{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 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 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 9 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 9 0 0 0 0 1 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 260 "" 1 20 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 265 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 270 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 275 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 280 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 285 "" 1 9 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 1 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 290 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 291 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 295 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 296 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 297 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 300 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 301 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 302 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 303 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 304 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 305 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 306 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 307 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 308 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 309 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 310 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 311 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 312 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 313 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 314 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 315 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 316 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 317 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 318 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 319 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 320 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 321 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 322 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 323 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 324 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 325 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 326 "" 1 10 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 327 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 328 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 329 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 330 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 331 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 332 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 333 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 334 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 335 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 336 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 337 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 338 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 339 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 340 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 341 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 342 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 343 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 344 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 345 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 346 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 347 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 348 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 349 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 350 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 351 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 352 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 353 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 354 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 355 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 356 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 357 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 358 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 359 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 360 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 361 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 362 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 363 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 364 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 365 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 366 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 367 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 368 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 369 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 370 "" 1 9 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 371 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 372 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 373 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 374 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 375 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 376 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 377 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 378 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 379 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 380 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 381 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 382 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 383 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 384 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 385 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 386 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 387 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 388 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 389 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 390 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 391 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 392 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 393 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 394 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 395 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 396 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 397 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 398 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 399 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 400 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 401 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 402 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 403 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 404 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 405 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 406 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 407 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 408 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 409 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 410 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 411 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 412 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 413 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 414 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 415 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 416 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 417 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 418 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 419 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 420 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 421 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 422 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 423 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 424 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 425 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 426 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 427 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 428 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 429 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 430 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 431 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 432 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 433 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 434 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 435 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 436 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 437 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 438 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 439 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 440 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 441 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 442 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 443 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 444 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 445 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 446 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 447 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 448 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 449 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 450 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 451 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 452 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 453 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 454 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 455 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 456 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 457 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 458 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 459 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 460 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 461 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 462 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 463 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 464 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 465 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 466 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 467 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 468 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 469 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 470 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 471 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 472 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 473 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 474 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 475 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 476 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 477 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 478 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 479 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 480 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 481 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 482 "" 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 483 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 484 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 485 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 486 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 487 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 488 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 489 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 490 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 491 "" 1 8 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 492 "" 1 8 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 493 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 494 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 495 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 496 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 497 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 498 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 499 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 500 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 501 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 502 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 503 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 504 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 505 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 506 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 507 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 508 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 509 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 510 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 511 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 512 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 513 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 514 "" 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 515 "" 1 8 0 0 0 0 0 0 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 "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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Co urier" 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 "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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 "Maple 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 10 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 2" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 10 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 "Heading 2" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2 " -1 260 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 1 1 1 2 2 2 1 1 1 1 } 3 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 261 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 260 "" 0 "" {TEXT -1 33 "Introductory Scientific \+ Computing" }}{PARA 260 "" 0 "" {TEXT -1 17 "A Maple Tutorial*" }} {PARA 259 "" 0 "" {TEXT -1 23 "copyright, January 2001" }{TEXT 356 2 " , " }{TEXT 355 11 " RH Landau" }}{PARA 259 "" 0 "" {TEXT -1 43 "Physi cs Department, Oregon State University" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT 260 21 "Maple Building Blocks" }}{PARA 256 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 " From Unix Prompt (= %)" }}{PARA 4 "" 0 "" {TEXT -1 1 " " }{TEXT 258 2 "% " }{TEXT 474 6 "xmaple" }{TEXT 286 1 " " }{TEXT 476 1 "&" }{TEXT 475 1 " " }{TEXT -1 28 " \+ " }{TEXT 285 76 " Start X Windows version \+ of Maple in background (background = &)" }}{PARA 0 "" 0 "" {TEXT -1 22 " % maple & " }{TEXT 287 108 " \+ Start text version of Maple in background (bac kground = &)" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 " Select Modes" }}{PARA 0 "" 0 "" {TEXT -1 64 " T \"text\" input \+ " }{TEXT 357 1 " " }{TEXT 288 61 "Useful fo r writing notes or writing up homework on worksheet " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 112 " [> Maple input \+ \+ " }{TEXT 289 20 "To enter mathematics" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{XPPEDIT 19 1 "Sigma;" "6#%&SigmaG" }{TEXT -1 83 " calcul ation \+ " }{TEXT 358 43 "Insert and edit math into text (use window)" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 " Execute Commands" }}{PARA 0 "" 0 "" {TEXT -1 58 "Place mouse anyplace after > and press [Enter] to ex ecute." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "restart; \+ " }{TEXT -1 14 " " }{TEXT 290 72 "De-assign all variables (like a new session); good to do for new group" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 4 "3+7;" }{TEXT -1 73 " \+ " }{TEXT 332 40 "Enter and Return may/may not be same key" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 36 " Basic Ope rations & Representations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(4/2)*3-7^8+7**8; " }{TEXT -1 8 " " }{TEXT 291 78 " \+ After many operations (2 forms of power 8) this should be 6" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "2485/3479; \+ " }{TEXT 292 41 "Maple reduces to 5/7, no loss of precisio" }{TEXT 359 1 "n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "2485./34 79; " }{TEXT 360 84 " Decimal point => fl oat; default to 10 digits, loss of precision" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Digits := 40; " }{TEXT -1 3 " " }{TEXT 361 85 " Change number of digits varia ble to 40 (NB := not =)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " 2485./3479;" }{TEXT -1 26 " " }{TEXT 362 95 " Try again with 40 digits now" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf( 2485/3479, 20 ); " }{TEXT 363 71 " Evaluate rat ional number as float, (optional: 20 digits) " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "1.0*10^(-6); " }{TEXT -1 39 " \+ " }{TEXT 364 44 "Floating point number in scientific notation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Flo at( 1, -6 ); " }{TEXT 365 88 " \+ Alternative form of above" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "1E-6; \+ " }{TEXT 366 34 "Alternative form of above, not ``" }{TEXT 267 3 "e''" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "1.*E-6; \+ " }{TEXT 367 8 "Variable" }{TEXT 370 3 " E \+ " }{TEXT 368 3 "to " }{TEXT 268 2 "-6" }{TEXT 369 6 " power" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "log(1.*E-6); \+ " }{TEXT 371 4 "test" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "exp(1.); exp(1); " } {TEXT 372 16 "Two versions of " }{TEXT 269 2 " e" }{TEXT 373 23 " (bas e of natural logs)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "log( \+ exp(1) ); " }{TEXT 374 4 "test " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "1.E-6; \+ " }{TEXT 376 25 "Syntax error without the " }{TEXT 270 3 "*, " }{TEXT 375 11 "or with the" }{TEXT 271 4 " \".\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sqrt(10!); " }{TEXT 377 96 " \+ Maple even simplifies for you" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Pi; " }{TEXT -1 28 " " } {TEXT 378 103 " \+ Name for 3.1415... " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ln(x); log10(x); abs(x); cos(x); " }{TEXT -1 23 " " }{TEXT 379 27 "Functions needing argument " }{TEXT 336 1 "x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "arcco s(x); cosh(x); P(l,x); BesselK(k,x); " }{TEXT -1 1 "\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sin(Pi); sin(pi); " } {TEXT 380 51 "The first one is what you want unless you define pi" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "(2+3*I)/(5-4*I); \+ " }{TEXT 381 15 "Complex numbers" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "convert( %, polar ); \+ " }{TEXT 382 28 "Polar form of complex number" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "?help; " }{TEXT -1 15 " \+ " }{TEXT 383 82 " Use ? in front of any thing for help on that command" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 " Sums & Products" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "sum( (-1)^i * x^(2*i)/(2*i) !, i=0..2 ); " }{TEXT 384 37 "Evaluate first 3 terms in cos series" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sum( (-1)^i * x^(2*i)/(2* i)!, i=0..infinity ); " }{TEXT 385 26 " Evaluate all terms " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "Sum( (-1)^i * x^(2*i)/(2*i)! , i=0..infinity ); " }{TEXT 386 18 " Symbolic sum" }{TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "value(%); \+ " }{TEXT 293 48 "Evaluate previous expression (% replac es old \")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Product( (i^ 2+3*i-11)/(i+3), i=0..10 ); " }{TEXT -1 11 " " }{TEXT 387 23 "Form product of symbols" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "value(%); " }{TEXT 388 28 "Evalu ate previous expression" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 " Symbolic Manipulations" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "restart; \+ " }{TEXT -1 41 " " } {TEXT 389 15 "Clean the slate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Sum( i, i=1..n );" }{TEXT -1 55 " \+ " }{TEXT 390 14 "This should be" }{TEXT 294 9 " n(n+1)/2" }{TEXT 391 15 " when evaluated" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "sum( i,i = 1 .. n ); " }{TEXT 392 37 "The active form. lowercase not upper" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "value(%); " }{TEXT -1 72 " \+ " }{TEXT 393 37 " Not form of expected result" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "expand(%); factor(%); expand(%); " } {TEXT 394 19 "so be manipulative!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expand( (x+y)^15 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "simplify( cos(x)^2 + sin(x)^2 ); " } {TEXT 395 30 "Simplify using math identities" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "convert( sin(x), exp ); " }{TEXT -1 5 " " }{TEXT 396 47 "Convert to exponential notation (many variant s)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 50 " Statements, Expressions, Functions & Procedure s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "restart; " } {TEXT -1 54 " " } {TEXT 397 44 "De-assign all variables (like new workshhet)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "1+4; exp(x)-1; " }{TEXT -1 43 " " }{TEXT 398 39 "Expres sions (evaluated or stored symbol" }{TEXT -1 2 "s)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x :=3; y := 3* z^2 + 1; " }{TEXT -1 14 " " }{TEXT 399 56 " Assign value or expressions to x & y; has side effects" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "eval( y, z=2 ); " }{TEXT -1 1 " " }{TEXT 400 57 " \+ Evaluate " }{TEXT 258 1 "y" }{TEXT 401 5 " for " }{TEXT 259 3 "z=2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "f :=(x) -> x* sin(x); " }{TEXT -1 23 " \+ " }{TEXT 402 17 "Defines function " }{TEXT 272 4 "f(x)" }{TEXT 403 4 " as " }{TEXT 273 8 "x sin(x)" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 36 "R :=(x,y,z) -> sqrt( x*x+y*y+z*z ); " } {TEXT -1 2 " " }{TEXT 404 57 " Define funct ion of 3 variables" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "g := \+ unapply( 3*z^2+1, z ); g(2); " }{TEXT 405 53 " \+ Convert expression into function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "x := 'x'; " }{TEXT -1 51 " \+ " }{TEXT 406 65 " \+ De-assign " }{TEXT 256 1 "x" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "z := x * sin(x); " } {TEXT -1 37 " " }{TEXT 407 31 "A p rocedure setting variable z " }{TEXT 333 19 "equal to expression" } {TEXT 408 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "zfun := u napply( z,x ); " }{TEXT 409 16 "Define function " } {TEXT 334 7 "zfun(x)" }{TEXT 410 16 " from procedure " }{TEXT 335 1 "z " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 " Solving Equations" }}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 44 " Single Equation (subscripte d variable)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve( a* x^2 +b*x +c , x ); " }{TEXT -1 25 " " }{TEXT 411 12 "Search for " }{TEXT 297 1 "x" }{TEXT 298 11 " satisfing " } {TEXT 299 15 "a*x^2+b*x+c = 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve( a*x^2 +b*x +c = 0 , x ); " }{TEXT -1 17 " \+ " }{TEXT 337 39 " Alternate form of above" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "y := a* x^2 +b*x +c = 0; \+ " }{TEXT 338 41 " Alternate form using variab le" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve( y, x ); " }{TEXT -1 1 "\"" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "eval( y, x = a/2 ); " }{TEXT -1 60 " \+ " }{TEXT 339 42 " \+ Verify answer" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "roots( x^2-1 ); " }{TEXT -1 23 " \+ " }{TEXT 296 2 " " }{TEXT 412 56 "Gives real, interger ro ots & multiplicity of polynomials" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "roots( x^2 +1, I ); " }{TEXT 295 44 "Gives complex, interger roots & multiplicity" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "ans := solve( a* x^2 +b*x +c =0, x); " } {TEXT 340 37 "Form sequence (subscripted variables)" }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ans[2]; " }{TEXT -1 76 " \+ " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve( x*sin(x) -1 , x ); \+ " }{TEXT -1 21 " " }{TEXT 413 48 "Solve for one f loating point (numeric) values of" }{TEXT 301 2 " x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fsolve( x*sin(x) -1 , x=0..6 ); " } {TEXT -1 18 " " }{TEXT 414 31 "Solve for 1 numeric v alues of " }{TEXT 300 9 " 0 < x <6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 " Simul taneous Equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "eqn1 := a +3*b +4*c = 41; " }{TEXT -1 57 " \+ " }{TEXT 415 23 "2 equations, 3 unknowns" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eqn2 := 5*a +6*b +7*c = 20; \+ " }{TEXT -1 1 "\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve( \{eqn1, eqn2\}, \{a, b\} );" }{TEXT -1 55 " \+ " }{TEXT 416 9 "So lve for" }{TEXT 302 4 " a,b" }{TEXT 417 5 " wrt " }{TEXT 303 1 "c" } {TEXT -1 93 " \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x := Linsolve(A,b) mod 5; " }{TEXT 418 21 "S olve matrix equation" }{TEXT -1 6 " [A] " }{TEXT 330 1 "x" }{TEXT -1 3 " = " }{TEXT 331 1 "b" }{TEXT -1 1 " " }{TEXT 419 20 "(see too linea r alg)" }{MPLTEXT 1 0 106 " \+ " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 16 " Plotting Along" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "restart; " }{TEXT 420 15 "Clean the slate" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "with( pl ots ); " }{TEXT 421 30 "Load extended plo tting package" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "with( plottools ); " }{TEXT 422 28 "Load extended plotting too ls" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot( tan(x), x=-7... 3 ); " }{TEXT 423 47 " \+ Basic plot" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 77 "plot( tan(x), x =-7..7, y =-5..5, labels =[`x`,`tan(x)`], title =`y=tan(x)` );" }{TEXT -1 379 " \+ \+ \+ \+ \+ " }{TEXT 424 32 "With \+ embellishments, strings in " }{TEXT 275 4 "back" }{TEXT 425 7 " quotes " }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 54 "plot( \{ cos(x), sin( x), x^2 \}, x = -Pi..Pi ); " }{TEXT 426 30 "Multiple functions on one plot" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 46 "plot( max (0, cos(x)), x = -2*Pi..2*Pi ); " }{TEXT -1 9 " " }{TEXT 427 30 "Limit range to positive [also " }{TEXT 274 14 "min(.), abs(.) " }{TEXT 428 1 "]" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 58 "plot ([sin(x), cos(x), x =0..2*Pi], scaling = constrained);" }{TEXT 277 18 "Phase-space, same " }{TEXT 276 4 "x,y " }{TEXT 278 5 "scale" }}} {EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 59 "implicitplot(\{x^2+y^2 = 1 , y=exp(x)\},x =-2..2, y =-2..2); " }{TEXT 430 24 "Implicit 2 variabl e eqtn" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 58 "plot3d( x*(x^2- 3*y^2), x=-1..1, y=-1..1,title='saddle' ); " }{TEXT -1 3 " " }{TEXT 429 29 " 3D plot of saddle function" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 50 "animate( cos(t*x) *sin(t*x), x = 0..Pi, t=1..20 );" } {TEXT -1 5 " " }{TEXT 431 38 "2D animation, click graph for contro ls" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "animate3d( cos(t*x) * sin(t*y), x =0..Pi,y=0..Pi, t=1..2 );" }{TEXT 304 68 " \+ " }{TEXT 432 31 " 3D animate; click for controls" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 " " }{TEXT 503 17 "Plotting of Data " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(s tatplots);with(stats);" }{TEXT -1 31 " \+ " }{TEXT 499 36 "Need statistics packages (not math!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Xdata := [1,2,3,6,10];" }{TEXT -1 49 " " }{TEXT 500 23 " A list of all x values" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " Ydata := [1,4,9,36,100];" }{TEXT -1 47 " \+ " }{TEXT 501 32 "A list of corresponding y values" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "scatterplot( Xdata, Ydata, \+ color=RED);" }{TEXT -1 4 " " }{TEXT 502 44 " C an have several plots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 " Calculus" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 " Differentiation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart; " }{TEXT -1 76 " \+ " } {TEXT 433 15 "Clean the slate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f := (x) -> ln(x)/(1-x); " }{TEXT 434 32 "Def ine function to differentiate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff( f(x), x ); " }{TEXT -1 54 " \+ " }{TEXT 435 30 "Derivative of expressi on wrt x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "diff( f(x), x$2 ); " }{TEXT -1 63 " \+ " }{TEXT 436 22 "Second derivative (nb " }{TEXT 283 1 "$ " }{TEXT 437 4 " not" }{TEXT 284 2 " ^" }{TEXT 438 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "diff( (sin(x))^y, x ); " } {TEXT -1 34 " " }{TEXT 439 23 "Partia l derivative of " }{TEXT 279 6 "f(x,y)" }{TEXT 440 6 " wrt " }{TEXT 280 1 "x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "diff( (sin(x))^ y, x,y ); " }{TEXT -1 19 " " }{TEXT 441 41 "Sec ond partial derivative of f(x,y) wrt" }{TEXT -1 1 " " }{TEXT 281 2 " x " }{TEXT 442 4 "and " }{TEXT 282 1 "y" }{TEXT 443 0 "" }{MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Diff( f(x), x ); \+ " }{TEXT -1 64 " \+ " }{TEXT 444 19 "Inert form of above" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f_prime := value(%); \+ " }{TEXT 445 32 "Evaluate derivative and call it " }{TEXT 256 7 "f_ prime" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "D(f)(x); \+ " }{TEXT -1 15 " " }{TEXT 446 23 "Derivative of function " }{TEXT 306 1 "f" }{TEXT 308 5 " wrt " }{TEXT 307 1 "x" }{TEXT 309 3 ". (" }{TEXT 310 1 "D" }{TEXT 311 13 " = operator, " }{TEXT 312 5 "D iff " }{TEXT 313 23 "= command). (See below)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Diff( f(x,y,z), x,x,y,z,z,z ); " }{TEXT -1 1 " " }{TEXT 447 60 " Differentiate multivariat e functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "g := (x) -> \+ D(f)(x); " }{TEXT -1 1 " " }{TEXT 448 53 "Define new functio n as derivative of another function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "h := (x,y,z) -> sin(x*y*z);" }{TEXT -1 50 " \+ " }{TEXT 449 29 "Define multiv ariate function " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g := D \+ [1] (h);" }{TEXT 450 98 " \+ Differentiate " }{TEXT 256 1 "h " }{TEXT 305 23 " wrt its first argument" }}}{EXCHG {PARA 257 "> " 0 " " {MPLTEXT 1 0 32 "Limit( (1+x/n)^n, n =infinity );" }{TEXT 451 63 " \+ Limit (then " }{TEXT 342 9 "value(%) " }{TEXT 452 8 " or use " }{TEXT 343 5 "limit" }{TEXT 453 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 25 "D - Differential operator" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D (cos);" }{TEXT -1 39 " \+ " }{TEXT 329 58 "Derivative of cos (transfo rms one function into another) " }{TEXT -1 14 " " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "D (cos) (x);" }{TEXT -1 61 " " }{TEXT 477 35 " Explicit dependence on x shown" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "D (f) (x); " }{TEXT 341 10 "Derivative" }{MPLTEXT 1 0 16 " " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "g := (x) -> D(f)( x); " }{TEXT 478 49 "Define new function, derivative of other fu nction" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "h := (x,y,z) -> s in(x*y*z);" }{TEXT -1 13 " " }{TEXT 479 29 "Define multiva riate function " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g := D[1 ](h); " }{TEXT 327 14 "Differentiate " }{TEXT 326 1 "h" }{TEXT 328 23 " wrt its first argument" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 " Int egration" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart; \+ " }{TEXT 314 97 " \+ Clean the slate" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Int( f_prime, x); \+ " }{TEXT -1 0 "" }{TEXT 344 25 "Antiderivative (integral)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "value (%); \+ " }{TEXT -1 1 "\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "simp lify (%); " }{TEXT -1 1 "\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Int ( x/sqrt(1+x), x ); value(%); \+ " }{TEXT 345 43 "Indefinite integrate wrt x (inert); evaluat" } {TEXT 480 1 "e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int ( x/s qrt(1+x), x ); " }{TEXT 346 24 "Indefinite integral wrt " }{TEXT 256 1 "x" }{MPLTEXT 1 0 1 " " }{TEXT 347 33 "(implied constant of inte gration)" }{MPLTEXT 1 0 3 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "diff ( %, x ); " }{TEXT -1 36 " \+ " }{TEXT 481 43 " Check answer by differntia tion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Int ( x/sqrt(1+x), \+ x = 0..1 ); " }{TEXT 348 37 "Evaluate definite integration (i nert)" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 42 " int ( x/sqrt(1+ x), x = 0..1 ); evalf(%); " }{TEXT -1 11 " " }{TEXT 349 53 " Evaluate definite integration (active); floats " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "g := unapply ( int( f(x), x ),x ); \+ " }{TEXT 482 51 " Integrate to produce a function " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "g := (y) -> int( f(x,y) , x = a..b ); " }{TEXT 350 22 " Defines function of " }{TEXT 258 2 " y " }{TEXT 351 20 "after integrate out " }{TEXT 257 1 "x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 " Series Expansions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "ans := series ( exp(x)/x, x=0 );" }{TEXT -1 24 " \+ " }{TEXT 454 29 "Power series expansion about " }{TEXT 261 3 "x= 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "truncate := convert ( \+ ans, polynom ); " }{TEXT -1 1 " " }{TEXT 455 41 "Truncate series to p olynomial for plottin" }{TEXT -1 1 "g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot ( \{ exp(x)/x, truncate \}, x = 0..4 ); " } {TEXT 315 30 "Plot exact vs truncated series" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Order \+ := 12; " }{TEXT -1 48 " \+ " }{TEXT 456 62 " Trunacate as 12th order polynomial" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "truncate := convert( ans, polynom); " }{TEXT -1 1 "\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 " Di fferential Equations" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " Fir st Order ODE" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "restart; \+ " }{TEXT 457 15 "Clean the slat e" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "with( DEtools ); " } {TEXT -1 51 " " } {TEXT 458 32 "Load differential equation tools" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 39 "diff_eq := D( D(x) ) (t) = -w*w *x; " } {TEXT 352 23 "Simple harmonic motion," }{XPPEDIT 18 0 "d^2*x/(dt^2) = \+ -omega^2*x;" "6#/*(%\"dG\"\"#%\"xG\"\"\"*$%#dtGF&!\"\",$*&%&omegaGF&F' F(F+" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "diff _eq := ( D@@2 ) (x) (t) = -w*w *x; " }{TEXT 353 23 "Alternate form of above" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 0 "" 0 "" {TEXT 262 31 " Second Order ODE with Plot " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with( DEtools );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "DEplot( [diff ( theta(t), t ) - omega = \+ 0, diff( omega(t), t) + sin(theta) = 0], [t, theta, omega], 0..12, \{ \+ [0,0,1.0] \}, scene = [t,omega] );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 " Second Order PDE" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with( DEtools );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff_eq1 := \+ D ( D(y) ) (x) + 5*D(y)(x) + 6*y(x) = 0; " }{TEXT -1 1 " " }{XPPEDIT 18 0 "diff(y(x),x,x) + 5*diff(y(x),x) + 6*y(x) = 0" "6#/,(-%%diffG6%-% \"yG6#%\"xGF+F+\"\"\"*&\"\"&F,-F&6$-F)6#F+F+F,F,*&\"\"'F,-F)6#F+F,F,\" \"!" }{TEXT -1 35 "; " }{TEXT 354 43 "operator acts on expressions, not functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "init_con := y(0)=0, D(y)(0)=1; \+ " }{TEXT 459 18 "Initial conditions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "dsolve( \{diff_eq1, init_con\} , \{y(x)\} ); \+ " }{TEXT 460 18 "Solve the equation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " System of ODE's" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "sys := (D@@2)(y )(x) = z(x), (D@@2)(z)(x) = y(x); " }{XPPEDIT 18 0 "diff(y(x),x,x) = z(x),diff(z(x),x,x) = y(x);" "6$/-%%diffG6%-%\"yG6#%\"xGF*F*-%\"zG6#F */-F%6%-F,6#F*F*F*-F(6#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "dsolve( \{sys\}, \{y(x), z(x)\}); " }{TEXT 461 48 "Maple \+ will generate initial condition parameters" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 " Linear \+ Algebra" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 32 " Defining Matric es &Vectors" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "with(LinearAl gebra); with (linalg); " }{TEXT 483 59 "Need for more tha n basics; good way to see what's available" }}{PARA 7 "" 1 "" {TEXT -1 64 "Warning, the assigned name GramSchmidt now has a global binding \n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7fq%$AddG%(AdjointG%3BackwardSub stituteG%+BandMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalFormG%-Bilinea rFormG%5CharacteristicMatrixG%9CharacteristicPolynomialG%'ColumnG%0Col umnDimensionG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatrixG%0Condi tionNumberG%/ConstantMatrixG%/ConstantVectorG%2CreatePermutationG%-Cro ssProductG%-DeleteColumnG%*DeleteRowG%,DeterminantG%/DiagonalMatrixG%* DimensionG%+DimensionsG%+DotProductG%,EigenvaluesG%-EigenvectorsG%&Equ alG%2ForwardSubstituteG%.FrobeniusFormG%2GenerateEquationsG%/GenerateM atrixG%2GetResultDataTypeG%/GetResultShapeG%5GivensRotationMatrixG%,Gr amSchmidtG%-HankelMatrixG%,HermiteFormG%3HermitianTransposeG%/Hessenbe rgFormG%.HilbertMatrixG%2HouseholderMatrixG%/IdentityMatrixG%2Intersec tionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*IsUnitaryG%2Jordan BlockMatrixG%+JordanFormG%(LA_MainG%0LUDecompositionG%-LeastSquaresG%, LinearSolveG%$MapG%%Map2G%*MatrixAddG%.MatrixInverseG%5MatrixMatrixMul tiplyG%+MatrixNormG%5MatrixScalarMultiplyG%5MatrixVectorMultiplyG%2Min imalPolynomialG%&MinorG%)MultiplyG%,NoUserValueG%%NormG%*NormalizeG%*N ullSpaceG%3OuterProductMatrixG%*PermanentG%&PivotG%0QRDecompositionG%- RandomMatrixG%-RandomVectorG%%RankG%$RowG%-RowDimensionG%-RowOperation G%)RowSpaceG%-ScalarMatrixG%/ScalarMultiplyG%-ScalarVectorG%*SchurForm G%/SingularValuesG%*SmithFormG%*SubMatrixG%*SubVectorG%)SumBasisG%0Syl vesterMatrixG%/ToeplitzMatrixG%&TraceG%*TransposeG%0TridiagonalFormG%+ UnitVectorG%2VandermondeMatrixG%*VectorAddG%,VectorAngleG%5VectorMatri xMultiplyG%+VectorNormG%5VectorScalarMultiplyG%+ZeroMatrixG%+ZeroVecto rG%$ZipG" }}{PARA 7 "" 1 "" {TEXT -1 104 "Warning, the previous bindin g of the name GramSchmidt has been removed and it now has an assigned \+ value\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSc hmidtG%,JordanBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcolG%'addro wG%$adjG%(adjointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%'bezoutG %,blockmatrixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%)colspac eG%(colspanG%*companionG%'concatG%%condG%)copyintoG%*crossprodG%%curlG %)definiteG%(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotprodG%*eige nvalsG%,eigenvaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG%&equalG %,exponentialG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG%*froben iusG%*gausselimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)hadamardG%( hermiteG%(hessianG%(hilbertG%+htransposeG%)ihermiteG%*indexfuncG%*inne rprodG%)intbasisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jacobianG%' jordanG%'kernelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'matrixG% &minorG%(minpolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normalizeG%*nul lspaceG%'orthogG%*permanentG%&pivotG%*potentialG%+randmatrixG%+randvec torG%%rankG%(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scal armulG%-singularvalsG%&smithG%,stackmatrixG%*submatrixG%*subvectorG%)s umbasisG%(swapcolG%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*transpose G%,vandermondeG%*vecpotentG%(vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "M := matrix(3,3, [4,-2,1,3,6,-4,2,1 ,8]); " }{TEXT -1 14 " " }{TEXT 484 35 "Define 3 x 3 matr ix with 9 elements" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "N := matrix(2 ,2, [2,x,1, y^3]);" }{TEXT -1 43 " \+ " }{TEXT 485 32 "Define 2 x 2 matrix with symbol" }{TEXT -1 1 "s" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7%7%\"\"%!\"# \"\"\"7%\"\"$\"\"'!\"%7%\"\"#F,\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"NG-%'matrixG6#7$7$\"\"#%\"xG7$\"\"\"*$)%\"yG\"\"$F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A := matrix(3,3, (i,j)-> i*j); \+ " }{TEXT 505 32 "Matrix with function as elements" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%\"\"\"\"\"#\"\"$ 7%F+\"\"%\"\"'7%F,F/\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "B := array(1..3, 1..3, [[-2,2,-3],[2,1,-6],[-1,-2,0]]); " }{TEXT 486 32 "Another way to do matrix M above" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7%7%!\"#\"\"#!\"$7%F+\"\"\"!\"'7%!\"\"F*\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ID := IdentityMatrix(3) ; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IDG-%'RTABLEG6$\")sg`=-%'MATR IXG6#7%7%\"\"\"\"\"!F/7%F/F.F/7%F/F/F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "v := vector([1,2,3]); " }{TEXT 488 24 "Enter column vector with" }{TEXT -1 1 " " }{TEXT 487 35 "list; displayed as row with commas" }{TEXT -1 2 " " }{MPLTEXT 1 0 3 " \+ " }{TEXT -1 0 "" }{MPLTEXT 1 0 231 " \+ \+ \+ " }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 55 "ucol := matrix(3, 1,[1,2,3]); \+ " }{TEXT 489 24 "An explict column vector" }{MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6#7%\"\"\"\"\"#\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ucolG-%'matrixG6#7%7#\"\"\"7 #\"\"#7#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "urow := ma trix(1,3,[1,2,3]);" }{TEXT -1 57 " \+ " }{TEXT 490 37 "An explicit row vector, NB no co mmas!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%urowG-%'matrixG6#7#7%\"\" \"\"\"#\"\"$" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 " " }{TEXT 504 17 "Matrix Operations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "evalm(A &* B); " }{TEXT 506 38 "M atrix multiply of too square matrices" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%!\"\"!\"#!#:7%F)!\"%!#I7%!\"$!\"'!#X " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(A &* ID);" } {TEXT -1 89 " \+ " }{TEXT 507 27 "Multiply by identity \+ matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\"\"\"# \"\"$7%F)\"\"%\"\"'7%F*F-\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(A^2);" }{TEXT -1 99 " \+ " } {TEXT 508 17 "Square of matrrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' matrixG6#7%7%\"#9\"#G\"#U7%F)\"#c\"#%)7%F*F-\"$E\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "evalm(1/B); \+ " }{TEXT 509 29 "inverse of nonsingular matrix" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%#!\"%\"#:#\"\"#F*#! \"\"\"\"&7%F+#F.F*#!\"#F/7%F1#F3F*F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "det(A); " }{TEXT -1 90 " \+ " } {TEXT 510 32 "Find determinant (0 => singular)" }{MPLTEXT 1 0 96 " \+ \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);" }{TEXT -1 95 " \+ \+ " }{TEXT 511 40 "Find inverse another way, eve n symbolic." }}{PARA 8 "" 1 "" {TEXT -1 36 "Error, (in inverse) singul ar matrix\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "P := multipl y(A,B); " }{TEXT -1 58 " \+ " }{TEXT 512 33 "Matrix multiplication another way" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7%7%!\"\"!\"#!#:7% F+!\"%!#I7%!\"$!\"'!#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "e valm(A &* v); " }{TEXT -1 68 " \+ " }{TEXT 513 32 "Multiply square ma trix by column" }{TEXT -1 1 " " }{TEXT 514 6 "vector" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "multiply(A, v); \+ " }{TEXT 515 19 "Or in other words, " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "multiply (v, A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG 6#7%\"#9\"#G\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"#9 \"#G\"#U" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"#9\"#G\"#U " }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 53 " Eigenvalues, Eige nvectors, Linear Equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "eigenvals(B); " }{TEXT 493 41 "Eigenvalues of matrix B, note double root" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*e igenvalsG6#%\"BG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eigenve cts(B); " }{TEXT -1 0 "" }{MPLTEXT 1 0 2 " " }{TEXT 494 79 " Eigenvectors of 3x3 matrix (eigenvalue,multiplicity, vectors; ...)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+eigenvectsG6#%\"BG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A := matrix(3,3, [4,-2, 1,3,6,-4,2,1,8]); " }{TEXT -1 25 " " }{TEXT 495 13 "Define matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matr ixG6#7%7%\"\"%!\"#\"\"\"7%\"\"$\"\"'!\"%7%\"\"#F,\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "b := vector([12, -25,32]); \+ " }{TEXT 496 14 "Define vector" }{TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7%\"#7!#D\"#K" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "x := linsolve (A,b); \+ " }{TEXT 497 35 " Solve " }{TEXT 491 7 "A x = b" }{TEXT 498 20 " for unknown vector " }{TEXT 492 1 "x" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%)linsolveG6$%\"AG%\"bG" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 " Generating Fortran & C Code (Ma ple V)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with (linalg);" }} {PARA 7 "" 1 "" {TEXT -1 104 "Warning, the previous binding of the nam e GramSchmidt has been removed and it now has an assigned value\n" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRde compG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG% (backsubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%) choleskyG%$colG%'coldimG%)colspaceG%(colspanG%*companionG%'concatG%%co ndG%)copyintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delrowsG%$detG %%diagG%(divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+ eigenvectsG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffgausselimG %*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqns G%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransp oseG%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG% *issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsq rsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%) multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG% *potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG% )rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackm atrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvest erG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG %'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A \+ := matrix ( 3, 3 ); " }{TEXT 462 51 " \+ Define 3 x 3 matrix" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "print (A); " } {TEXT 463 11 "View matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A_inv := inverse( A ); " }{TEXT 465 7 "Define " }{TEXT 316 6 "A_inv " }{TEXT 464 27 "to contain symbolic inverse" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "codegen[ fortran ] (A_inv); \+ " }{TEXT -1 41 " " } {TEXT 466 20 "Produce Fortran Code" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "codegen[C] (A_inv); " }{TEXT 467 51 " generate C code" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 22 " Statistics & Fitting" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 " Initialize (load)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with ( \+ stats );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 " Least Square Fits" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "with ( fit ); \+ " }{TEXT 468 20 "Load fitting package" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "X := [2,4,6,8]; \+ " }{TEXT 469 27 "Define independent variable" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Y := [0,20,28,44]; " }{TEXT 317 48 " Define dependent variable" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 69 "leastsquare [ [x,y], y = a*x^2+b* x+c, \{ a, b, c \} ] ( [X,Y] ); " }{TEXT 470 13 "Fit quadratic" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 " Mean & Variance" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "with ( describe ); " } {TEXT 471 28 "Load package for means et al" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "mean_X := mean ( X );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "median ( X );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "v ariance ( X );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dev := standardde viation ( X );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 32 " Statisitcal Plots (Maple V) " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "with(statplots); \+ " }{TEXT 318 33 "Load statistical plotting package " }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 90 "X := [4.5,4.0,5.4,1.6 ,5.7,3.5,7.8,8.1,6.0,13.4,2.8,5.1,3.7,8.0,3.6, 7.2,3.8,2.1,2.6,4.6]; \+ " }{TEXT -1 152 " \+ \+ X data." }}{PARA 257 "> " 0 "" {MPLTEXT 1 0 97 " Y := [7.4,4.4,2.8,5.4,9.9,-1.4,1.0,1.1,4.8,0.45,-0.78,9.9,4.8, -3.1,4. 4,5.3,1.91,-0.79,1.4,1.6]; " }{TEXT -1 61 " \+ Y data." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "scatterplot( X, Y, color=black); " }{TEXT 319 16 "Make scatterplot" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 " Maple Pro cedures " }{TEXT 263 37 "(see too Generating Fortran & C Code)" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "sub := proc (x, y) " }}{PARA 0 "" 0 "" {TEXT -1 10 " " }{MPLTEXT 1 0 5 "x^y; " }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{MPLTEXT 1 0 39 "end; \+ " }{TEXT 322 10 "Procedure " }{TEXT 266 3 "sub" }{TEXT 323 10 " \+ to raise " }{TEXT 264 1 "x" }{TEXT 324 8 " to the " }{TEXT 265 1 "y" } {TEXT 325 6 " power" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 50 "su b (2,5); " }{TEXT 472 15 "This \+ should be " }{TEXT 321 6 "2^5=32" }}{PARA 257 "> " 0 "" {MPLTEXT 1 0 50 "sub (i,j); " }{TEXT 473 26 "This should be algebraic, " }{TEXT 320 3 "i^j" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 258 "" 0 "" {TEXT -1 36 "Wit h loops, ifs, and local variables" }}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 0 243 "Chebyshev := proc( n )\n local p, k;\n p[0] \+ := 1;\n p[1] := x;\n if n <= 1 then\n RETURN ( eval (p) )\n fi;\n for k from 2 to n do\n p[k] := expand( \+ 2*x*p[k-1] - p[k-2] )\n od;\n RETURN ( eval(p) )\nend;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a := Chebyshev(5); a[3];" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 230 "* Development supported \+ in part by the National Science Foundation Curriculum Development Gran t NSF?? and the Education, Outreach and Training Thrust Area of the Na tional Partnership for Advanced Computational Infractrure (NPACI)." }} }{MARK "25 1 0 0" 0 }{VIEWOPTS 1 0 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 18536072 }{RTABLE M6R0 I5RTABLE_SAVE/18536072X,%)anythingG6#%)identityG6"][[[[_o!"$"$F' }