\`E&F0$\"3k.&>;T CvY$FT7$$\"3_d2q'G\"=%)[F0$\"3SI7Mz(p)zNFT7$$\"3;Iulh*HH[%F0$\"3m-Jlt% ero$FT7$$\"3\"ylRc8L1+%F0$\"3f-5(Ho&f/QFT7$$\"3&z3%RU$4[`$F0$\"3Ne0o? 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