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IV. Differentialligninger – 3. Generelle metoder 352 I et givet punkt (Pn,tn) vil differentialet være dP = 0.08Pn(1 − Pn 1000 )dt og P ≈ Pn + 0.08Pn(1 − Pn 1000 )(t − tn) 3.12. Eulers metode ☞ [S] 7.5 The logistic equation Eulers metode Tabellæg løsning til dP P = 0.08P(1 − ), P(0) = 100 dt 1000 n tn Pn 1 10.0 172.0 2 20.0 285.9 3 30.0 449.3 4 40.0 647.2 5 50.0 829.9 n tn Pn 6 60.0 942.8 7 70.0 985.9 8 80.0 997.0 9 90.0 999.4 10 100.0 999.9 3.13. Grafisk ☞ [S] 7.6 Predator-prey systems Eksempel For Lotka-Volterra systemet dR dt = kR − aRW
IV. Differentialligninger – 3. Generelle metoder 353 dW = −rW + bRW dt er hastighedsfeltet i RW -planen givet ved vektorerne dR dW , = (kR − aRW, −rW + bRW) dt dt 3.14. Grafisk ☞ [S] 7.6 Predator-prey systems Eksempel 1 For Lotka-Volterra systemet k = 0.08,a = 0.001,r = 0.02,b = 0.00002 dR = 0.08R − 0.001RW dt dW = −0.02W + 0.0002RW dt tegnes hastighedsfeltet i RW -planen. 3.15. Grafisk ☞ [S] 7.6 Predator-prey systems Eksempel 1 - figur
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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 - 3. Tangentplan
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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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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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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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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