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IV. Differentialligninger – 3. Generelle metoder 354 W 100 0 1000 Hastighedsfeltet 3.16. Eulers metode ☞ [S] 7.6 Predator-prey systems Eksempel 1 - Eulers metode For Lotka-Volterra systemet k = 0.08,a = 0.001,r = 0.02,b = 0.00002 dR dt = 0.08R − 0.001RW R
IV. Differentialligninger – 3. Generelle metoder 355 dW = −0.02W + 0.0002RW dt prøver vi at tilnærme løsningen med differentialet. I et givet punkt (Rn,Wn) vil differentialet være dR = (0.08Rn − 0.001RnWn)dt dW = (−0.02Wn + 0.0002RnWn)dt 3.17. Eulers metode ☞ [S] 7.6 Predator-prey systems Eksempel 1 - Eulers metode Tabellæg løsning til R = 1000 og W = 75 månedsvis: n Rn Wn 0 1000 75 1 1005 75 2 1010 75 3 1015 75 4 1020 75 5 1025 75 6 1030 75 n Rn Wn 7 1035 75 8 1040 75 9 1045 75 10 1050 75 11 1055 75 12 1060 75 13 1065 76 n Rn Wn 14 1069 76 15 1074 76 16 1079 76 17 1083 76 18 1087 76 19 1091 76 20 1095 76 3.18. Grafisk ☞ [S] 7.6 Predator-prey systems Eksempel
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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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II. Integration - 1. Dobbelt integr
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II. Integration - 2. Itereret integ
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II. Integration - 3. Generelle omr
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II. Integration - 4. Koordinatskift
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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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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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VIII. Appendiks - 1. Polære koordi
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IX. Opgaver - 1. August 2002 524 1.
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IX. Opgaver - 5. Januar 2005 594 (t
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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etningsafledede, 89, 102 retningsfe
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