{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 10 255 0 0 1 2 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 2 2 1 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 2 2 1 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 0 1 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Ou tput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier " 1 10 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 3" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 4 " -1 259 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 260 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 2 2 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 256 9 "intro.mws" }{TEXT -1 24 " Introduction to Maple " }}{PARA 0 "" 0 "" {TEXT -1 97 " Revised by Lou Gross from versi ons posted to Web by Matthew Miller at Uuniv. South Carolina" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "OBJECTIVES:" }} {PARA 0 "" 0 "" {TEXT -1 123 "\n - learn basic command structure for \+ Maple including: entering mathematical expressions, plotting, and solv ing equations " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1126 "WHAT IS MAPLE AND HOW CAN IT BE USED? \n\nThe manipulat ion of symbols and expressions that you use to solve equations and inv estigate functions can also be performed by software packages called c omputer algebra systems (CAS). A CAS can be use to produce the exact s ymbolic solutions you obtained by hand, the numerical approximations y ou found using a calculator, and the graphs you have drawn. Maple is o ne of several CASs; other major examples are (all commercially produce d) Mathematica, MATLAB, Macsyma, Derive, and MathCad. There are some \+ free versions of general math software packages available (one is simp ly called R), but none of these have the versatility of commercial pac kages. Maple is generally preferable over MATLAB for symbolic maniputa ions and simple plotting of functions, but MATLAB has advantages for n umerical analysis, particularly using matrixes. Maple can find roots o f equations, optimize functions, estimate derivatives and integrals nu merically, compute derivative and integral formulas, plot and analyze \+ data, and visualize geometric objects and transformations. \n\n\nDOCUM ENTATION and ON-LINE HELP\n" }}{PARA 0 "" 0 "" {TEXT -1 383 " The help pages describe the syntax of each command, a brief description of the algorithm that has been implemented, and a few examples illustrating \+ the use of the command. To obtain help on the command func, type: ?fu nc. The Help Browser, an interactive interface to the entire Maple he lp system, can be brought up by clicking on Help, found at the top rig ht of the Maple window.\n" }}{PARA 0 "" 0 "" {TEXT -1 436 "RUNNING MAP LE\n\nFor our sessions in the computer labs, Maple can be strated by s imply going to the Program Menu (button on the lower left of the scree n) and going to Maple in the Program applications, or by finding where it is installed on the hard drive and clicking on the wmaple icon. It will also start automatically from any \"Maple leaf\" icon, which typ ically stand for files with a .mws extension standing for Maple Worksh eet file." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "GETTING STARTED " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 1039 "After opening Maple, position the cursor arrow on the menu item File and click the left button once. You can select New to \+ obtain a fresh, empty worksheet. Or you can select Open to choose an e xisting worksheet (the name will always end with .mws), either by doub le clicking on the name or by selecting the name and then Load. Once i n a worksheet the current location is marked by a vertical bar. You ca n move around by moving the mouse and then clicking the left button on ce, by using the arrow keys, or by using the scroll bar up and down ar rows on the right side of this window followed by finer adjustment wit h the mouse. A command is entered and executed by positioning the curs or anywhere on the desired line and pressing Return. Several workshee ts can be open simultaneously, and if you use the Window option to arr ange them side by side, this can be quite useful because you can cut a nd paste between them. They do, however, share the computational engin e, so beware: if x = 3 in one worksheet it will also be 3 in all the o thers!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 " TOOLBAR" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 251 "There is a toolbar at the top of the window with many options to \+ open a new worksheet, open an exosting one, save or print the current \+ worksheet, cut and paste, undo the last operation insert text, insert \+ a new operation point, stop calculation, etc. " }}{PARA 0 "" 0 "" {TEXT -1 102 "\nIt is probably a good idea to begin EVERY worksheet th at you create with the following two commands. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(plots): " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 260 "" 0 "" {TEXT 259 132 "BASIC FACTS\n\nThe basic symbols:\n\n - assignm ents are made with := (plain = has a different meaning) -- think of \+ this as giving the " }{TEXT 257 5 "value" }{TEXT 260 31 " of the right hand side to the " }{TEXT 258 4 "name" }{TEXT 261 881 " that appears \+ on the left hand side\n - every command is terminated by a semi-colon \+ ( ; ) or colon ( : ) -- with the latter the computation is done, but t he result is not displayed\n - the percent symbol ( % ) refers to t he result of the immediately preceding computation (which might not ha ve been the previous line)\n - Maple is case sensitive -- that is, the names x and X are different, pi and Pi are not the same thing\n - \{ \+ \} -- set notation (mostly used in the context of plotting a bunch o f functions simultaneously)\n - .. as in a .. b -- this is how Maple indicates the interval [a, b], that is, the real numbers from a to b \n - ? or help -- a request to Maple for information\n\nMathematical f unctions have their standard names, or ones that are easily guessed:\n + (plus) , - (minus) , * (times) , / (divided by) , ^ (raised to the power) , sin, cos, tan, abs, sqrt, ..." }{TEXT -1 1 "\n" }}{PARA 0 " " 0 "" {TEXT -1 375 "In the following lines,commands are exectuted as \+ you press the \"Enter\" key. You can do this consectively, or you can \+ group commands. The brackets to the left of commands are section range s which can be modified to make sections readable and to structure the entire worksheet. To junp to any ommand, use the mouse and click in \+ front of the command line (after the > prompt). " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "N:= 4 * 6 + 12 / 6 - 1 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "power:= ( -3)^3 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "abs( % );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Pi ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "v:= sin( Pi / 4 ) : # Note that lines that end w ith : differ from those with ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sin( -Pi / 2 \+ ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"NG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "3 / ( 5 - sqrt( N ) ) ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&\"\"\"F%,&\"\"&\"\"\"*$-%%sqrtG6#%\"NGF%!\"\"!\" \"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "4! ; " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "50! ;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "Digits:= 70: evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Digits:= 10: e:= exp(1); evalf(e);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f:= 2 * x^2 - 7 * x + 5 ;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve( f = 0 , x ) ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor( f ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve( z = 3 * t + 4 , t );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve( a * x^2 + b * x + c = 0 , x ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve( 25 * e xp( k * 400 ) = 50 , k );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "evalf( % ); # Hint: this is short for \"floating point evaluation. \"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 251 "\nTo produce the input pro mpt > you can use the Insert key on the menu bar, followed by Execut ion Group and either After Cursor or Before Cursor. Alternatively, us e the [> button in the menu bar if you want the cursor after the pre sent location. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 254 "PLOTTING \n\nGraphs of functions are produced by the plot command. In its simpl est form, plot needs to know the function to be plotted and the range \+ of values for the independent variable. Note that a .. b is Maple's wa y of describing the interval [a, b]. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot( 3 * t - 2 , t = -3 .. 6 ) ; # WAIT FOR THE GRAPH TO APP EAR!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot( sin(3*x), x \+ = -2*Pi .. 2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "y:= 3. 5 * exp ( 0.2 * t );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plo t( y, t = 0 .. 10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "We illustrate how to plot data points, and the \+ logarithm function." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "pop:= [ 508 , 711, 912, 1131, 1590, 1811, 2015, 2249, 2509, 3008, 3610, 3967 ];\ny r:= [ 1650, 1750, 1800, 1850, 1900, 1920, 1930, 1940, 1950, 1960, 1970 , 1975 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$popG7.\"$3&\"$6(\"$7* \"%J6\"%!f\"\"%6=\"%:?\"%\\A\"%4D\"%3I\"%5O\"%nR" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yrG7.\"%];\"%]<\"%+=\"%]=\"%+>\"%?>\"%I>\"%S>\"%]>\" %g>\"%q>\"%v>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 259 "The map command is very flexible. It gives you a way \+ to systematically do the same thing to a whole list of numbers. The z ip command joins together two lists in alternation! An alternative i s to use the seq (sequence) command, doing the zipping \"manually\"." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "log10pop:= evalf( map( log10, pop ));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lnpop:= evalf( map( ln, pop) ); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "adjustedyr:= map( n -> n - 1650, yr );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)log10popG7.$\"+7P 'eq#!\"*$\"+,'p=&GF($\"+Q[**fHF($\"+0EY`IF($\"+CrR,KF($\"+]%=zD$F($\"+ ]]F/LF($\"+b%*)>N$F($\"+h1]*R$F($\"+KyFyMF($\"+-s]dNF($\"++AY)f$F(" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%&lnpopG7.$\"+[9[Ii!\"*$\"+ICnmlF($\" +!**Rc\"oF($\"+wu&3.(F($\"+&H*[rtF($\"+eWj,vF($\"+uWP3wF($\"+_4C=xF($ \"+Y&Rw#yF($\"+&oI!4!)F($\"+^IY\">)F($\"+@aw&G)F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+adjustedyrG7.\"\"!\"$+\"\"$]\"\"$+#\"$]#\"$q#\"$!G\" $!H\"$+$\"$5$\"$?$\"$D$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " data:= zip( (a,b) -> [op( [a,b] )] , adjustedyr, pop );" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 66 "log10data:= zip( (a,b) -> [op( [a,b] )] , adj ustedyr, log10pop );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "lndata:= zi p( (a,b) -> [op( [a,b] )] , adjustedyr, lnpop );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dataG7.7$\"\"!\"$3&7$\"$+\"\"$6(7$\"$]\"\"$7*7$\"$+# \"%J67$\"$]#\"%!f\"7$\"$q#\"%6=7$\"$!G\"%:?7$\"$!H\"%\\A7$\"$+$\"%4D7$ \"$5$\"%3I7$\"$?$\"%5O7$\"$D$\"%nR" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%*log10dataG7.7$\"\"!$\"+7P'eq#!\"*7$\"$+\"$\"+,'p=&GF*7$\"$]\"$\"+Q[ **fHF*7$\"$+#$\"+0EY`IF*7$\"$]#$\"+CrR,KF*7$\"$q#$\"+]%=zD$F*7$\"$!G$ \"+]]F/LF*7$\"$!H$\"+b%*)>N$F*7$\"$+$$\"+h1]*R$F*7$\"$5$$\"+KyFyMF*7$ \"$?$$\"+-s]dNF*7$\"$D$$\"++AY)f$F*" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%'lndataG7.7$\"\"!$\"+[9[Ii!\"*7$\"$+\"$\"+ICnmlF*7$\"$]\"$\"+!**Rc \"oF*7$\"$+#$\"+wu&3.(F*7$\"$]#$\"+&H*[rtF*7$\"$q#$\"+eWj,vF*7$\"$!G$ \"+uWP3wF*7$\"$!H$\"+_4C=xF*7$\"$+$$\"+Y&Rw#yF*7$\"$5$$\"+&oI!4!)F*7$ \"$?$$\"+^IY\">)F*7$\"$D$$\"+@aw&G)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "data2:= [ seq( [adjustedyr[k], pop[k]], k = 1 .. 12 ) ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&data2G7.7$\"\"!\"$3&7$\"$+\" \"$6(7$\"$]\"\"$7*7$\"$+#\"%J67$\"$]#\"%!f\"7$\"$q#\"%6=7$\"$!G\"%:?7$ \"$!H\"%\\A7$\"$+$\"%4D7$\"$5$\"%3I7$\"$?$\"%5O7$\"$D$\"%nR" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 277 "F inally we do the actual plotting. There is a large variety of styles t hat you can select, either in the command itself, or after the fact fr om the menu which you can bring up by clicking on the graph region its elf. You can change for example the style = POINT to style = LINE " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot( data , style = POINT , title \+ = `Population vs. time` );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7.7$\"\"!$\"$3&F(7$$\"$+\"F($\"$6(F(7$$\"$] \"F($\"$7*F(7$$\"$+#F($\"%J6F(7$$\"$]#F($\"%!f\"F(7$$\"$q#F($\"%6=F(7$ $\"$!GF($\"%:?F(7$$\"$!HF($\"%\\AF(7$$\"$+$F($\"%4DF(7$$\"$5$F($\"%3IF (7$$\"$?$F($\"%5OF(7$$\"$D$F($\"%nRF(-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(- %&STYLEG6#%&POINTG-%&TITLEG6#%4Population~vs.~timeG-%+AXESLABELSG6$%!G F^p-%%VIEWG6$%(DEFAULTGFbp" 1 5 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "plot( data2, style = LINE, title = `Population vs. time`, thickness = 2, color = g reen );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CU RVESG6#7.7$\"\"!$\"$3&F(7$$\"$+\"F($\"$6(F(7$$\"$]\"F($\"$7*F(7$$\"$+# F($\"%J6F(7$$\"$]#F($\"%!f\"F(7$$\"$q#F($\"%6=F(7$$\"$!GF($\"%:?F(7$$ \"$!HF($\"%\\AF(7$$\"$+$F($\"%4DF(7$$\"$5$F($\"%3IF(7$$\"$?$F($\"%5OF( 7$$\"$D$F($\"%nRF(-%*THICKNESSG6#\"\"#-%'COLOURG6&%$RGBGF($\"*++++\"! \")F(-%&STYLEG6#%%LINEG-%&TITLEG6#%4Population~vs.~timeG-%+AXESLABELSG 6$%!GFbp-%%VIEWG6$%(DEFAULTGFfp" 1 6 0 1 2 2 6 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "pl ot( log10data, style = POINT, title = `Log10 of pop vs. time`); " }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7.7$ \"\"!$\"1+++7P'eq#!#:7$$\"$+\"F($\"1+++,'p=&GF+7$$\"$]\"F($\"1+++Q[**f HF+7$$\"$+#F($\"1+++0EY`IF+7$$\"$]#F($\"1+++CrR,KF+7$$\"$q#F($\"1+++]% =zD$F+7$$\"$!GF($\"1+++]]F/LF+7$$\"$!HF($\"1+++b%*)>N$F+7$$\"$+$F($\"1 +++h1]*R$F+7$$\"$5$F($\"1+++KyFyMF+7$$\"$?$F($\"1+++-s]dNF+7$$\"$D$F($ \"1++++AY)f$F+-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%&STYLEG6#%&POINTG-%&TI TLEG6#%6Log10~of~pop~vs.~timeG-%+AXESLABELSG6$%!GF_p-%%VIEWG6$%(DEFAUL TGFcp" 1 5 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "plot( lndata, style = POINT, title = `Ln of pop vs. time`);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7.7$\"\"!$\"1+++[9[Ii!#:7$$\"$+\"F($\"1+++I CnmlF+7$$\"$]\"F($\"1+++!**Rc\"oF+7$$\"$+#F($\"1+++wu&3.(F+7$$\"$]#F($ \"1+++&H*[rtF+7$$\"$q#F($\"1+++eWj,vF+7$$\"$!GF($\"1+++uWP3wF+7$$\"$!H F($\"1+++_4C=xF+7$$\"$+$F($\"1+++Y&Rw#yF+7$$\"$5$F($\"1,++&oI!4!)F+7$$ \"$?$F($\"1*****40j9>)F+7$$\"$D$F($\"1,++@aw&G)F+-%'COLOURG6&%$RGBG$\" #5!\"\"F(F(-%&STYLEG6#%&POINTG-%&TITLEG6#%3Ln~of~pop~vs.~timeG-%+AXESL ABELSG6$%!GF_p-%%VIEWG6$%(DEFAULTGFcp" 1 5 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 341 "We have two ways to make logarithmic plo ts. We can either take log of the data values, as we did above, or we can use the built-in Maple command. The output is labeled differently , as you will see. To make the comparison easier we will give the plot s names (NOTE: named plot commands must end with a colon!) and displa y them side by side. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Pl otA:=plot(log10data, title=`Log10 of pop vs. time`, thickness=2):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "PlotB:=logplot(data, title=`Logplo t of pop vs. time`, thickness=2):" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#> %&PlotAG-%/INTERFACE_PLOTG6'-%'CURVESG6$7.7$\"\"!$\"1+++7P'eq#!#:7$$\" $+\"F-$\"1+++,'p=&GF07$$\"$]\"F-$\"1+++Q[**fHF07$$\"$+#F-$\"1+++0EY`IF 07$$\"$]#F-$\"1+++CrR,KF07$$\"$q#F-$\"1+++]%=zD$F07$$\"$!GF-$\"1+++]]F /LF07$$\"$!HF-$\"1+++b%*)>N$F07$$\"$+$F-$\"1+++h1]*R$F07$$\"$5$F-$\"1+ ++KyFyMF07$$\"$?$F-$\"1+++-s]dNF07$$\"$D$F-$\"1++++AY)f$F0-%'COLOURG6& %$RGBG$\"#5!\"\"F-F--%*THICKNESSG6#\"\"#-%&TITLEG6#%6Log10~of~pop~vs.~ timeG-%+AXESLABELSG6$%!GFdp-%%VIEWG6$%(DEFAULTGFhp" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Digits:= 4: # Needed to avoid bug in displa y( array ) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "display( array( [Pl otA, PlotB] ) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%(displayG6#-%'ve ctorG6#7$-%/INTERFACE_PLOTG6'-%'CURVESG6$7.7$\"\"!$\"1+++7P'eq#!#:7$$ \"$+\"F2$\"1+++,'p=&GF57$$\"$]\"F2$\"1+++Q[**fHF57$$\"$+#F2$\"1+++0EY` IF57$$\"$]#F2$\"1+++CrR,KF57$$\"$q#F2$\"1+++]%=zD$F57$$\"$!GF2$\"1+++] ]F/LF57$$\"$!HF2$\"1+++b%*)>N$F57$$\"$+$F2$\"1+++h1]*R$F57$$\"$5$F2$\" 1+++KyFyMF57$$\"$?$F2$\"1+++-s]dNF57$$\"$D$F2$\"1++++AY)f$F5-%'COLOURG 6&%$RGBG$\"#5!\"\"F2F2-%*THICKNESSG6#\"\"#-%&TITLEG6#%6Log10~of~pop~vs .~timeG-%+AXESLABELSG6$%!GFip-%%VIEWG6$%(DEFAULTGF]q-%(logplotG6%7.7$F 2\"$3&7$F8\"$6(7$F=\"$7*7$FB\"%J67$FG\"%!f\"7$FL\"%6=7$FQ\"%:?7$FV\"% \\A7$Fen\"%4D7$Fjn\"%3I7$F_o\"%5O7$Fdo\"%nR/%&titleG%8Logplot~of~pop~v s.~timeG/%*thicknessGFap" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Digits:= 10:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Here are a few more functions and their graphs." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f:= sin(x); g:= 2 * x^2 ; \+ p:= f * g ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "h := cos ( (1/4) * x ) ; s:= 0.2 * sin(2*x) + h ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"f G-%$sinG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,$*$)%\"xG\" \"#\"\"\"F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,$*&-%$sinG6#%\"x G\"\"\")F*\"\"#\"\"\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG-%$co sG6#,$%\"xG#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,&-%$ sinG6#,$%\"xG\"\"#$F+!\"\"-%$cosG6#,$F*#\"\"\"\"\"%F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "p:= p; plot( p, x = -3 .. 3); # \+ p:= p; is not necessary but it is a handy way for us to remember what \+ we are plotting here." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,$*&-%$ sinG6#%\"xG\"\"\")F*\"\"#\"\"\"F-" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7^o7$$!\"$\"\"!$!15w2X,;SD!#:7$$!1+ +]P&3Y$HF-$!1nzc\"yi'RNF-7$$!1+++vq@pGF-$!12E3xsOHWF-7$$!1+]78.K7GF-$! 1B8)>L;\\6&F-7$$!1++D^NUbFF-$!16;.A'3#>dF-7$$!1++]K3XFEF-$!1cG3z?6!z'F -7$$!1+++I./jDF-$!10nZmR@%=(F-7$$!1++]F)H')\\#F-$!1S5T/KS'[(F-7$$!1+]( oXDXV#F-$!1h&[Y1G.q(F-7$$!1++D'3@/P#F-$!1r$)H5(pC$yF-7$$!1++]2YqSBF-$! 1LI&4O=u'yF-7$$!1++vG\"))4J#F-$!1h!f@[Yk)yF-7$$!1+++];F\"G#F-$!1p**=B& 3,*yF-7$$!1++Dr^b^AF-$!1?2Q62(*yyF-7$$!1++D'y:+>#F-$!1JapMaM6yF-7$$!1+ +D,kZG@F-$!1&Gai=uzo(F-7$$!1++D\"GK[1#F-$!1)y]Bi^u](F-7$$!1++Dh\")=,?F -$!1Kt;!of!zsF-7$$!1++DO\"3V(=F-$!1KN>'G?\\q'F-7$$!1+++NkzViUC\"F-$!1!)p`$\\jF$HF-7$$!1++Dh kaI6F-$!1P1&*[z^7BF-7$$!1+++]XF`**!#;$!1Ljf(=JAm\"F-7$$!1++++Az2))Fcs$ !18(=]G0m>\"F-7$$!1++]7RKvuFcs$!1%\\$Hum&yf(Fcs7$$!1-+++P'eH'Fcs$!1:p( z&!#B7$$\"1++](QIKH\"Fcs$\"1p(fg^lOJ %Fju7$$\"1****\\7:xWCFcs$\"1K,Qj(4M*GFdu7$$\"1,++vuY)o$Fcs$\"1AzFwJ95) *Fdu7$$\"1)******4FL(\\Fcs$\"1$H4%\\G.gBFcs7$$\"1)****\\d6.B'Fcs$\"1!) Q1qW\"*HXFcs7$$\"1++](o3lW(Fcs$\"1\"F-7$$\"1+++Ik-,5F-$\"1k6^T\"4vo\"F-7$$\"1+++D-eI6F-$\"13n agGp7BF-7$$\"1++v=_(zC\"F-$\"1@*G?]#)R&HF-7$$\"1+++b*=jP\"F-$\"1ahyF)* 348nF-7$$ \"1+++!)RO+?F-$\"1hv/3Z\"eF(F-7$$\"1++D;:*R1#F-$\"1Q*3?w7#F-$\"1&*Rw.q)eo(F-7$$\"1+]i?(>2>#F-$\"1L!\\DHWC\"yF-7$$\"1++v)Q ?QD#F-$\"1l+'*QyK!)yF-7$$\"1+D1p=\"GG#F-$\"1`u*[I(G!*yF-7$$\"1+]P\\L!= J#F-$\"1%Q1!G?8')yF-7$$\"1+voH[zSBF-$\"1SM`DmLnyF-7$$\"1+++5jypBF-$\"1 k?!eT'QLyF-7$$\"1++DE8COCF-$\"1Aq%Gh*o&p(F-7$$\"1++]Ujp-DF-$\"1*fFe*)f *puF-7$$\"1+++gEd@EF-$\"1y`N.$)**HoF-7$$\"1++v3'>$[FF-$\"1&4tN1D!*y&F- 7$$\"1+++5h(*3GF-$\"18fA+\"pE:&F-7$$\"1++D6EjpGF-$\"1MVfZ&eSU%F-7$$\"1 +]i0j\"[$HF-$\"1,V0a7mONF-7$$\"\"$F*$\"15w2X,;SDF--%'COLOURG6&%$RGBG$ \"#5!\"\"F*F*-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(F]`l%(DEFAULTG" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "# For display purposes it is a good idea to \+ put a blank (or comment, as here) command line after a plot command li ne." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 487 "\nPosition the cursor on \+ a point on the graph and click the left button. The numbers that appea r on the upper-left third line of the menu bar are the coordinates of \+ the current location of the cursor. Use this technique to identify the maximum and minimum values of p(x) on the interval [-3, 3], and the x -values at which these are found. By highlighting the graph in this w ay, you can also modify a variety of graph attributes, including the s cale and for 3-d plots the viewing angle. " }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 102 "\nTo plot more than one function in a single window, j ust specify the functions to be plotted as a set." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 59 "h:= h; s:= s; plot( \{ h , s \}, x = - 6* Pi .. 6 * Pi ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "g:= g; p:= p; plot( \{ g , - g , p \} , x= -16 .. 16 );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 195 "The foll owing plotting commands are just for fun. Since we have already assig ned a value to v, if we want to use this letter over again, we have to reset v to be just plain \"v\" and not a number." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "v:= 'v';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "fieldplot( [ v, -sin(w) - 0.1*v], w = -2 .. 8, v = -2 .. 2, grid=[20, 20], arrows=S LIM, color=BLUE);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 483 "H OUSECLEANING\n\nIf you click on a plot a box enclosing the plot will a ppear and the menu bar will change--the keys Style, Axes, and Projecti on are very useful for making after the fact modifications to the appe arance of the plot--try them! Also you can expand or contract the bou nding box by dragging the little blips on the edges. To get rid of th e plot entirely simultaneously hold down the Control (Cntrl) key and t ap Delete (Del); or use the menu bar Edit and Delete Paragraph. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 229 "DERIVATIVES AND INTEGRAL S \n\nMaple can do derivatives and integrals. For this, we first load the student package. Try to predict the effect of each command befor e mashing Return. After the given problems, try some of your own. " } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "f:= 3 * x^ 4 - 2 * x + 5 / x^3 ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff( f , x ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff( Pi * R^2 * H , R );" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "F:= t * sin(t) ;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "deriv_of_F:= diff( F , t ); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "easy_integral:= Int( f \+ , x ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "value( easy_inte gral ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "g:= z^2 * exp(- z^3 ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot( g , z = 0 .. 2 ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "medium_integra l:= Int( g , z = 0 .. 2 ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "value( medium_integral );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf( % ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "hard_ integral:= Int( 1 / ( y * (10 - y )) , y );" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 196 "OOPS! Maple remembered, although I did not, that y al ready has a definite value, and can't be a variable of integration. L et's recall that value, and then reset y before attempting the integra l." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "y:= 'y'; hard_integral:= Int( 1 / ( y * (10 - y )) , y );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "value( ha rd_integral );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "SA VING A WORKSHEET" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 408 "To save it select File in the menu bar, and then either \+ Save (which will destroy the original version of intro.ms) or Save As. .. (which will leave intro.mws untouched, and will request a new name \+ for this modified version). Worksheet names should always end with .mw s; also unless you really need the output it is usually a good idea to remove it before saving -- to do this, select Edit, then Remove Outpu t." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# Have you saved your work? \+ Check out the options under File." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "# quit The only Maple command that doesn't need a \+ semicolon!" }}}}{MARK "39 0 0" 67 }{VIEWOPTS 1 1 0 1 1 1803 }