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ølgeligningen, 50 begrænset:, 269 begrœnsningen, 142, 147, 157 begyndelsesværdi, 312 begyndelsesværdiproblem, 347 begyndelsesværdiproblemet, 324 Beregning af determinant, 424, 425 bestemte integral, 164 bibetingelsen, 142, 147, 157 binomialrækken, 282 Cosinusrækken, 281 definitionsmængden, 19 definitionsmœngden, 11 Den geometriske række, 280 Den kommutative lov holder ikke, 380 Determinanten, 419, 421 diagonalisere, 459 diagonalmatrix, 383, 457 differentiabel, 63 Differentialet, 65 differentialligningen, 346 dimensionale koordinatvektorrum, 366 Distributive love, 370, 380 divergent, 257, 260, 265, 272 Dobbelt integralet, 169, 202 dobbelte Riemann sum, 171 Dobbeltintegralet, 204 egenrummet, 443 egentlig, 436 egentlig løsning, 432 egenværdi, 436 egenvektor, 436 Eksponentialrækken, 280, 283 enhedsvektor, 474 Enten-eller-princip (22), 412 Eulers formel, 518 fuldstændig løsning, 396 fuldstœndige løsning, 326 funktion af to variable, 10 Gør prøve, 418 geometriske række, 273 Grænseværdien, 19 gradienten, 98, 102 Grafen, 12 hastighedsfeltet, 353 Hesse matricen, 124, 125 homogen, 326 homogene part, 326, 334 homogent, 334, 396 hovedkvadratroden, 507 606
Identitetsmatricen, 383 Identitetsmatricen (enhedsmatricen), 457 ikke-nul (egentlige), 441 imaginærdel, 500 imaginære enhed, 500 imaginœre akse, 501 inhomogene, 326, 334 inhomogent, 396 invers matrix, 390 invertibel, 390 itererede integral, 186, 187 Jacobideterminanten, 431 Jakobimatricen, 80 karakteristiske polynomium, 441, 442 koefficienter, 282, 371 koefficientmatricen, 333 koefficientmatrix, 396 Kommutativ lov, 370 kompleks tal, 500 komplekse eksponentialfunktion, 518 komplekse logatitmefunktion, 520 komplekse plan, 500 komplekse tal, 344 komplekse trigonometriske funktioner, 521 konjugerede tal, 504 kontinuert i D, 21 Kontinuitet, 21, 22 konturlinjen, 12 konvergensintervallet, 284 konvergensradius, 284 konvergent, 257, 260, 265, 272 koordinat, 366 kritisk punkt, stationœrt punkt, 119 kvadratisk, 457 kvadratisk matrix, 383 løsning, 333, 346 løsningsrummet, 398 lœngden, normen, 473, 478 Lagrange multiplikator, 145, 148 Lagrange multiplikatorer, 157 Laplaces ligning, 50 ligevægt, 359 lineær afbildning, 385 lineære approximation, 59, 60 lineære ligninger, 395 lineœre 1. ordens differentialligning, 325 lineœrt differentialligningssystem, 333 lineariseringen, 59, 60 linearkombinationen, 371 Logaritmerækken, 281, 282 logistiske ligning, 322 lokal ekstremumsværdi, 117 lokal maksimumsværdi, 113 607
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 1. Kontinuitet
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I. Differentiation - 2. Partielle a
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I. Differentiation - 3. Tangentplan
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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III. Potensrækker - 3. Potensrækk
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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V. Matricer - 2. Lineære afbildnin
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V. Matricer - 3. Lineære ligninger
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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VII. Skalarprodukt og projektion -
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IX. Opgaver - 1. August 2002 524 1.
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IX. Opgaver - 1. August 2002 ⎡
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IX. Opgaver - 1. August 2002 546 fu
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