Web skærmformat. - Aarhus Universitet

More documents

Recommendations

Info

IV. Differentialligninger – 2. 1. ordens ligninger 332 I den partikulære løsning bestemmes C ved y(0) = 2. I alt er løsningen y(0) = Ce 0 + 3 = 2 2 C = 2 − 3 1 = 2 2 y(x) = 1 2 e−2x + 1 2 x2e −2x + 3 2 = 1 2 (1 + x2 )e −2x + 3 2 2.16. Rovdyr-byttedyr ☞ [S] 7.6 Predator-prey systems Lotka-Volterra ligningerne dR = kR − aRW dt 1 dW = −rW + bRW dt er et system af koplede differentialligninger, der beskriver en udviklingen i en bestand af rovdyr W(t) (ulve) og byttedyr R(t) (harer) med tiden t. Det er ikke muligt at løse disse analytisk (ved udtryk i elementære funktioner af t).
IV. Differentialligninger – 2. 1. ordens ligninger 333 2.17. Lineært system ☞ [LA] 15 Lineært system Definition 1 Ved et lineœrt differentialligningssystem (2 ligninger) med konstante koefficienter forstås dy1 dx = a11y1 + a12y2 + b1 dy2 dx = a21y1 + a22y2 + b2 En løsning er differentiable funktioner x ↦→ y1(x),x ↦→ y2(x) som indsat opfylder lignningerne. 2.18. Lineært system ☞ [LA] 15 Lineært system Definition 1 - matrixform For 2 × 2-matricen A = (aij), koefficientmatricen, og 2-søjlerne b = (bi), y(x) = (yi(x)) skrives differentialligningssystem eller dy1 dx dy2 = dx En løsning skrives dy = Ay + b dx a11 a12 y1 a21 a22 x ↦→ y(x) = y2 + y1(x) y2(x) b1 b2
Page 1:
CALCULUS "SLIDES" TIL CALCULUS 1 +
Page 4 and 5:
3. Generelle områder 201 4. Koordi
Page 7:
Forord "Slides" til forelæsningern
Page 10 and 11:
I. Differentiation - 1. Kontinuitet
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
I. Differentiation - 2. Partielle a
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
I. Differentiation - 3. Tangentplan
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
I. Differentiation - 4. Kædereglen
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
I. Differentiation - 5. Gradient 88
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
I. Differentiation - 6. Maksimum/mi
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
I. Differentiation - 7. Lagrangemet
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
II. Integration - 1. Dobbelt integr
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
II. Integration - 2. Itereret integ
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
II. Integration - 3. Generelle omr
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
II. Integration - 4. Koordinatskift
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
III. Potensrækker - 1. l’Hospita
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
III. Potensrækker - 2. Talfølger
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
III. Potensrækker - 3. Potensrækk
Page 282 and 283: III. Potensrækker - 3. Potensrækk
Page 298 and 299: III. Potensrækker - 4. Taylorpolyn
Page 311 and 312: 1. Grafiske/numeriske metoder IV Di
Page 313 and 314: IV. Differentialligninger - 1. Graf
Page 325 and 326: IV. Differentialligninger - 2. 1. o
Page 331: IV. Differentialligninger - 2. 1. o
Page 347 and 348: IV. Differentialligninger - 3. Gene
Page 365 and 366: 1. Vektorer og matricer V Matricer
Page 367 and 368: V. Matricer - 1. Vektorer og matric
Page 383 and 384:
V. Matricer - 1. Vektorer og matric
Page 385 and 386:
V. Matricer - 2. Lineære afbildnin
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
V. Matricer - 3. Lineære ligninger
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
Page 415 and 416:
Page 417 and 418:
Page 419 and 420:
V. Matricer - 4. Determinanter 419
Page 421 and 422:
Page 423 and 424:
V. Matricer - 4. Determinanter = (
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
1. Egenvektorer VI Egenvektorer og
Page 437 and 438:
VI. Egenvektorer og diagonalisering
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475:
Page 478 and 479:
VII. Skalarprodukt og projektion -
Page 480 and 481:
Page 482 and 483:
Page 484 and 485:
Page 486 and 487:
Page 488 and 489:
Page 490 and 491:
Page 492 and 493:
Page 494 and 495:
Page 496 and 497:
Page 498 and 499:
Page 500 and 501:
VIII. Appendiks - 1. Polære koordi
Page 502 and 503:
Page 504 and 505:
Page 506 and 507:
Page 508 and 509:
Page 510 and 511:
Page 512 and 513:
Page 514 and 515:
Page 516 and 517:
Page 518 and 519:
Page 520 and 521:
Page 522 and 523:
Page 524 and 525:
IX. Opgaver - 1. August 2002 524 1.
Page 526 and 527:
IX. Opgaver - 1. August 2002 526 Op
Page 528 and 529:
IX. Opgaver - 1. August 2002 528 In
Page 530 and 531:
Page 532 and 533:
IX. Opgaver - 1. August 2002 ⎡
Page 534 and 535:
IX. Opgaver - 1. August 2002 534 Do
Page 536 and 537:
IX. Opgaver - 1. August 2002 536 An
Page 538 and 539:
Page 540 and 541:
IX. Opgaver - 1. August 2002 540 y
Page 542 and 543:
Page 544 and 545:
IX. Opgaver - 1. August 2002 544 2
Page 546 and 547:
IX. Opgaver - 1. August 2002 546 fu
Page 548 and 549:
IX. Opgaver - 2. Januar 2003 548 2.
Page 550 and 551:
IX. Opgaver - 2. Januar 2003 550 3)
Page 552 and 553:
IX. Opgaver - 2. Januar 2003 552 z
Page 554 and 555:
IX. Opgaver - 2. Januar 2003 554 y
Page 556 and 557:
IX. Opgaver - 2. Januar 2003 556 hv
Page 558 and 559:
IX. Opgaver - 2. Januar 2003 558 y
Page 560 and 561:
Page 562 and 563:
IX. Opgaver - 2. Januar 2003 562 Re
Page 564 and 565:
IX. Opgaver - 2. Januar 2003 564
Page 566 and 567:
Page 568 and 569:
IX. Opgaver - 2. Januar 2003 568 De
Page 570 and 571:
Page 572 and 573:
IX. Opgaver - 3. Januar 2004 572 2)
Page 574 and 575:
IX. Opgaver - 3. Januar 2004 574 L
Page 576 and 577:
Page 578 and 579:
Page 580 and 581:
IX. Opgaver - 3. Januar 2004 580 Eg
Page 582 and 583:
IX. Opgaver - 4. August 2004 582 =
Page 584 and 585:
IX. Opgaver - 4. August 2004 584 gi
Page 586 and 587:
IX. Opgaver - 4. August 2004 586 vi
Page 588 and 589:
Page 590 and 591:
IX. Opgaver - 4. August 2004 590 L
Page 592 and 593:
Page 594 and 595:
IX. Opgaver - 5. Januar 2005 594 (t
Page 596 and 597:
Page 598 and 599:
Page 600 and 601:
IX. Opgaver - 5. Januar 2005 600 Gr
Page 603 and 604:
Litteratur • Arnold, Ordinary dif
Page 605 and 606:
0-række/søjle, 423 n-te afsnitssu
Page 607 and 608:
Identitetsmatricen, 383 Identitetsm
Page 609:
etningsafledede, 89, 102 retningsfe
show all

Web skærmformat. - Aarhus Universitet

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?