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"" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 418 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 419 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 420 "" 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 421 "" 1 14 0 0 0 0 2 2 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 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 1 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 1 2 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 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" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 14 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 "Normal" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 261 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 262 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 1 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 {PARA 256 "" 1 "" {TEXT 256 1 "S" }{TEXT 259 0 "" }{TEXT 260 0 "" }{TEXT 258 53 "ample Interactive Introductory Lesson from Calculu s +" }}{PARA 258 "" 0 "" {TEXT 330 28 "http://calculusplus.cuny.edu" } }{PARA 258 "" 0 "" {TEXT 331 62 "Modified and updated for Maple 10 by \+ John Pais, June 20, 2005 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 491 "In this lesson you will get a brief introduc tion to the numeric, symbolic, and graphical features of Maple. In ord er to leisurely navigate this worksheet and check everything out step- by-step, after expanding the buttons below, execute each of the self-e xplanatory commands by clicking in the red area and then pressing [Ent er]. On the other hand, if you're in a hurry to browse everything in \+ this worksheet, then click on the !!! button on the toolbar above to e xecute the whole worksheet." }}{PARA 259 "" 0 "" {TEXT -1 0 "" }} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 336 18 "Maple can be use d " }{TEXT 334 0 "" }{TEXT 335 0 "" }{TEXT 337 16 "as a calculator." } }{PARA 0 "" 0 "" {TEXT 421 41 "First, we show you the most common erro r." }{TEXT 332 41 "\nClick in the red area and press [Enter]." }{TEXT 333 1 " " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "2/ 3+8/7 \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 262 "" 0 "" {TEXT -1 0 "" }{TEXT 261 39 "Remember every command should end with " }{TEXT -1 1 ";" } {TEXT 263 14 " (a semicolon)" }{TEXT 262 1 "." }}{EXCHG {PARA 0 "" 0 " " {TEXT 340 40 "Click in the red area and press [Enter]." }{TEXT 341 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "2/3 + 8/7;\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 342 40 "Click in the red \+ area and press [Enter]." }{TEXT 343 1 " " }{TEXT -1 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 264 51 "Maple as a computer algebra (and \+ much more) system." }}{SECT 1 {PARA 5 "" 0 "" {TEXT 265 9 "Factoring" }}{EXCHG {PARA 0 "" 0 "" {TEXT 338 40 "Click in the red area and press [Enter]." }{TEXT 339 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "factor(x^2+5*x-6);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 266 27 "Multiplying two polynomials" }} {EXCHG {PARA 0 "" 0 "" {TEXT 344 40 "Click in the red area and press [ Enter]." }{TEXT 345 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "expand((x+6)*(x-1));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 267 29 "Solving an algebraic equation" }}{EXCHG {PARA 0 "" 0 "" {TEXT 346 40 "Click in the red area and press [Enter]. " }{TEXT 347 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve((x^2+5*x-6),x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{PARA 5 "" 0 "" {TEXT 268 241 " \+ \+ \+ " } }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 269 39 "Substituting in an algebraic expression" }}{EXCHG {PARA 0 "" 0 "" {TEXT 348 40 "Click in the red area and press [Enter]." }{TEXT 349 1 " " }{TEXT -1 0 "" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(x=3,(x^2+5*x-6));\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 270 36 "Solving a general alg ebraic equation" }}{EXCHG {PARA 0 "" 0 "" {TEXT 350 40 "Click in the r ed area and press [Enter]." }{TEXT 351 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(a*x^2+b*x+c=0,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 271 29 "Solving a system \+ of equations" }}{EXCHG {PARA 0 "" 0 "" {TEXT 352 40 "Click in the red \+ area and press [Enter]." }{TEXT 353 1 " " }{TEXT -1 0 "" }}{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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 " " }{TEXT 272 39 "Solving a dependent system of equations" }}{PARA 260 "" 0 "" {TEXT -1 0 "" }{TEXT 273 79 "Maple solves a dependent system o f equations. In the following, Maple chooses " }}{PARA 260 "" 0 "" {TEXT 412 38 "arbitrarily one variable and expresses" }{TEXT 358 1 " \+ " }{TEXT 359 0 "" }{TEXT 274 50 "the remaining variables in terms of t hat variable." }{TEXT 360 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 354 40 " Click in the red area and press [Enter]." }{TEXT 355 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "solve(\{-2*x+y-3*z=1,2*x-2*y +z=-3\},\{x,y,z\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 275 48 "Solving a recurrence equation as a function of n" }}{PARA 5 "" 0 "" {TEXT 276 62 "Using the rsolve \+ command, Maple solves a recurrence equation." }}{PARA 5 "" 0 "" {TEXT 413 28 "If possible, returning f as " }{TEXT 278 16 "a function \+ of n." }{TEXT 414 1 " " }{TEXT 361 1 " " }{TEXT -1 0 "" }{TEXT 277 1 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT 356 40 "Click in the red area and pr ess [Enter]." }{TEXT 357 1 " " }{TEXT -1 0 "" }}{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 "" {TEXT 362 40 "Click in the red area and press [Enter]." }{TEXT 363 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%, 2);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 279 34 "Clearing memory of Maple variables" }}{PARA 257 "" 0 "" {TEXT 364 94 "Sometimes Maple holds on to values assigned to variables. If you \+ see any strange output, then" }{TEXT -1 1 " " }}{PARA 257 "" 0 "" {TEXT 365 96 "assign the variable its own name, as below, using the single quotes around f. This frees the " }}{PARA 257 "" 0 "" {TEXT 366 27 "variable for further use. " }}{EXCHG {PARA 0 "" 0 "" {TEXT 367 40 "Click in the red area and press [Enter]." }{TEXT 368 1 " " } {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:='f'; x:='x';\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 280 20 "Defining a function " }}{PARA 0 "" 0 "" {TEXT 281 95 "Maple distinguishes between an expression and a function. Define \+ a function (see below) using " }{TEXT 371 4 "the " }}{PARA 0 "" 0 "" {TEXT 372 76 "assignment symbol := and create an arrow using a - (min us sign) followed by" }{TEXT 373 2 " >" }{TEXT 282 23 " (greater than) symbol." }}{EXCHG {PARA 0 "" 0 "" {TEXT 369 40 "Click in the red area and press [Enter]." }{TEXT 370 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x->x^2 + 1;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 283 21 "Evaluating a function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 284 46 "Define the function first. Then use evalf( )." }}{EXCHG {PARA 0 "" 0 "" {TEXT 415 40 "Click in the red area and press [Enter]. " }{TEXT 416 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f:=x->x^2 + 1;\nevalf(f(4));\nevalf(f(3+h));\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 285 66 "Maple does not evaluate f(3 + h) unless the value for h is given. \+ " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 286 41 "Creating a t able of values for a function" }}{EXCHG {PARA 0 "" 0 "" {TEXT 374 40 " Click in the red area and press [Enter]." }{TEXT 375 1 " " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x -> x^3;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 376 40 "Click in the red area and press [Enter]." }{TEXT 377 1 " " } {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "for i from -2 by 0. 5 to 2 do \nif i = -2 then print('f'(x)=f(x))fi:\nprint ('f'(i)=f(i)) \+ od;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 287 28 "Plotting graphs of functi ons" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 288 88 "To plot a graph of a function, with labels on the y-axis and title, enter the following. " }{TEXT 379 1 " " }}{PARA 0 "" 0 "" {TEXT 290 0 "" }{TEXT -1 0 "" } {TEXT 289 65 "Titles must be enclosed between two backward quote ( ` ) symbols." }{TEXT 378 2 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT 380 40 "Cl ick in the red area and press [Enter]." }{TEXT 381 1 " " }{TEXT -1 0 " " }}{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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 291 94 "The graph can be reduced or enlarged by resizing the plot window. T o do this place the mouse" }}{PARA 0 "" 0 "" {TEXT 294 1 " " }{TEXT 382 96 "pointer near the graph. Click the left mouse button. This ma kes the plot window visible. Drag" }{TEXT 383 1 " " }}{PARA 0 "" 0 " " {TEXT 293 100 "the right bottom corner of the window in or out with \+ the mouse pointer which turns into a two sided " }}{PARA 0 "" 0 "" {TEXT 295 6 "arrow." }}{PARA 0 "" 0 "" {TEXT 292 74 "Two or more funct ions are plotted with the same reference axes as follows." }}{EXCHG {PARA 0 "" 0 "" {TEXT 384 40 "Click in the red area and press [Enter]. " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(\{t*sin(t), t^2*sin(t)\},t=-3*Pi..3*Pi,title=`My Second Graph`);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 296 7 "To plot" }{TEXT 385 1 " " }{TEXT 297 69 "more complicated functions we need to activate the built-in package: " }{TEXT 391 1 " \+ " }{TEXT 386 6 "plots." }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT 307 0 "" }{TEXT -1 30 "We plot the piecewise function" }{TEXT 304 3 " " }{TEXT 308 4 " " }{TEXT -1 2 "f(" }{TEXT 298 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 9 " for " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 4 " < 1" }}{PARA 0 "" 0 "" {TEXT -1 67 " \+ = " } {XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#" }{TEXT -1 11 " for 1 <= " } {XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 4 " < 4" }}{PARA 0 "" 0 "" {TEXT -1 76 " \+ = 5 for " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1 36 " >= 4 \+ " }}{PARA 0 "" 0 "" {TEXT -1 81 " (wher e <= means 'less than or equal to', >= means 'greater than or equal t o') " }}{PARA 260 "" 0 "" {TEXT 387 5 "using" }{TEXT 388 1 " " }{TEXT 301 3 "the" }{TEXT 389 7 " plots " }{TEXT 300 7 "package" }{TEXT 390 1 " " }{TEXT 299 11 "as follows." }}{EXCHG {PARA 0 "" 0 "" {TEXT 392 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 302 44 "Fi rst we define the given piecewise function" }{TEXT 393 1 "." }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 394 40 "Click in the red area a nd press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "f:=x->piecewise(x<1,x,x>=1 and x<4,x^2,x>=4,5);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 303 32 "The graph is plotted as follows." }}{EXCHG {PARA 0 "" 0 "" {TEXT 395 40 "Click in the red area and press [Enter]." }{TEXT -1 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(f(x),x=-2..6);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 305 54 "Maple connects the discontinuities by a vertica l line." }}{PARA 0 "" 0 "" {TEXT 306 45 "To show discontinuites we use the condition: " }{TEXT 397 15 "discont = true." }}{EXCHG {PARA 0 "" 0 "" {TEXT 396 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(f(x),x=-2..6,discont =true);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 309 26 "Polar functions and graph s" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 310 34 "Polar functions are \+ plotted using " }{TEXT 398 13 "the polarplot" }{TEXT 311 30 " command. We plot r = sin(3t)." }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 399 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "polarplot(sin(3*t),t=0..2*Pi,color= blue);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 312 31 "Parametric functions and \+ graphs" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 420 36 "Next we plot the parametric function" }{TEXT -1 1 " " }{TEXT 417 4 "x = " } {XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT 418 8 " , y = 2" } {XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT 419 16 ", -1 <= t <= 1. " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 404 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot([t^2,2*t^3,t=-1..1],color=magenta);\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 313 9 "3D g raphs" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 401 0 "" }{TEXT 316 46 " Three dimensional graphs are plotted with the " }{TEXT 402 6 "plot3d" }{TEXT 317 24 " command. Here we graph" }{TEXT 403 1 " " }}{PARA 0 " " 0 "" {TEXT -1 34 "z = cos xy, x = -3..3, y = -3..3, " }}{PARA 0 "" 0 "" {TEXT 318 4 "and " }{TEXT -1 4 "r = " }{XPPEDIT 18 0 "Theta;" "6# %&ThetaG" }{TEXT -1 6 " cos (" }{XPPEDIT 18 0 "phi;" "6#%$phiG" } {TEXT -1 2 ") " }{TEXT 319 17 "on the interval -" }{XPPEDIT 18 0 "Pi; " "6#%#PiG" }{TEXT -1 4 " <= " }{XPPEDIT 18 0 "Theta;" "6#%&ThetaG" } {TEXT 320 4 " <= " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT 321 6 " and \+ " }{TEXT 314 1 "-" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 4 " <= " } {XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT 315 4 " <= " }{XPPEDIT 18 0 "Pi ;" "6#%#PiG" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 322 100 "The grap hs can be rotated by clicking on the image and dragging. The shading changes accordingly. " }}{PARA 0 "" 0 "" {TEXT 323 45 "A choice of ax es is available on the toolbar." }{TEXT 400 1 " " }{TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT 405 40 "Click in the red area and press [ Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot3d(co s(x*y),x=-3..3,y=-3..3);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 324 40 "Plotting graphs in spherical coordinates" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 406 40 "Click in the red area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "sphereplot(theta*cos(phi) ,theta=-Pi..Pi,phi=-Pi..Pi);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 325 34 "Plot ting the intersecting surfaces" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 327 41 "We plot the intersection of two surfaces:" }{TEXT 407 3 " " }{TEXT -1 4 "z = " }{XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#" } {TEXT -1 4 " - " }{XPPEDIT 18 0 "y^2;" "6#*$%\"yG\"\"#" }{TEXT -1 10 " and x = 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT 408 40 "Click in the red a rea and press [Enter]." }{TEXT -1 0 "" }}{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 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }{TEXT 326 17 " A Little Calculus" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 328 104 "Lim its, derivatives, partial derivatives, derivatives of higher order, in definite, definite and improper" }{TEXT 409 1 " " }}{PARA 0 "" 0 "" {TEXT 329 36 "integrals are calculated as follows." }{TEXT 410 1 " " } {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 411 40 "Click in the red \+ area and press [Enter]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(sin(x)/x,x=0);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "Limit((1+1/x)^x, x=infinity)=limit((1+1/x)^x,x=infinity);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Limit ((x^2-1)/(x^3-1),x=1)=limit((x^2-1)/(x^3-1),x=1);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Diff(x^4/(x^3+1),x)=diff(x^4/(x^3+1),x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Diff((x-2)*y^2,x)=diff((x-2)*y^2,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Diff((x -2)*y^2,y)=diff((x-2)*y^2,y);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Diff(x^6,x,x,x)= diff(x^6,x,x,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Int(x^2-3,x)=int(x^2-3,x);\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 39 "Int(x^2-3,x=-2..2)=int(x^2-3,x=-2..2);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "Int(1/x^.5,x= 0..1)=int(1/x^.5,x= 0..1);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{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 Urban Calculus Reform program s: Adopting the Best\" 1998-2001 \+ " }}}{MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }