{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 163 163 163 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "Maple Input" -1 269 "Courier" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 14 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 301 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 302 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 303 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Map le Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 48 "Integrating Maple in Ot her Computer Environments" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 611 "This session examines how to use Maple in conjunc tion with other computer programs. MatLab uses Maple V Release 4 as th e underlying package for its Symbolic package. There is a code generat ion routine that allows the production of Fortran and C code. Maple ca n link to spreadsheet software, such as Excel. There good text feature s such as generating LaTeX output or HTML for webpages. We also includ e features to improve your work on a Maple worksheet. Inside the works heet there are features that allow the production of technical type in the comments and the use of hyperlinks to navigate about the workshee t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 468 "We begin this lecture using the XWin32 program to let the PCs simulate \+ X-Terminals. Logging onto an X-Terminal allows the use of rohan and a \+ UNIX environment. Maple is totally portable between PC and UNIX enviro nments. (There is a Mac version of Maple, but I am not as familiar wit h this environment.) A Maple worksheet is saved with an .mws extension . This file is recognizable independent of the platform, which very us eful for transporting information using Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 257 23 " XWin32 - Maple on rohan" }}{PARA 0 "" 0 "" {TEXT -1 167 "In the introd uction to this webpage there is information on how to set up the progr am XWin32 to let the PC simulate an X-Terminal. Once you have establis hed a link to " }{TEXT 261 5 "rohan" }{TEXT -1 72 ", then you can log \+ on using your regular rohan account. When you have a " }{TEXT 259 14 " command window" }{TEXT -1 14 " or under the " }{TEXT 260 3 "run" } {TEXT -1 31 " option for programs, you type " }{TEXT 258 6 "xmaple" } {TEXT -1 428 ". With minor exceptions (such as the help being on the f ar right), the Maple environment on rohan should appear very much and \+ function similarly to the Maple environment on the PCs. It will most l ikely be slower because of the heavy usage of rohan, but it has more c omputing power for larger problems. You can run Maple at home on rohan without the window environment (unless you have an X-Terminal simulat or) using the command " }{TEXT 262 5 "maple" }{TEXT -1 172 ". This giv es you line action Maple with very poor graphics capabilities, but can prove invaluable in a rush for certain algebraic operations on homewo rks for other classes." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 373 "Today we will simply set up XWin32, log into rohan, and try a few simple Maple commands to see that it behaves the same. \+ You can save your Maple worksheets on either a PC or rohan, then FTP t he Maple files to the other, and they will work. (If you have purchase d the student Maple, then there might be problems because it is the ne wer Maple 7.0.) Maple defaults storage as " }{TEXT 263 4 ".mws" } {TEXT -1 7 " files." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 264 16 "Maple and MatLab" }}{PARA 0 "" 0 "" {TEXT -1 148 "Maple can be used inside MatLab with modified comma nds. There is a package that is supposed to allow MatLab commands to b e issued from within Maple." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Ma ple Inside Matlab" }}{EXCHG {PARA 0 "" 0 "" {TEXT 277 6 "MatLab" } {TEXT -1 7 " has a " }{TEXT 278 16 "Symbolic Toolbox" }{TEXT -1 11 " t hat uses " }{TEXT 279 17 "Maple V Release 4" }{TEXT -1 52 " (which is \+ 3 versions earlier than the most current " }{TEXT 280 9 "Maple 7.0" } {TEXT -1 464 "). MatLab has adapted a collection of the Maple commands to allow the user to perform symbolic calculations in MatLab without \+ exiting the MatLab environment. These commands are in a slightly diffe rent format from Maple though they actually use the Maple environment. We will demonstrate a few of these commands in MatLab, but I do not h ave extensive experience, so suggest that the reader use the MatLab he lp to expand his/her knowledge of the capabilities of the " }{TEXT 281 16 "Symbolic Toolbox" }{TEXT -1 68 ". (Below the MatLab commands a re after the MatLab command prompt >>)" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 59 "In MatLab you declare your symbolic v ariables. For example," }}{PARA 0 "" 0 "" {TEXT -1 32 ">> syms a b x\n Type in a function" }}{PARA 0 "" 0 "" {TEXT -1 26 " >> f = exp(-b*x)*s in(a*x)" }}{PARA 0 "" 0 "" {TEXT -1 41 "This can be differentiated and integrated" }}{PARA 0 "" 0 "" {TEXT -1 13 " >> diff(f,x)" }}{PARA 0 " " 0 "" {TEXT -1 13 " >> int(f,x)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 281 "Matlab can use Maple to sove differentia l equations. The dsolve command is slightly different from Maple, but \+ it does allow easy access to the solution. The D2 gives two derivative s of y, and all expressions must be between single quotes to note a co uple of differences from Maple." }}{PARA 0 "" 0 "" {TEXT -1 61 ">> dso lve('D2y + 4*Dy +5*y = 12*t^2', 'y(0)=1', 'Dy(0)=-2')\n " }}{PARA 0 " " 0 "" {TEXT -1 513 "A more powerful use of Maple in MatLab is to allo w Maple to perform symbolic computations on matrices, then these matri ces could be further analyzed in MatLab. Below we show the generation \+ of a Jacobian Matrix, then find the determinant of this matrix. This e xample is for the tranformation from rectangular to spherical coordina tes. This operation performs differentiation of a column vector with r espect to a row vector. Consider the transformation from Euclidean (x, y, z) to spherical coordinates as given by " }{XPPEDIT 18 0 "rho;" "6 #%$rhoG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT -1 103 ". (We us e the standard transformation in most Calculus books.) We will use the symbols r, t, and p for " }{XPPEDIT 18 0 "rho;" "6#%$rhoG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 6 ", and " } {XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT -1 15 ", respectively." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "To calcu late the Jacobian matrix, J, of this transformation, use the jacobian \+ function. The MatLab commands are" }}{PARA 0 "" 0 "" {TEXT -1 284 ">> \+ syms r t p\n>> x = r*cos(t)*sin(p); y = r*sin(t)*sin(p); z = r*cos(p); \n>> J = jacobian([x; y; z], [r t p])\n \nJ =\n[ cos(t)*sin(p), -r* sin(t)*sin(p), r*cos(t)*cos(p)]\n[ sin(t)*sin(p), r*cos(t)*sin(p) , r*sin(t)*cos(p)]\n[ cos(p), 0, -r*s in(p)]\n " }}{PARA 0 "" 0 "" {TEXT -1 164 "The determinant of the Jaco bian is used for the scaling the area from rectangular spherical coord inates in the integral. This is computed with the following command" } }{PARA 0 "" 0 "" {TEXT -1 9 ">> det(J)" }}{PARA 0 "" 0 "" {TEXT -1 40 "And can be made simple using the command" }}{PARA 0 "" 0 "" {TEXT -1 24 ">> detJ = simple(det(J))" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "As noted above, we suggest that users of MatLab explore the opportunities that the " }{TEXT 282 16 "Symbolic Toolbox " }{TEXT -1 78 " provides them for expanding their use of MatLab. It s hould be noted that the " }{TEXT 283 16 "Symbolic Toolbox" }{TEXT -1 282 " is provided in the Student Version of MatLab automatically, but \+ must be purchased separately with the main product, so may not be avai lable at a particular location that has MatLab. (SDSU has a complete s ite license with all MatLab packages available on all computers with M atLab.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "MatLab Inside Maple" }} {PARA 0 "" 0 "" {TEXT -1 100 "There is a very nice example on the Mapl e Help page showing the mixing of Maple and Matlab commands." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(Matlab):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 265 "This command tells Maple to go out to th e computing environment and search for MatLab and a valid MatLab licen se. When these are confirmed, you can execute MatLab commands inside M aple. The Help example uses the MatLab Signal Processing Fourier Trans form function, " }{TEXT 284 2 "ft" }{TEXT -1 48 ". We will simply down load this example in class." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 " " }{TEXT 265 15 "Maple and Excel" }}{PARA 0 "" 0 "" {TEXT -1 207 "For \+ students who particularly like spreadsheet environments, Maple does ha ve a spreadsheet environment that can be employed and is shown below. \+ Also, there have been links created to allow transfers between " } {TEXT 285 5 "Maple" }{TEXT -1 5 " and " }{TEXT 286 5 "Excel" }{TEXT -1 134 ". To perform these transfers between Maple and Excel and to us e Maple inside of Excel, you have to launch the Excel program and go t o " }{TEXT 287 5 "Tools" }{TEXT -1 8 " on the " }{TEXT 288 8 "Menu Bar " }{TEXT -1 12 ". Under the " }{TEXT 289 7 "Add Ins" }{TEXT -1 16 ", y ou check the " }{TEXT 290 6 "Maple " }{TEXT -1 36 " option. You should see a series of " }{TEXT 291 15 "Red Maple leafs" }{TEXT -1 21 " appe ar on the lower " }{TEXT 292 8 "Menu Bar" }{TEXT -1 16 ". These provid e " }{TEXT 293 4 "Copy" }{TEXT -1 5 " and " }{TEXT 294 5 "Paste" } {TEXT -1 15 " abilities and " }{TEXT 295 4 "Help" }{TEXT -1 13 " infor mation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "We begin with the Maple Spreadsheet showing a few features. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "M aple Spreadsheet" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 95 "Note that Maple cells are referenced with a tilde in fron t of the cell reference name, such as " }{TEXT 296 3 "~C3" }{TEXT -1 25 " gives the entry in cell " }{TEXT 297 2 "C3" }{TEXT -1 45 ". The s preadsheet is invoked with the command" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(Spread);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "CreateSpreadsheet(name); " }}{PARA 0 "" 1 "" {SPREADSHEET {NAME "name" } {ROWHEIGHTS 1 38 2 38 3 38 4 73 5 50 6 50 } {COLWIDTHS 3 200 4 246 } {SSOPTS {CELLOPTS 2 10 4 2 1 255 255 255 }1 }717 352 0 {CELL 1 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "Function" 20 "6#%)F unctionG" }0 }{CELL 1 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "exp(- x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 1 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "Differentiation*of*Product" 20 "6#*(%0Differentiati onG\"\"\"%#ofGF%%(ProductGF%" }0 }{CELL 1 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "Integration*of*Product" 20 "6#*(%,IntegrationG\"\"\"%#o fGF%%(ProductGF%" }0 }{CELL 2 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 } {R5MATHOBJ "x" 20 "6#%\"xG" }0 }{CELL 2 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "exp(-x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 2 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "diff(~A2*~B2,x)" 20 "6#,&-%$e xpG6#,$%\"xG!\"\"\"\"\"*&F(F*F$F*F)" }0 }{CELL 2 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "int(~A2*~B2,x)" 20 "6#,&*&%\"xG\"\"\"-%$expG6#, $F%!\"\"F&F+F'F+" }0 }{CELL 3 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 } {R5MATHOBJ "x^2" 20 "6#*$)%\"xG\"\"#\"\"\"" }0 }{CELL 3 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "exp(-x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 3 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "diff(~A3*~B3,x)" 20 "6#,&*&%\"xG\"\"\"-%$expG6#,$F%!\"\"F&\"\"#*&)F%F,F&F'F&F+" }0 } {CELL 3 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "int(~A3*~B3,x)" 20 "6#,(*&)%\"xG\"\"#\"\"\"-%$expG6#,$F&!\"\"F(F-*(F'F(F&F(F)F(F-*&F'F(F) F(F-" }0 }{CELL 4 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "x^3" 20 " 6#*$)%\"xG\"\"$\"\"\"" }0 }{CELL 4 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 } {R5MATHOBJ "exp(-x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 4 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "diff(~A4*~B4,x)" 20 "6#,&*&)% \"xG\"\"#\"\"\"-%$expG6#,$F&!\"\"F(\"\"$*&)F&F.F(F)F(F-" }0 }{CELL 4 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "int(~A4*~B4,x)" 20 "6#,**&) %\"xG\"\"$\"\"\"-%$expG6#,$F&!\"\"F(F-*(F'F()F&\"\"#F(F)F(F-*(\"\"'F(F &F(F)F(F-*&F2F(F)F(F-" }0 }{CELL 5 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 } {R5MATHOBJ "sin(x)" 20 "6#-%$sinG6#%\"xG" }0 }{CELL 5 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "exp(-x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 5 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "diff(~A5*~B5,x)" 20 "6#,&*&-%$cosG6#%\"xG\"\"\"-%$expG6#,$F(!\"\"F)F)*&-%$sinGF'F)F*F)F ." }0 }{CELL 5 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "int(~A5*~B5, x)" 20 "6#,&*&-%$cosG6#%\"xG\"\"\"-%$expG6#,$F(!\"\"F)#F.\"\"#*&#F)F0F )*&-%$sinGF'F)F*F)F)F." }0 }{CELL 6 1 {CELLOPTS 0 -1 -1 0 0 0 0 0 } {R5MATHOBJ "cos(x)" 20 "6#-%$cosG6#%\"xG" }0 }{CELL 6 2 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "exp(-x)" 20 "6#-%$expG6#,$%\"xG!\"\"" }0 }{CELL 6 3 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "diff(~A6*~B6,x)" 20 "6#,&*&-%$sinG6#%\"xG\"\"\"-%$expG6#,$F(!\"\"F)F.*&-%$cosGF'F)F*F)F ." }0 }{CELL 6 4 {CELLOPTS 0 -1 -1 0 0 0 0 0 }{R5MATHOBJ "int(~A6*~B6, x)" 20 "6#,&*&-%$cosG6#%\"xG\"\"\"-%$expG6#,$F(!\"\"F)#F.\"\"#*(#F)F0F )-%$sinGF'F)F*F)F)" }0 }}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%nameG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 274 "The table above shows how you can nicely create differentiation or integration tables. The Maple Sprea dsheet allows many of the spreadsheet options for easily manipulating \+ of repetitive symbolic computations. The commands entered into the cel ls are standard Maple commands." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {PARA 4 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 " Using Maple Inside Excel" }}{PARA 0 "" 0 "" {TEXT -1 187 "There is an \+ Excel Spreadsheet that is available from the webpage that shows the us e of Maple inside Excel. One first has to Add In Maple 6 from the Exce l Tools Menu. The hyperlink to the " }{URLLINK 17 "Excel Spreadsheet" 4 "http://www-rohan.sdsu.edu/~jmahaffy/courses/f01/math241/lectures/se ssion4/maplexcel.xls" "" }{TEXT -1 18 " is provided here." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Connectin g Maple and Excel" }}{EXCHG {PARA 256 "" 0 "" {TEXT 298 25 "Analyzing \+ Data from Excel" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "There is an " }{URLLINK 17 "Excel Spreadsheet" 4 "http:// www-rohan.sdsu.edu/~jmahaffy/courses/f01/math241/lectures/session4/map lexcel.xls" "" }{TEXT -1 18 " with the data on " }{TEXT 299 19 "Triato ma phyllosoma" }{TEXT -1 179 " from Session 3. An alternate method of \+ processing these data is to copy the data from the Excel spreadsheet, \+ using the special Maple copy button on the toolbar. Maple produces a \+ " }{TEXT 300 6 "Matrix" }{TEXT -1 107 " of these values after pasting \+ into the Maple worksheet as shown below. The data are reprocessed usin g the " }{TEXT 301 3 "seq" }{TEXT -1 51 " command into the form that w e used before for the " }{TEXT 302 15 "leastsquare fit" }{TEXT -1 219 " routine in Maple. Here we fit a cubic polynomial. This equation is c opied and pasted back into the Excel worksheet, where it can be easily graphed. A nice graph of the data and model are shown on the Excel sp readsheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "The special package that is needed for the analysis is added." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(stats): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "After typing a label " }{TEXT 303 5 "A : \+ =" }{TEXT -1 47 " , the data is pasted from the Excel worksheet." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 331 "A := Matrix(1..15,1..2,\{(1 ,1)=1,(1,2)=116.6,(2,1)=2,(2,2)=120.1,(3,1)=3,(3,2)=114.9,(4,1)=4,(4,2 )=129.9,(5,1)=5,(5,2)=116.5,(6,1)=6,(6,2)=107.7,(7,1)=7,(7,2)=99,(8,1) =8,(8,2)=104,(9,1)=9,(9,2)=100.7,(10,1)=10,(10,2)=87.5,(11,1)=11,(11,2 )=82.7,(12,1)=12,(12,2)=53.8,(13,1)=13,(13,2)=54,(14,1)=14,(14,2)=72.4 ,(15,1)=15,(15,2)=81.1\}):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Th e data are processed using the sequence command to prepare for the lea st squares best fit command below." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "td := [seq(A[i,1],i=1..15)]: yd := [seq(A[i,2],i=1..1 5)]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "The mathematical model is inserted for the data analysis." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "model := a*t^3 + b*t^2 + c*t + d;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&modelG,**&%\"aG\"\"\")%\"tG\"\"$F(F(*&%\"bGF()F*\" \"#F(F(*&%\"cGF(F*F(F(%\"dGF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 " Find the least squares best fit of the cubic model to the data." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "eqn := fit[leastsquare[[t,y] , y=model, \{a,b,c,d\}]]([td, yd]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%$eqnG/%\"yG,**$)%\"tG\"\"$\"\"\"$\"+l6:%>\"!#5*&$\"+*>r%\\H!\"*F,)F *\"\"#F,!\"\"*&$\"+2H2p:!\")F,F*F,F,$\"+13'=(**F:F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 126 "The right hand side of the equation above is s eparated off, then copied into the Excel spreadsheet where it is easil y graphed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "rhs(eqn);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"tG\"\"$\"\"\"$\"+l6:%>\"!#5*&$ \"+*>r%\\H!\"*F()F&\"\"#F(!\"\"*&$\"+2H2p:!\")F(F&F(F($\"+13'=(**F6F( " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 266 34 "Maple Generates Fortran and C Code" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 283 "One useful feature in Maple is its abili ty to generate Fortran and C code. This allows a user to use Maple to \+ perform a series of mathematical operations in Maple, then take the fi nal output into Fortran and C code, which can be inserted into a progr am. Below we show this operation." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(LinearAlgebra): with(codegen);" }}{PARA 7 "" 1 " " {TEXT -1 41 "Warning, the name eqn has been redefined\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7<%\"CG%%GRADG%)GRADIENTG%(HESSIANG%)JACOBIANG% %costG%(declareG%+dontreturnG%$eqnG%(fortranG%'hornerG%-intrep2mapleG% *joinprocsG%+makeglobalG%*makeparamG%)makeprocG%)makevoidG%-maple2intr epG%)optimizeG%)packargsG%+packlocalsG%+packparamsG%+prep2transG%*rena mevarG%&splitG%)swapargsG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "Consider the symbolic matrix " }{XPPEDIT 18 0 "A " "6#%\"AG" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A := Matrix( 3, 3, (i,j) -> a[i,j] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6$\")79Q;-%'MATRIXG6#7%7%&%\"aG6$\"\"\" F1&F/6$F1\"\"#&F/6$F1\"\"$7%&F/6$F4F1&F/6$F4F4&F/6$F4F77%&F/6$F7F1&F/6 $F7F4&F/6$F7F7" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "Compute the symbolic inverse of the matrix. Store the res ult as " }{XPPEDIT 18 0 "A_inv" "6#%&A_invG" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "A_inv := MatrixInverse(A);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%&A_invG-%'RTABLEG6$\")SY]=-%'MATRIXG 6#7%7%*&,&*&&%\"aG6$\"\"#F4\"\"\"&F26$\"\"$F8F5F5*&&F26$F4F8F5&F26$F8F 4F5!\"\"F5,.*(&F26$F8F5F5&F26$F5F4F5F:F5F5*(FAF5&F26$F5F8F5F1F5F>*(&F2 6$F4F5F5FCF5F6F5F>*(FIF5FFF5FF>,$*&,&*&FCF5F6F5F5*&FFF5FF5F?F>F>*&,&*&FCF5F:F5F5*&FFF5F1F5F >F5F?F>7%,$*&,&*&FAF5F:F5F>*&FIF5F6F5F5F5F?F>F>*&,&*&FAF5FFF5F>*&FMF5F 6F5F5F5F?F>,$*&,&*&FIF5FFF5F>*&FMF5F:F5F5F5F?F>F>7%*&,&*&FAF5F1F5F>*&F IF5F,$*&,&*&FAF5FCF5F>*&FMF5FF>*&,&*&FIF5FCF5F>* &FMF5F1F5F5F5F?F>" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 269 7 "fortran" }{TEXT -1 60 " command genera tes the necessary FORTRAN code for computing " }{XPPEDIT 18 0 "A_inv" "6#%&A_invG" }{TEXT -1 22 ". This code should be " }{TEXT 276 9 "optim ized" }{TEXT -1 21 " using that option. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "fortran(A_inv);" }}{PARA 6 "" 1 "" {TEXT -1 72 " \+ unknown(1,1) = (a(2,2)*a(3,3)-a(2,3)*a(3,2))/(a(3,1)*a(1,2)*a(2,3)" } }{PARA 6 "" 1 "" {TEXT -1 72 " #-a(3,1)*a(1,3)*a(2,2)-a(2,1)*a(1,2 )*a(3,3)+a(2,1)*a(1,3)*a(3,2)+a(" }}{PARA 6 "" 1 "" {TEXT -1 46 " \+ #1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 "" {TEXT -1 72 " unknown(1,2) = -(a(1,2)*a(3,3)-a(1,3)*a(3,2))/(a(3,1)*a(1,2) *a(2,3" }}{PARA 6 "" 1 "" {TEXT -1 72 " #)-a(3,1)*a(1,3)*a(2,2)-a( 2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3)*a(3,2)+a" }}{PARA 6 "" 1 "" {TEXT -1 47 " #(1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 " " {TEXT -1 72 " unknown(1,3) = (a(1,2)*a(2,3)-a(1,3)*a(2,2))/(a(3 ,1)*a(1,2)*a(2,3)" }}{PARA 6 "" 1 "" {TEXT -1 72 " #-a(3,1)*a(1,3) *a(2,2)-a(2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3)*a(3,2)+a(" }}{PARA 6 "" 1 " " {TEXT -1 46 " #1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }} {PARA 6 "" 1 "" {TEXT -1 72 " unknown(2,1) = -(-a(3,1)*a(2,3)+a(2 ,1)*a(3,3))/(a(3,1)*a(1,2)*a(2," }}{PARA 6 "" 1 "" {TEXT -1 72 " # 3)-a(3,1)*a(1,3)*a(2,2)-a(2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3)*a(3,2)+" }} {PARA 6 "" 1 "" {TEXT -1 48 " #a(1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)* a(3,2))" }}{PARA 6 "" 1 "" {TEXT -1 72 " unknown(2,2) = (-a(3,1)* a(1,3)+a(1,1)*a(3,3))/(a(3,1)*a(1,2)*a(2,3" }}{PARA 6 "" 1 "" {TEXT -1 72 " #)-a(3,1)*a(1,3)*a(2,2)-a(2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3) *a(3,2)+a" }}{PARA 6 "" 1 "" {TEXT -1 47 " #(1,1)*a(2,2)*a(3,3)-a( 1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 "" {TEXT -1 72 " unknown(2,3) = -(-a(2,1)*a(1,3)+a(1,1)*a(2,3))/(a(3,1)*a(1,2)*a(2," }}{PARA 6 "" 1 "" {TEXT -1 72 " #3)-a(3,1)*a(1,3)*a(2,2)-a(2,1)*a(1,2)*a(3,3)+a (2,1)*a(1,3)*a(3,2)+" }}{PARA 6 "" 1 "" {TEXT -1 48 " #a(1,1)*a(2, 2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 "" {TEXT -1 72 " \+ unknown(3,1) = (-a(3,1)*a(2,2)+a(2,1)*a(3,2))/(a(3,1)*a(1,2)*a(2,3" }} {PARA 6 "" 1 "" {TEXT -1 72 " #)-a(3,1)*a(1,3)*a(2,2)-a(2,1)*a(1,2 )*a(3,3)+a(2,1)*a(1,3)*a(3,2)+a" }}{PARA 6 "" 1 "" {TEXT -1 47 " # (1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 "" {TEXT -1 72 " unknown(3,2) = -(-a(3,1)*a(1,2)+a(1,1)*a(3,2))/(a(3,1)*a(1,2 )*a(2," }}{PARA 6 "" 1 "" {TEXT -1 72 " #3)-a(3,1)*a(1,3)*a(2,2)-a (2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3)*a(3,2)+" }}{PARA 6 "" 1 "" {TEXT -1 48 " #a(1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}{PARA 6 "" 1 " " {TEXT -1 72 " unknown(3,3) = (-a(2,1)*a(1,2)+a(1,1)*a(2,2))/(a( 3,1)*a(1,2)*a(2,3" }}{PARA 6 "" 1 "" {TEXT -1 72 " #)-a(3,1)*a(1,3 )*a(2,2)-a(2,1)*a(1,2)*a(3,3)+a(2,1)*a(1,3)*a(3,2)+a" }}{PARA 6 "" 1 " " {TEXT -1 47 " #(1,1)*a(2,2)*a(3,3)-a(1,1)*a(2,3)*a(3,2))" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fortran(A_inv, optimized);" }}{PARA 6 "" 1 "" {TEXT -1 24 " t4 = a(3,1)*a(1,2)" }}{PARA 6 "" 1 "" {TEXT -1 24 " t6 = a(3,1)*a(1,3)" }}{PARA 6 "" 1 "" {TEXT -1 24 " t8 = a(2,1)*a(1,2)" }}{PARA 6 "" 1 "" {TEXT -1 25 " \+ t10 = a(2,1)*a(1,3)" }}{PARA 6 "" 1 "" {TEXT -1 25 " t12 = a(1,1) *a(2,2)" }}{PARA 6 "" 1 "" {TEXT -1 25 " t14 = a(1,1)*a(2,3)" }} {PARA 6 "" 1 "" {TEXT -1 72 " t17 = 1/(t4*a(2,3)-t6*a(2,2)-t8*a(3 ,3)+t10*a(3,2)+t12*a(3,3)-t14*a" }}{PARA 6 "" 1 "" {TEXT -1 12 " # (3,2))" }}{PARA 6 "" 1 "" {TEXT -1 54 " unknown(1,1) = (a(2,2)*a( 3,3)-a(2,3)*a(3,2))*t17" }}{PARA 6 "" 1 "" {TEXT -1 55 " unknown( 1,2) = -(a(1,2)*a(3,3)-a(1,3)*a(3,2))*t17" }}{PARA 6 "" 1 "" {TEXT -1 54 " unknown(1,3) = (a(1,2)*a(2,3)-a(1,3)*a(2,2))*t17" }}{PARA 6 "" 1 "" {TEXT -1 56 " unknown(2,1) = -(-a(3,1)*a(2,3)+a(2,1)*a(3, 3))*t17" }}{PARA 6 "" 1 "" {TEXT -1 44 " unknown(2,2) = (-t6+a(1, 1)*a(3,3))*t17" }}{PARA 6 "" 1 "" {TEXT -1 36 " unknown(2,3) = -( -t10+t14)*t17" }}{PARA 6 "" 1 "" {TEXT -1 55 " unknown(3,1) = (-a (3,1)*a(2,2)+a(2,1)*a(3,2))*t17" }}{PARA 6 "" 1 "" {TEXT -1 45 " \+ unknown(3,2) = -(-t4+a(1,1)*a(3,2))*t17" }}{PARA 6 "" 1 "" {TEXT -1 34 " unknown(3,3) = (-t8+t12)*t17" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "You can similarly generate " }{TEXT 268 1 "C" }{TEXT -1 7 " code. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "C( A_inv, optimized );" }}{PARA 6 "" 1 "" {TEXT -1 27 " t4 \+ = a[2][0]*a[0][1];" }}{PARA 6 "" 1 "" {TEXT -1 27 " t6 = a[2][0]* a[0][2];" }}{PARA 6 "" 1 "" {TEXT -1 27 " t8 = a[1][0]*a[0][1];" }}{PARA 6 "" 1 "" {TEXT -1 28 " t10 = a[1][0]*a[0][2];" }}{PARA 6 "" 1 "" {TEXT -1 28 " t12 = a[0][0]*a[1][1];" }}{PARA 6 "" 1 " " {TEXT -1 28 " t14 = a[0][0]*a[1][2];" }}{PARA 6 "" 1 "" {TEXT -1 77 " t17 = 1/(t4*a[1][2]-t6*a[1][1]-t8*a[2][2]+t10*a[2][1]+t12 *a[2][2]-t14*a" }}{PARA 6 "" 1 "" {TEXT -1 8 "[2][1]);" }}{PARA 6 "" 1 "" {TEXT -1 61 " unknown[0][0] = (-a[2][1]*a[1][2]+a[1][1]*a[2] [2])*t17;" }}{PARA 6 "" 1 "" {TEXT -1 61 " unknown[0][1] = -(a[0] [1]*a[2][2]-a[0][2]*a[2][1])*t17;" }}{PARA 6 "" 1 "" {TEXT -1 60 " \+ unknown[0][2] = (a[0][1]*a[1][2]-a[0][2]*a[1][1])*t17;" }}{PARA 6 " " 1 "" {TEXT -1 62 " unknown[1][0] = -(-a[2][0]*a[1][2]+a[1][0]*a [2][2])*t17;" }}{PARA 6 "" 1 "" {TEXT -1 48 " unknown[1][1] = (-t 6+a[0][0]*a[2][2])*t17;" }}{PARA 6 "" 1 "" {TEXT -1 38 " unknown[ 1][2] = -(-t10+t14)*t17;" }}{PARA 6 "" 1 "" {TEXT -1 61 " unknown [2][0] = (-a[2][0]*a[1][1]+a[1][0]*a[2][1])*t17;" }}{PARA 6 "" 1 "" {TEXT -1 49 " unknown[2][1] = -(-t4+a[0][0]*a[2][1])*t17;" }} {PARA 6 "" 1 "" {TEXT -1 36 " unknown[2][2] = (-t8+t12)*t17;" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 " " }{TEXT 267 30 "Maple Generates HTML and LaTeX" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 256 "In an earlier sec tion, we showed how to generate LaTeX with Maple for typesetting. This command is repeated here. We also discuss the useful option of savin g a Maple Worksheet as HTML and show some hyperlink properties that ar e available on the worksheet." }}{PARA 0 "" 0 "" {TEXT -1 77 "Here we \+ want to test creating technical mathematics inside the text of Maple. " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "Int(e^(-x^2),x = 0 .. infinity) = limit(1/2*sqrt(Pi)*erf(sqrt(ln(e))*x)/sqrt(ln(e)),x = infinity)" "6#/ -%$IntG6$)%\"eG,$*$%\"xG\"\"#!\"\"/F+;\"\"!%)infinityG-%&limitG6$*,\" \"\"F6F,F--%%sqrtG6#%#PiGF6-%$erfG6#*&-F86#-%#lnG6#F(F6F+F6F6-F86#-FB6 #F(F-/F+F1" }}{PARA 257 "" 0 "" {TEXT -1 88 "The equation above was ge nerated by the command below and then pasted into this comment." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Int(e^(-x^2),x=0..infinity)= int(e^(-x^2),x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$In tG6$)%\"eG,$*$)%\"xG\"\"#\"\"\"!\"\"/F,;\"\"!%)infinityG-%&limitG6$,$* &*&-%%sqrtG6#%#PiGF.-%$erfG6#*&-F;6#-%#lnG6#F(F.F,F.F.F.*$-F;6#FDF.F/# F.F-/F,F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 586 "This complicated ex pression is readily transformed into LaTeX code with the Maple command below. The output is ASCII characters that can be readily copied and \+ pasted into any LaTeX document. To get the proper look of this equatio n in LaTeX, you would surround this expression with $$ on each side or use it in between the commands \\begin\{equation\} and \\end\{equatio n\}. LaTeX is the preferred text editor of Mathematicians and Physicis ts for technical writing because of its superior appearance. If you wa nt to learn more about LaTeX, then I would suggest a text such as Lesl ie Lamport's " }{TEXT 270 40 "LaTeX: User's Guide and Reference Manual " }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "latex(%);" }}{PARA 6 "" 1 "" {TEXT -1 70 "\\in t _\{0\}^\{\\infty \}\\!\{e\}^\{-\{x\}^\{2\}\}\{dx\}=\\lim _\{x\\right arrow \\infty \}1/" }}{PARA 6 "" 1 "" {TEXT -1 69 "2\\,\{\\frac \{\\sq rt \{\\pi \}\{\\it erf\}(\\sqrt \{\\ln (e)\}x)\}\{\\sqrt \{\\ln (e)\} \}\}" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 271 4 "HTML" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 255 "Maple provides a valuable tool for preparing technical d ocuments to post on the Web. You use the text button above to write te xt like you are reading now. The Maple commands like the one above cre ate good looking mathematical formula. When you choose the " }{TEXT 272 7 "Save As" }}{PARA 0 "" 0 "" {TEXT -1 7 "option " }{TEXT 273 4 "H TML" }{TEXT -1 568 ", then you can make the entire Maple worksheet int o an .htm or .html file. In fact, Maple automatically generates 3 HTML documents. If you name your file foo.html, then you obtain a document foo.html, foo1.html, and fooTOC.html. The main text is in foo1.html w ith foo.html creating a frames environment with the left frame being t he fooTOC.html (Table of Contents) frame which gives automatic hyperli nks to sections created on the Worksheet, and foo1.html being the righ t frame with the entire Maple worksheet. The technical formulae and gr aphs are saved in a folder, " }{TEXT 274 6 "images" }{TEXT -1 197 ", w ith the images numbered sequentially as foo1.gif. foo2.gif, etc. These .gifs can be readily extracted and renamed for use in any other web d ocument that you might be composing. Software such as " }{TEXT 275 9 " Photoshop" }{TEXT -1 63 " can be used to add labels on graphs or other cosmetic changes." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 16381412 18504640 }{RTABLE M7R0 I5RTABLE_SAVE/16381412X,%)anythingG6"6"[gl!"%!!!#*"$"$&%"aG6$"""F*&F(6$""#F*&F( 6$""$F*&F(6$F*F-&F(6$F-F-&F(6$F0F-&F(6$F*F0&F(6$F-F0&F(6$F0F06" } {RTABLE M7R0 I5RTABLE_SAVE/18504640X,%)anythingG6"6"[gl!"%!!!#*"$"$*&,&*&&%"aG6$""#F-"""&F+6 $""$F1F.F.*&&F+6$F-F1F.&F+6$F1F-F.!""F.,.*(&F+6$F1F.F.&F+6$F.F-F.F3F.F.*(F:F.&F +6$F.F1F.F*F.F7*(&F+6$F-F.F.F