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}{PSTYLE "Map le Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 13 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 1 "" {TEXT 256 1 "S" }{TEXT 261 0 "" }{TEXT 262 0 "" }{TEXT 260 24 "ample Interactive Lesson" }}{PARA 0 "" 0 "" {TEXT -1 97 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 104 "In this lesson you will get a brief intr oduction to the numeric, symbolic and graphic features of Maple." }} {PARA 0 "" 0 "" {TEXT -1 94 "Input the following commands. They are s elf-explanatory. Maple response follows each command." }}{PARA 0 "" 0 "" {TEXT -1 64 "Thus, both input and output are listed on this Maple w orksheet. " }}{PARA 0 "" 0 "" {TEXT -1 48 "If you get an error message , correct the syntax." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "First of all, Maple can be used " }{TEXT 258 0 "" } {TEXT 259 0 "" }{TEXT -1 16 "as a calculator:" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 263 22 "Maple as a calculator:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "2/3+8/7 \+ \n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 39 "R emember every command should end with " }{TEXT -1 1 ";" }{TEXT 266 14 " (a semicolon)" }{TEXT 265 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "2/3 + 8/7;\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} }{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 270 34 "Maple as a compu ter algebra system" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 272 96 " Maple performs symbolic operations, like factoring, the four operatio ns, substitution, solving " }}{PARA 257 "" 0 "" {TEXT -1 49 "sophistic ated equations or systems of equations. " }{TEXT 271 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 273 9 "Factoring" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "factor(x^2+5*x-6);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 274 27 "Multiplying \+ two polynomials" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand((x +6)*(x-1));\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 275 29 "Solving an algebraic equation" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve((x^2+5*x-6),x);\n" }}} {PARA 5 "" 0 "" {TEXT 276 246 " \+ \+ \+ " } }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 277 39 "Substituting in an algebraic expression" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " subs(x=3,(x^2+5*x-6));\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 278 36 "Solving a general algebraic equation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(a*x^2+b*x+c=0,x);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 279 29 "Solving a system \+ of equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(\{-2*x +y-3*z=1,2*x-2*y+z=-3,x+y+z=-3\},\{x,y,z\}); \n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 280 39 " Solving a dependent system of equations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 281 94 "Maple solves a dependent system of equations. In th e following, Maple chooses arbitrarily one" }}{PARA 0 "" 0 "" {TEXT 283 23 "variable and expresses " }{TEXT -1 0 "" }{TEXT 282 50 "the rem aining variables in terms of that variable." }}{PARA 0 "" 0 "" {TEXT 284 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "solve(\{-2*x+y-3 *z=1,2*x-2*y+z=-3\},\{x,y,z\});\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 285 48 "Solving a recurrence equation as a function of n" }}{PARA 5 "" 0 "" {TEXT 286 1 " " }{TEXT 287 10 "Using the " } {TEXT 289 6 "rsolve" }{TEXT 290 76 " command, Maple solves a recurren ce equation, if possible, returning f as " }}{PARA 0 "" 0 "" {TEXT 291 18 "a function of n. " }{TEXT -1 0 "" }{TEXT 288 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "rsolve(\{f(n)=f(n-1)+f(n-2),f(0)=1, f(1)=3\},\{f(n)\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%,2);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 293 34 "Clearing memory of Maple \+ variables" }}{PARA 258 "" 0 "" {TEXT -1 95 "Sometimes Maple holds on t o values assigned to variables. If you see any strange output, then \+ " }}{PARA 259 "" 0 "" {TEXT -1 96 "assign the variable its own name, \+ as below, using the single quotes around f. This frees the " }} {PARA 260 "" 0 "" {TEXT -1 27 "variable for further use. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:='f'; x:='x';\n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 294 20 "Defining a function " }}{PARA 0 "" 0 "" {TEXT 295 82 "Maple di stinguishes between an expression and a function. Define a function u sing" }}{PARA 0 "" 0 "" {TEXT 298 51 "the assignment symbol, :=. Crea te an arrow use a " }{TEXT 296 1 "-" }{TEXT 297 26 " (minus sign) fol lowed by " }{TEXT 299 1 ">" }{TEXT 300 23 " (greater than) symbol." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x->x^2 + 1;\n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" } {TEXT 301 21 "Evaluating a function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 302 46 "Define the function first. Then use evalf( )." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(f(4));evalf(f(3+h));\n " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 303 66 "Maple does not evaluate f(3 + h) unless the value for h \+ is given. " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 " " {TEXT -1 0 "" }{TEXT 304 41 "Creating a table of values for a functi on" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 305 86 "To create a table o f values (x, f(x)) from -2 to 2 with increments of 0.5 for f(x) = " } {XPPEDIT 18 0 "x^3;" "6#*$%\"xG\"\"$" }{TEXT 306 2 ", " }}{PARA 0 "" 0 "" {TEXT 307 68 "use the following steps. We also separate x and f (x) by enclosing " }}{PARA 0 "" 0 "" {TEXT 308 85 "five spaces between two backward quote ( ` ) symbols. The backward quote symbol is " }} {PARA 0 "" 0 "" {TEXT 309 65 "the key located next to 1 on the top lef t corner of the keyboard." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x -> x^3;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for x fr om -2 by 0.5 to 2 do print (x, ` `, f(x)) od;\n" }}}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 310 28 "Plotting graphs of functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 311 91 "To plot a graph of the function, with la bels on the y-axis and title, enter the following. " }}{PARA 0 "" 0 " " {TEXT 313 0 "" }{TEXT -1 0 "" }{TEXT 312 67 "Titles must be enclosed between two backward quote ( ` ) symbols. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "plot(t*sin(t), t=-3*Pi..3*Pi,`t*sin(t)` = -10..10, title=`My First Graph`);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 314 94 "The graph can be reduced or enlarged by resizing the plot window. T o do this place the mouse" }}{PARA 0 "" 0 "" {TEXT 317 98 " pointer ne ar the graph. Click the left mouse button. This makes the plot windo w visible. Drag " }}{PARA 0 "" 0 "" {TEXT 316 100 "the right bottom c orner of the window in or out with the mouse pointer which turns into \+ a two sided " }}{PARA 0 "" 0 "" {TEXT 319 6 "arrow." }}{PARA 0 "" 0 " " {TEXT 318 2 " " }}{PARA 0 "" 0 "" {TEXT 315 74 "Two or more functio ns are plotted with the same reference axes as follows." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(\{t*sin(t),t^2*sin(t)\},t=-3*P i..3*Pi,title=`My Second Graph`);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 320 7 "To plot" }{TEXT -1 1 " " }{TEXT 321 70 "more complicated functions we need to activate the built-in package: \+ " }{TEXT -1 8 "plots. " }}{PARA 0 "" 0 "" {TEXT 332 0 "" }{TEXT -1 30 "We plot the piecewise function" }{TEXT 329 3 " " }{TEXT 333 4 " \+ " }{TEXT -1 2 "f(" }{TEXT 322 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 9 " for " }{XPPEDIT 18 0 "x;" "6#%\" xG" }{TEXT -1 4 " < 2" }}{PARA 0 "" 0 "" {TEXT -1 67 " \+ = " }{XPPEDIT 18 0 "x ^2;" "6#*$%\"xG\"\"#" }{TEXT -1 11 " for 2 <= " }{XPPEDIT 18 0 "x" "6 #%\"xG" }{TEXT -1 4 " < 3" }}{PARA 0 "" 0 "" {TEXT -1 76 " \+ = 5 for " } {XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 36 " >= 3 \+ " }}{PARA 0 "" 0 "" {TEXT -1 81 " (where <= means 'less than \+ or equal to', >= means 'greater than or equal to') " }}{PARA 0 "" 0 " " {TEXT 324 5 "using" }{TEXT -1 1 " " }{TEXT 326 3 "the" }{TEXT -1 7 " plots " }{TEXT 325 7 "package" }{TEXT -1 1 " " }{TEXT 323 11 "as foll ows." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(plots);\n" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 327 45 "First we define the given piecewise function." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f:=x->piecewise(x<2,x,x< 3,x^2,5);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 328 32 "The graph is plotted as follows." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(f(x),x=-2..6);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 330 54 "Maple connects the d iscontinuities by a vertical line." }}{PARA 0 "" 0 "" {TEXT 331 45 "To show discontinuites we use the condition: " }{TEXT -1 14 "discont = t rue" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(f(x),x=-2..6,dis cont=true);\n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 334 26 "Polar functions and graphs" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 335 34 "Polar function s are plotted using " }{TEXT -1 9 "polarplot" }{TEXT 336 29 " command. We plot r = sin 3t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "polarplot(sin(3*t),t=0..2*Pi);\n" }}}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 337 31 "Parametric functions and graphs" }}{PARA 0 "" 0 "" {TEXT -1 37 "Next we plot the parametric function " }{TEXT 338 4 "x = \+ " }{XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT 339 8 " , y = 2" } {XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT 340 15 " -1 <= t <= 1." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot([t^2,2*t^3,t=-1..1]); \n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 341 9 "3D graphs" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 344 46 "Three dimensional graphs \+ are plotted with the " }{TEXT -1 6 "plot3d" }{TEXT 345 25 " command. \+ Here we graph " }}{PARA 0 "" 0 "" {TEXT -1 34 "z = cos xy, x = -3..3, \+ y = -3..3, " }}{PARA 0 "" 0 "" {TEXT 346 4 "and " }{TEXT -1 4 "r = " } {XPPEDIT 18 0 "Theta;" "6#%&ThetaG" }{TEXT -1 6 " cos (" }{XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT -1 2 ") " }{TEXT 347 17 "on the interval - " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 4 " <= " }{XPPEDIT 18 0 "Th eta;" "6#%&ThetaG" }{TEXT 348 4 " <= " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT 349 6 " and " }{TEXT 342 1 "-" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 4 " <= " }{XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT 343 4 " <= \+ " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 350 104 "The graphs can be rotated by grabbing o ne corner by the mouse arrow. The shading changes accordingly. " }} {PARA 0 "" 0 "" {TEXT 351 46 "A choice of axes is available on the too lbar. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot3d(cos(x*y),x=-3..3,y=-3..3);\n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 352 41 " Plotting graphs in spherical coordinates" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sphereplot(t heta*cos(phi),theta=-Pi..Pi,phi=-Pi..Pi);\n" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 353 34 "P lotting the intersecting surfaces" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 355 44 "We plot the intersection of two surfaces: " }{TEXT -1 4 "z = " }{XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#" }{TEXT -1 4 " - " } {XPPEDIT 18 0 "y^2;" "6#*$%\"yG\"\"#" }{TEXT -1 10 " and x = 1" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "implicitplot3d(\{z = x^2 - \+ y^2, x = 1\}, x = -5..5, y = -5..5,z = -10..30, title = `Intersecting \+ Surfaces: z = x^2 - y^2, x = 1`);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 354 20 "Calculus using Ma ple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 356 105 " Limits, derivatives, partial derivatives, derivatives of higher order, indefinite, definite and improper " }}{PARA 0 "" 0 "" {TEXT 357 37 "i ntegrals are calculated as follows. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(sin(x)/x,x=0);\n" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "limit((1+1/x)^x,x=infinity);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "limit((x^2-1)/(x^3-1),x=1);\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "diff(x^4/(x^3+1),x);\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 19 "diff((x-2)*y^2,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "diff((x-2)*y^2,y);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "diff(x^6,x,x,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(x^2-3,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(x^2-3,x=-2..2);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(1/x^.5,x= 0..1);\n " }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 1 " " }}{PARA 0 "" 0 " " {TEXT -1 53 "_____________________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 161 "MSIP Grant #P120A80089-98: \"Three Ur ban Calculus Reform programs: Adopting the Best\" 1998-2001 \+ " }}}{MARK "10 \+ 33 16 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }