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0 } {PSTYLE "" 17 267 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 266 "" 0 "" {TEXT 256 29 "A Quick Introduction to Maple" }{TEXT 257 2 "\n\n" }{TEXT 258 12 "Tim McLarnan" }{TEXT 259 2 "\n\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 260 1 "\n" }{TEXT 261 13 "Introduction\n" }}{PARA 256 "" 0 "" {TEXT 262 606 "Maple is a tool for doing nearly anything you think of as computa tional in mathematics, as well as many things you may be surprised to \+ find a machine doing. Examples include:\n\n* Anything you can do with a calculator.\n* Exact computations with fractions.\n* Adding, multip lying, and factoring polynomials.\n* Solving equations, either exactly or approximately.\n* Simplifying algebraic expressions.\n* Plotting f unctions.\n\nThis leaflet is a quick introduction to some of the salie nt things Maple can do. The idea has been to use the most common Mapl e functions in order to give you examples of their syntax.\n\n" } {TEXT 263 20 "Four Essential Facts" }{TEXT 264 1 "\n" }}{PARA 256 "" 0 "" {TEXT 265 311 "(1) The Maple prompt is the symbol >.\n(2) Maple c ommands always end with a semicolon ;\n(3) Maple commands are always f ollowed by ENTER. If you want to type a command with more than one lin e, use SHIFT-ENTER to go down a line without executing a command.\n(4) Maple is case sensitive. Pi is not the same as pi.\n\n" }{TEXT 266 14 "Basic Commands" }{TEXT 267 1 "\n" }}{PARA 256 "" 0 "" {TEXT 268 1 "+" }{TEXT 269 3 ", -" }{TEXT 270 0 "" }{TEXT 271 2 ", " }{TEXT 272 1 "*" }{TEXT 273 6 ", and " }{TEXT 274 1 "/" }{TEXT 275 20 " do what you expect:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+5;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "1 23456789 * 987654321;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"3p_j76jK>7 " }}}{EXCHG {PARA 256 "" 0 "" {TEXT 276 79 "Unlike most calculators, h owever, Maple does operations with fractions exactly:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6##\"$B#\"$S\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 277 32 "Other arithmetic operations are\n" }{TEXT 278 3 "a^b" }{TEXT 279 32 ", which means a to the power b,\n" }{TEXT 280 2 "n!" }{TEXT 281 39 ", which means n factorial (1*2*3*4**n)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "2^1000;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"i]lw$p!oc?PoQCElJ)H/mn@a'oxk>rX\"H1xg%Ral\"fvw)Rn7%>e $)\\ZYI:#=az(=9rB10Y2@a)4BC[xnX$R![d)puvd%)fVSJ#p&GXr=Do9`v\"Hn%fF\"ee p:)y$)>$\\Ah$\\7^5Nq$)Q]PW2O`0<\"[Sh0\"=+g!\\]U[4Kni=2'3:2\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "(355/113)^10;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6##\";Dc^.6(3$G!y[*yJ\"6\\[JAA**QnXR$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "4!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "125!;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"]x+++++++++++++++!)3xJr+lbPEV_bqaevX$))=yf !QT$>>;I1ud+$fW0kkLJ#f\\*)G$H)o'))f8;LcJN3:B)f()eU#\\r[OS&fd3g\"\\-xwV (*4E*))o " 0 "" {MPLTEXT 1 0 14 "ifactor (315);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*() -%!G6#\"\"$\"\"#\"\"\"-F&6#\"\"&F*-F&6#\"\"(F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "20!-12!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"4 +%Qwp2?!HV#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 287 291 "The most recen t result (2432902007697638400) can be easily included in any subsequen t calculation without having to type it. The percent character (%) i s used to refer to the last expression computed by Maple. Similarly, \+ %% is the expression before %, and %%% is the expression before %%." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "if actor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*.)-%!G6#\"\"#\"#5\"\"\") -F&6#\"\"$\"\"&F*)-F&6#F/F(F*-F&6#\"\"(F*)-F&6#\"#6F.F*-F&6#\")>h(>%F* " }}}{EXCHG {PARA 256 "" 0 "" {TEXT 288 92 "(How long would that have \+ taken by hand?) This result can be checked by multiplying it out:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"4+%Qwp2?!HV#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 289 22 "Decimal Approximations" }{TEXT 290 1 "\n" }}{PARA 256 "" 0 "" {TEXT 291 94 "Maple's normal mode of computation is exact arithmetic, \+ with no roundoff or truncation errors." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "(2^30/3^20)*sqrt(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-% %sqrtG6#\"\"#\"\"\"#\"+C=ut5\"+,Wy'[$" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 292 13 "The function " }{TEXT 293 7 "evalf()" }{TEXT 294 58 " gi ves a numerical approximation to this exact expression:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+%=;]N%!#5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 295 33 "If 10 digits a ren't enough, give " }{TEXT 296 5 "evalf" }{TEXT 297 65 " an optional \+ second argument to tell it how many digits you need:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(%%, 60);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"gn(R,F-S^n7W!>9)\\t!)**pM+yEa(p(\\=;]N%!#g" }}}{EXCHG {PARA 256 " " 0 "" {TEXT 298 11 "Maple uses " }{TEXT 299 2 "Pi" }{TEXT 300 23 ", n ot pi, to represent " }{XPPEDIT 19 1 "Pi;" "6#%#PiG" }{TEXT 470 118 ". Notice what this means: variable names in Maple are case-sensitive. \nWould you like to know the first few digits of " }{XPPEDIT 18 0 "Pi; " "6#%#PiG" }{TEXT 473 1 "?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval f(Pi, 80);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#$\"[p!4iG1k\"yI#fW\\(4#e 5v$*Rpr>%)G]zKQVEYQKz*e`EfTJ!#z" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 301 1 "\n" }{TEXT 438 1 "V" }{TEXT 302 19 "ariable Expressions" } {TEXT 303 1 "\n" }}{PARA 256 "" 0 "" {TEXT 304 32 "Maple also works wi th variables." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(x+7) * (x^2+1) * \+ (x-2)^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"\"\"(F&F&,& *$)F%\"\"#F&F&F&F&F&),&F%F&F+!\"\"\"\"&F&" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*$) %\"xG\"\")\"\"\"F(*&\"\"$F()F&\"\"(F(!\"\"*&\"#HF()F&\"\"'F(F-*&\"$(>F ()F&\"\"&F(F(*&\"$5&F()F&\"\"%F(F-*&\"$G(F()F&F*F(F(*&\"$/(F()F&\"\"#F (F-*&\"$G&F(F&F(F(\"$C#F-" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 305 135 " At this point, Maple has forgotten where it got this polynomial. It' s just a random polynomial of degree 8. But Maple can factor it:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"\"\"(F&F&,&*$)F%\"\"#F&F&F&F&F&),&F%F&F+ !\"\"\"\"&F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 306 187 "Could you hav e factored this polynomial as fast as Maple did? Could you have facto red it at all?\n(If you think about it a bit, your answers to these qu estions should be \"no\" and \"yes.\")\n" }}{PARA 256 "" 0 "" {TEXT 307 29 "Assignment and Simplification" }{TEXT 308 1 "\n" }}{PARA 256 " " 0 "" {TEXT 309 97 "Often we need to assign a name to the result of a computation. Maple does this using the syntax\n" }{TEXT 310 8 "varia ble" }{TEXT 311 1 " " }{TEXT 312 2 ":=" }{TEXT 313 1 " " }{TEXT 314 5 "value" }{TEXT 315 73 ";\nIn making an assignment, Maple does some obv ious simplifications first." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "e1 : = (x+y)^3*(x+y)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G*$),&%\"xG \"\"\"%\"yGF)\"\"&F)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 316 37 "Maple \+ has a built in function called " }{TEXT 317 8 "simplify" }{TEXT 318 139 ", which tries to simplify expressions. It does not always find t he simplest form of an expression, but it is a start. Here is an exam ple:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "e2 := (x^3-y^3)/(x^2+x-y-y^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G*&,&*$)%\"xG\"\"$\"\"\"F+ *$)%\"yGF*F+!\"\"F+,**$)F)\"\"#F+F+F)F+F.F/*$)F.F3F+F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(e2);" }{TEXT -1 0 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*&%\"yGF) F'F)F)*$)F+F(F)F)F),(F'F)F)F)F+F)!\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 319 57 "To understand what went on here, we can use the commands " }{TEXT 320 5 "numer" }{TEXT 321 5 " and " }{TEXT 322 5 "denom" } {TEXT 323 69 " (to take the numerator and denominator of a fraction) t ogether with " }{TEXT 324 6 "factor" }{TEXT 325 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(numer(e2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yG!\"\"F&,(*$)F%\"\"#F&F&*&F'F&F%F&F&*$)F'F,F& F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(denom(e2)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(%\"xG\"\"\"F&F&%\"yGF&F&,&F%F& F'!\"\"F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 326 8 "So what " }{TEXT 327 8 "simplify" }{TEXT 328 94 " did was to find and remove the common factor of (xy). In this particular case, the commands " }{TEXT 329 6 "factor" }{TEXT 330 5 " and " }{TEXT 331 8 "simplify" }{TEXT 332 19 " do the same thing:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(e2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*&%\"yGF) F'F)F)*$)F+F(F)F)F),(F'F)F)F)F+F)!\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 333 17 "Solving Equations" }{TEXT 334 1 "\n" }}{PARA 256 "" 0 " " {TEXT 335 176 "Maple can also solve equations, even symbolic ones. \+ Notice the syntax of the commands below. You have to specify first th e equation, then the variables you want to solve for." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(x^2+5*x+2 = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&#!\"&\"\"#\"\"\"*&#F'F&F'-%%sqrtG6#\"# \+ " 0 "" {MPLTEXT 1 0 25 "fsolve(x^2+5*x+2 = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!+8GbhX!\"*$!+s=Z%Q%!#5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 341 5 "solve" }{TEXT 342 5 " and " }{TEXT 343 6 "fsolve" }{TEXT 344 114 " can also deal with systems of more than one equation. You n eed to give them a set of equations (in set brackets " }{TEXT 345 3 " \{ \}" }{TEXT 346 66 ") followed by a set of variables to solve for. \+ Here's an example:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{x+y=5 , x-y=2\}, \{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG#\"\"$ \"\"#/%\"xG#\"\"(F(" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 347 92 "Now let 's get more adventuresome and try to solve an equation containing symb olic constants:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(a*x^2+b*x+ c=0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&%\"aG!\"\",&%\"bGF&*$- %%sqrtG6#,&*$)F(\"\"#\"\"\"F1*(\"\"%F1F%F1%\"cGF1F&F1F1F1#F1F0,$*&F%F& ,&F(F&F)F&F1F5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 348 58 "Do you recog nize this answer? It's the quadratic formula!" }}{PARA 256 "" 0 "" {TEXT 439 139 "\nDid you know that there was a similar formula for sol ving cubic equations? It's a bit more complicated: its output will f ill the screen." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve(a*x^3 + b* x^2 + c*x + d = 0, x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%,(*&%\"aG!\" \",**(%\"cG\"\"\"%\"bGF*F%F*\"#O*(\"$3\"F*%\"dGF*)F%\"\"#F*F&*&\"\")F* )F+\"\"$F*F&**\"#7F*-%%sqrtG6#F5F*-F96#,,*&)F)F5F*F%F*\"\"%*&)F)F1F*)F +F1F*F&*,\"#=F*F)F*F+F*F%F*F/F*F&*(\"#FF*)F/F1F*F0F*F**(F@F*F/F*F4F*F* F*F%F*F*#F*F5#F*\"\"'*&#F1F5F**(,&*&F)F*F%F*F5*$FCF*F&F*F%F&F'#F&F5F*F &*&#F*F5F**&F+F*F%F&F*F&,*F$#F&F7**FJF*FPF*F%F&F'FSF**&#F*F5F*FVF*F&*( ^##F*F1F*F8F*,&F$FK**#F1F5F*FPF*F%F&F'FSF*F*F*,*F$FX**FJF*FPF*F%F&F'FS F**&#F*F5F*FVF*F&*(^##F&F1F*F8F*FinF*F*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 349 184 "\nLook at this answer a bit until you undertand the not ation. There are three roots, which are written separated by commas. \+ The second and third roots also involve the square root of " } {XPPEDIT 18 0 "-1;" "6#,$\"\"\"!\"\"" }{TEXT 471 24 ", which Maple wri tes as " }{TEXT 440 1 "I" }{TEXT 441 3 ".\n\n" }{TEXT 350 14 "Warning \+ again:" }{TEXT 351 1 " " }{TEXT 459 1 "I" }{TEXT 460 8 " isn't " } {TEXT 461 1 "i" }{TEXT 462 93 ". Case matters to Maple.\nMaple can al so solve the general fourth degree equation (add in an " }{XPPEDIT 454 0 "x^4" "6#*$%\"xG\"\"%" }{TEXT 453 69 " term), though the output \+ now fills several screens. Can it do more?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f = 0, x) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#,.*&%\"aG\"\"\")%#_ZG \"\"&F)F)*&%\"bGF))F+\"\"%F)F)*&%\"cGF))F+\"\"$F)F)*&%\"dGF))F+\"\"#F) F)*&%\"eGF)F+F)F)%\"fGF)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 352 371 " \nWhy can't Maple solve this equation? Because Evariste Galois proved shortly before his death at the age of 20 that there is not general f ormula like the quadratic formula which solves polynomial equations of degree 5 and higher. (That is, there is no formula solving all such equations. For particular values of the coefficients, there are ofte n simple solutions.)\n\n" }{TEXT 353 6 "fsolve" }{TEXT 354 79 " still \+ works to find approximate solutions to equations of high degree, thoug h:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fsolve(x^5+x+1=0, x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!+imx[v!#5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 355 15 "Plotting Graphs" } {TEXT 356 1 "\n" }}{PARA 256 "" 0 "" {TEXT 442 169 "Maple only found o ne solution to the last equation. How can we convince ourselves there is only one? One way to begin to build evidence might be to graph th e function." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot( x^5+x+1, x=-2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 210 152 152 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"#\"\"!$!#LF*7$$!3MLLL$Q6G\">!#<$!3$ >>l#!#;7$$!3bmm;M!\\p$=F0$!30>:qW\"G`<#F37$$!3MLLL))Qj^&oIj!\\8F37$$!3wmm;C2G!e\"F0$!3H/+Jp 6cV5F37$$!3OLL$3yO5]\"F0$!3&\\9D\"*fm57)F07$$!3&*****\\nU)*=9F0$!3X&Gg U`)*=<'F07$$!3SLL$3WDTL\"F0$!3Z'GcgM\\1c%F07$$!35++]d(Q&\\7F0$!3!yaC?K qcH$F07$$!3hmmmc4`i6F0$!3z6IUog)eG#F07$$!3KLLLQW*e3\"F0$!3q&[Q7=fdf\"F 07$$!3w++++()>'***!#=$!3d1**QWm?x**Fco7$$!3E++++0\"*H\"*Fco$!3#GEsB\"R YtaFco7$$!35++++83&H)Fco$!3q63A1TYAAFco7$$!3\\LLL3k(p`(Fco$\"3<.*Rhj+, V$Fco7$$!3+,++v#\\N)\\Fco$\"37(Q&Qfy04ZFco7$$!3commmCC(>%Fco$\"3zJ3hoZ \\scFco7$$!39*****\\FRXL$Fco$\"3I:'**o'RBCmFco7$$!3t*****\\#=/8DFco$\" 3Z>8Jb^$pZ(Fco7$$!3=mmm;a*el\"Fco$\"3.QE=(ffGM)Fco7$$!3jomm;Wn(o)!#>$ \"3xVrIoI=J\"*Fco7$$!3IqLLL$eV(>Fep$\"3amjm;kD!)**Fco7$$\"3)Qjmm\"f`@' )F\\s$\"3w#>ME7?i3\"F07$$\"3%z****\\nZ)H;Fco$\"3+'3jtx*4j6F07$$\"3ckmm ;$y*eCFco$\"3t>;CgozY7F07$$\"3f)******R^bJ$Fco$\"3:bn=m$el\"F07$$\"3_ILLL&4Nn'Fco$\"3e:=kBar *z\"F07$$\"3A*******\\,s`(Fco$\"3_:a$o!*op*>F07$$\"3%[mm;zM)>$)Fco$\"3 buD-AnhIAF07$$\"3L*******pfa<*Fco$\"3\"f*=%Q,%)yc#F07$$\"38HLLeg`!)**F co$\"3%p2OeWf$))HF07$$\"3w****\\#G2A3\"F0$\"3aAmgwU7F37$$\"3H LLLGUYo;F0$\"3#*R=6mY!)f:F37$$\"3_mmm1^rZF37$$\"34++] sI@K=F0$\"3w$oh'>..[BF37$$\"34++]2%)38>F0$\"3IK@6rc(Q&GF37$$\"\"#F*$\" #NF*-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fc[l-%+AXESLABELSG6$Q\"x6\"Q!Fh[l -%%VIEWG6$;F(Fhz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 357 66 "Thi s at least suggests there is only one root between x=2 and x=2." }} {PARA 256 "" 0 "" {TEXT 358 50 "Maple sometimes makes an unhelpful cho ice of axes:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(x^3 - 1/x^2, x =-2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 206 137 137 {PLOTDATA 2 "6%-%'C URVESG6$7co7$$!\"#\"\"!$!3+++++++]#)!#<7$$!3MLLL$Q6G\">F-$!35Nn#*[]*>F (F-7$$!3bmm;M!\\p$=F-$!3=P:7()y\"\\\\'F-7$$!3MLLL))Qj^'***!#=$!3+\"zdrt?'**>F-7$$!3E++++0\"*H\"*Fbo$!3B!ekBP52'>F-7$$!3 5++++83&H)Fbo$!3!)*[r9a#3C?F-7$$!3\\LLL3k(p`(Fbo$!3!))=&)HfA&)=#F-7$$! 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[s&F-7$$\"3'o****\\7RV'\\Fbo$!3$4jFv?H`$RF-7$$\"3X'*****\\@fkeFbo$!3)p ;FsgFeq#F-7$$\"3_ILLL&4Nn'Fbo$!3S'fk9by\"[>F-7$$\"3A*******\\,s`(Fbo$! 3W^IACz3K8F-7$$\"3%[mm;zM)>$)Fbo$!3Pd(*f^R!yo)Fbo7$$\"3L*******pfa<*Fb o$!3Wja?@WH`TFbo7$$\"38HLLeg`!)**Fbo$!3,eCNux+K(*Ffu7$$\"3w****\\#G2A3 \"F-$\"3DV0)y3kg8%Fbo7$$\"3;LLL$)G[k6F-$\"3n)>!y\")[5;%)Fbo7$$\"3#)*** *\\7yh]7F-$\"33[5'*)famJ\"F-7$$\"3xmmm')fdL8F-$\"3T\"G\"*)R%p$4=F-7$$ \"3bmmm,FT=9F-$\"34_Z^6HlcBF-7$$\"3FLL$e#pa-:F-$\"3.r7@m>G\\HF-7$$\"3* )******Rv&)z:F-$\"3uT3p3hfUNF-7$$\"3HLLLGUYo;F-$\"3p4gFk2S&G%F-7$$\"3_ mmm1^rZF-$\"3Ve^Xu^\\GnF-7$$\"\"#F*$\"3+++++++]xF--%'COLOURG6&%$RGBG$\" #5!\"\"$F*F*Fgbl-%+AXESLABELSG6$Q\"x6\"Q\"yF\\cl-%%VIEWG6$;F(F\\bl;$!# 5F*$FeblF*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "C urve 1" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 360 31 "There are many opti ons for the " }{TEXT 361 4 "plot" }{TEXT 362 53 " command, and many ot her types of plots.\n(Try typing " }{TEXT 363 15 "?plot[options];" } {TEXT 364 4 " or " }{TEXT 365 7 "?plots;" }{TEXT 366 28 " to learn mor e about these.)" }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 443 73 "Here is an example of a plot of several functions at once, and a 3D plot. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot(\{x, x^2, x^3, x^4, x^5\}, x=-1.1 .. 1.1);" }}{PARA 13 "" 1 "" {GLPLOT2D 315 277 277 {PLOTDATA 2 "6)-%'CURVESG6$7S7$$!33+++++++6!#K 55F*F/7$$!36ML$eQ')Rj*!#=F27$$!3aML$3qU;;*F4F67$$!3Snm\"H)Ra\"p)F4F97$ $!3gLLe%H-dD)F4F<7$$!3=++DrMT/yF4F?7$$!3!QL$eC**oPtF4FB7$$!3?++DmJYsoF 4FE7$$!3%omm;E?RR'F4FH7$$!3%RLL3T>C(fF4FK7$$!3'******\\G4z\\&F4FN7$$!3 P+++v2X@]F4FQ7$$!3R+++:ZHiXF4FT7$$!3JMLeCqLXTF4FW7$$!3kmmm,S`\\OF4FZ7$ $!3]mmm1Q_HKF4Fgn7$$!3V++D,@&4u#F4Fjn7$$!3PnmmcL[3BF4F]o7$$!3v***\\7g' *R$=F4F`o7$$!33***\\P+t@Q\"F4Fco7$$!3'Gmm;zCu5*!#>Ffo7$$!3_lm;H4AyZFho Fjo7$$!33)RLL3(*e3\"!#?F]p7$$\"3_dm;aZ%=u%FhoFap7$$\"3A/+]7A;k*)FhoFdp 7$$\"3Rmm;u!QCN\"F4Fgp7$$\"37+++qKbB=F4Fjp7$$\"3]****\\xvW%G#F4F]q7$$ \"3%4+](=lQIFF4F`q7$$\"3$*)***\\#oDbA$F4Fcq7$$\"3NJLLV-VqOF4Ffq7$$\"3C +++D3YXTF4Fiq7$$\"3+nmTN\"4fd%F4F\\r7$$\"3&=++]$G]Y]F4F_r7$$\"3CJL3K[H *[&F4Fbr7$$\"3K,+v`+9_fF4Fer7$$\"3SKLLeel/kF4Fhr7$$\"3`)**\\(ozRyoF4F[ 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command, clicked on the picture, and then played with the choices \+ on the Tool Bar until I got the view I wanted. One can also view this 3-dimensional surface as a contour plot. You can make contour plots \+ from 3D plots using the Tool Bar.\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 256 "" 0 "" {TEXT 368 5 "Help!" }{TEXT 369 1 "\n" }}{PARA 256 " " 0 "" {TEXT 370 163 "In order to use Maple effectively, you'll need t o know where to get help. An excellent and convenient source is Maple 's online help, which is available under the " }{TEXT 468 4 "Help" } {TEXT 469 80 " menu item. You can also access help directly from the \+ Maple prompt, like this:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?coeffs; " }}}{EXCHG {PARA 256 "" 0 "" {TEXT 371 292 "The output appears in ano ther window, but here it is. It includes a calling sequence, usually s ome obtuse discussion. Most usefully, it ends with examples and with \+ suggestions of other related functions to look at. All functions and \+ libraries which Maple knows about have online help items." }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 10 "Function: " }{TEXT -1 62 "coeffs - extrac t all coefficients of a multivariate polynomial" }}{PARA 0 "" 0 "usage " {TEXT 26 17 "Calling Sequence:" }{TEXT -1 22 "\n coeffs(p, x, 't') ;" }}{PARA 0 "" 0 "" {TEXT 26 11 "Parameters:" }{TEXT -1 4 "\n " } {TEXT 23 4 "p - " }{TEXT -1 27 "multivariate polynomial\n " }{TEXT 23 4 "x - " }{TEXT -1 58 "(optional) indeterminate or list/set of inde terminates\n " }{TEXT 23 4 "t - " }{TEXT -1 15 "(optional) name" }}} {SECT 0 {PARA 0 "" 0 "synopsis" {TEXT 26 12 "Description:" }}{PARA 15 "" 0 "" {TEXT -1 135 "The coeffs function returns an expression sequen ce of all the coefficients of the polynomial p with respect to the ind eterminate(s) x. " }}{PARA 15 "" 0 "" {TEXT -1 109 "If x is not specif ied, coeffs computes the coefficients with respect to all the indeterm inates of p (see the " }{HYPERLNK 17 "indets" 2 "indets" "" }{TEXT -1 202 " function). If a third argument t is specified (call by name), it is assigned an expression sequence of the terms of p. There is a one- to-one correspondence between the coefficients and the terms of p. " } }{PARA 15 "" 0 "" {TEXT -1 78 "Note that p must be collected with resp ect to the appropriate indeterminates. " }}}{SECT 0 {PARA 0 "" 0 "exam ples" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "s := 3*v^2*y^2+2*v*y^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG, &*&)%\"vG\"\"#\"\"\")%\"yGF)F*\"\"$*(F)F*F(F*)F,F-F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "coeffs( s );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "coeffs( s, v, 't' );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$)%\"yG \"\"#\"\"\"\"\"$,$*$)F&F)F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%\"vG\"\"#\"\"\"F%" }}}} {SECT 0 {PARA 0 "" 0 "seealso" {TEXT 26 10 "See Also: " }{HYPERLNK 17 "collect" 2 "collect" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "coeff" 2 "coe ff" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "tcoeff" 2 "tcoeff" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "lcoeff" 2 "lcoeff" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "indets" 2 "indets" "" }{TEXT -1 2 " " }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 372 87 "Other sour ces located in the Math/CS Lounge on the second floor of Dennis includ e\n\n(1) " }{TEXT 373 21 "Maple V Flight Manual" }{TEXT 374 70 ", whic h covers all the basic commands needed in calculus classes.\n(2) " } {TEXT 375 30 "Maple for the Calculus Student" }{TEXT 376 55 ", a somew hat earlier version of the Flight Manual.\n(3) " }{TEXT 377 12 "First \+ Leaves" }{TEXT 378 53 ", which is a good general tutorial introduction .\n(4) " }{TEXT 379 33 "Maple V Language Reference Manual" }{TEXT 380 44 ", a more formal description of Maple V.\n(5) " }{TEXT 381 32 "Mapl e V Library Reference Manual" }{TEXT 382 105 ", a printed copy of all \+ the online manual pages.\n\nOther students, faculty, etc. are also goo d resources.\n" }}{PARA 256 "" 0 "" {TEXT 383 19 "Substitutions, etc. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 384 182 "H ere are a few more commands which are useful in calculus. We begin by defining an expression, making some substitutions, and computing its \+ derivative directly from the definition:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f := x^2+x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG ,&*$)%\"xG\"\"#\"\"\"F*F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=3, f);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subs (x=x+h, f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$),&%\"xG\"\"\"%\"hG F(\"\"#F(F(F'F(F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expa nd(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"#\"\"\"F(*(F'F (F&F(%\"hGF(F(*$)F*F'F(F(F&F(F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%-f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\" \"%\"hGF&\"\"#*$)F'F(F&F&F'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&%\"xG\"\"\"%\"hGF' \"\"#*$)F(F)F'F'F(F'F'F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"xG\"\"#%\"h G\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "limit(%, h=0 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"#\"\"\"F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 385 18 "Defi ning Functions" }{TEXT 386 1 "\n" }}{PARA 256 "" 0 "" {TEXT 387 52 "An irritating feature of this calculation was using " }{TEXT 388 12 "sub s(x=3, f)" }{TEXT 389 58 " to compute f when x=3. We'd like to be abl e just to say " }{TEXT 390 4 "f(3)" }{TEXT 391 177 ", but we can't, be cause f is just an expression, not a function. So how would we define a function in Maple? There are 2 ways. For simple one-line function s, we can do this:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g := x -> x^ 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG% &arrowGF(*$)9$\"\"#\"\"\"F(F(F(" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 466 43 "This defines g as the function taking x to " }{XPPEDIT 467 0 " x^2;" "6#*$%\"xG\"\"#" }{TEXT 465 49 ". We can now use g just like an y other function:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(x+h);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*$),&%\"xG\"\"\"%\"hGF'\"\"#F'" }}}{EXCHG {PARA 256 " " 0 "" {TEXT 392 91 "More complicated functions are defined in a more \+ complicated way. Begin the function with " }}{PARA 256 "" 0 "" {TEXT 393 5 "proc(" }{TEXT 444 9 "variables" }{TEXT 394 1 ")" }{TEXT 395 18 ", and end it with " }{TEXT 396 9 "end proc;" }{TEXT 397 122 ". Here, \+ for instance, is a function which takes 2 arguments, and returns the l arger of the two, assuming both are numbers:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "h := proc(x,y)\n\011\011if x>y then x\n\011\011else y \n\011\011end if\n\011end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"hGf*6$%\"xG%\"yG6\"F)F)@%29%9$F-F,F)F)F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "h(3, 5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h(5,3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" } {TEXT 398 23 "More Calculus Functions" }{TEXT 399 1 "\n" }}{PARA 256 " " 0 "" {TEXT 400 92 "Maple can directly compute derivatives, sums, int egrals and limits. Here are some examples:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(sin(x^2), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,$*&-%$cosG6#*$)%\"xG\"\"#\"\"\"F,F*F,F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "int(x^2, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* $)%\"xG\"\"$\"\"\"#F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " int(x^2, x=1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sum(k^2, k=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$&Q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sum(1/k^2, k=1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$ )%#PiG\"\"#\"\"\"#F(\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y := limit((x^2-3*x+2)/(x-1), x=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG!\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 401 5 "Oops!" } {TEXT 402 1 "\n" }}{PARA 256 "" 0 "" {TEXT 403 124 "Like any powerful \+ tool, Maple offers any number of ways for you to make mistakes. Here \+ are some particularly popular ones:\n" }}{PARA 256 "" 0 "" {TEXT 404 10 "Mistake 1:" }{TEXT 405 178 " Forgetting you have assigned a value to a variable. Right now, for instance, y has a value: it is -1. I'l l therefore get into loads of trouble if I try to use y as a variable: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(x^2, x=-1..1, y=-1..2);" } }{PARA 8 "" 1 "" {TEXT -1 35 "Error, (in plot) invalid arguments\n" }} }{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 406 97 "To fix this, I \+ need to tell Maple that y is now just the variable y again. I do that by saying " }{TEXT 407 7 "y:='y';" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "y := 'y';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"yGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 445 1 "\n " }{TEXT 446 10 "Mistake 2:" }{TEXT 447 162 " Forgetting a semicolon. \+ If you do this, Maple thinks the expression you want it to evaluate i s not over. It will therefore give you an unhelpful error message:" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "2+6" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, premature end of inpu t\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 448 70 "One possible response i s to type the semicolon and to hit enter again:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "2+6" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 408 10 "Mistake 3:" }{TEXT 409 35 " Or der of operations. Maple does " }{TEXT 410 1 "^" }{TEXT 411 13 " firs t, then " }{TEXT 412 1 "*" }{TEXT 413 5 " and " }{TEXT 414 1 "/" } {TEXT 415 7 ", then " }{TEXT 416 1 "+" }{TEXT 417 5 " and " }{TEXT 418 0 "" }{TEXT 419 26 ". Notice the difference:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x^1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"xG# \"\"\"\"\"#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 420 66 "Since Maple doe s exponentiation before division, it reads this as " }{XPPEDIT 456 0 " x^`1`/2" "6#*&)%\"xG%\"1G\"\"\"\"\"#!\"\"" }{TEXT 455 2 " ." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x^(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#%\"xG\"\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 421 33 "This is the correct way to write " }{XPPEDIT 458 0 "x^`1 /2`" "6#)%\"xG%$1/2G" }{TEXT 457 3 " .\n" }}{PARA 256 "" 0 "" {TEXT 422 10 "Mistake 4:" }{TEXT 423 14 " Leaving out " }{TEXT 424 1 "*" } {TEXT 425 45 " in multiplication. I do this all the time.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x^2+2x;" }}{PARA 8 "" 1 "" {TEXT -1 31 "Er ror, missing operator or `;`\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+bx+c=0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%% sqrtG6#,&%#bxG!\"\"%\"cGF)\"\"\",$F#F)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 426 47 "\nHere we got the wrong answer because we wrote " } {TEXT 427 2 "bx" }{TEXT 428 51 ", which Maple reads as a new variable, rather than " }{TEXT 429 3 "b*x" }{TEXT 430 26 ", which is what we me ant.\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 431 10 "Mistake 5:" }{TEXT 432 82 " Case sensitivity, or forgetting the name of a Maple command. Here are examples:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(pi); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+a EfTJ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lim(sin(x)/x, x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$limG6$*&-%$sinG6#%\"xG\"\"\"F*!\"\"/F*\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(sin(x)/x, x=0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 433 10 "Mistake 6:" }{TEXT 434 107 " Notation for trig functions. This is really just a flaw in normal mathematical notation. When we write " }{XPPEDIT 452 0 "`sin` ^2*x" "6#*&%$sinG\"\"#%\"xG\"\"\"" }{TEXT 449 18 ", what we mean is " }{XPPEDIT 451 0 "[sin(x)]^2" "6#*$7#-%$sinG6#%\"xG\"\"#" }{TEXT 450 125 ". This shorthand is horribly misleading, but it is universal. M aple is only capable of understanding the second expression." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sin^2*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#*&)%$sinG\"\"#\"\"\"%\"xGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(sin^2*1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%$sinG\"\" #\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sin(x)^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*$)-%$sinG6#%\"xG\"\"#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(sin(1)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$=M23(!#5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 435 6 "\nIndex" }{TEXT 436 1 "\n" }}{PARA 256 "" 0 "" {TEXT 437 443 "Is there more to learn about Maple? Yes! Maple is a very broad \+ and powerful system for mathematical computation. It has more than 20 00 built-in functions. The large majority of these have never been us ed by anyone at Earlham. Here is a very quick glossary of the most im portant functions for a calculus student. More information on all the se is available through Maple's online help, or in the written and hum an sources mentioned above:\n" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 3005 "+, -, *, / Add, subtract, multiply, divide.\n^ \+ Raise a number to a power.\n! Factorial.\n-> \+ Used in procedure definitions.\n= Use d in inputting equations.\n:= Used to assign a value t o a variable.\n<, >, <=, >=, <> Mean <, >, , , and , resp.\n%, %%, % %% Previous expressions.\n.. An interval.\n[ ] List. Lists are ordered.\n\{ \} Set. Se ts are unordered.\nabs Computes the absolute value of a number.\ncoeff Get one coefficient of a polynomial.\ncol lect Collect coefficients of like powers.\ncombine \+ Combine terms into a single term.\nconvert Convert from \+ one data type to another.\ncos Cosine. Arguments are in radians.\nD Differential operator.\ndenom \+ Denominator.\ndiff Differentiate.\nE, exp(1) \+ The base for natural logs.\nevalf Evaluate an expression as a decimal approximation.\nexp Exponential function. exp(x) = E^x.\nexpand Expand out an expression.\nfactor \+ Factor a polynomial.\nfor...do...end do Repeat commands. \nfsolve Find approximate solutions to one or more equatio ns.\nhelp Get help on a function.\nif...then...else...en d if Conditionals.\nifactor Factor an integer.\nint \+ Integrate a function.\nInt Write down the in tegral, but don't evaluate. Use with changevar.\nlimit Co mpute limits.\nLimit Write doen but don't evaluate a limi t.\nln, log Compute natural logs. ln(x)=log(x)log10(x).\nm ax Compute the maximum of 2 or more numbers.\nmin \+ Compute the minimum of 2 or more numbers.\nnormal \+ Put a fraction in normal form. A useful special case of simplify.\n numer Numerator.\nop Pick out one part of an expression.\nplot Plot a graph.\nplot3d \+ Plot a 3D graph.\nprint Pretty-print an expression.\nproc Define a procedure.\nproduct Product of fini tely or infinitely many terms.\nquo Quotient of 2 polyn omials.\nrem Remainder of 2 polynomials.\nsimplify \+ Try to simplify an expression.\nsin Sine. The ar guments to trig functions should be in radians.\nsolve So lve 1 or more equations exactly.\nsort Sort a list or th e terms in a polynomial.\nsqrt Square root.\nstudent \+ The student calculus package. Very useful.\nstudent[changevar ] Do a change of variables (integration by substitution).\nsum \+ Sum of finitely or infinitely many terms.\nSum \+ Sum written down, but not worked out.\nTaylor Taylor serie s expansion.\nvalue evaluate a Sum, Limit, or Int.\nwith \+ Load a library package. Example: with(student);" }}}} {MARK "15 0 4" 71 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }