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IV. Differentialligninger – 3. Generelle metoder 362 og F ′ (0) = k > 0: 0 Ustabil ligevœgt. F ′ (K) = −k: K Stabil ligevœgt. F ′ (P) = − 2k P + k K 3.28. Logistisk stabilitet ☞ [LA] 18 Stabilitet Eksempel 1 - figur P ′ Fasediagram P ′ = kP(1 − P K ) P
IV. Differentialligninger – 3. Generelle metoder 363 3.29. Lotka-Volterra stabilitet ☞ [LA] 18 Stabilitet Eksempel 2 For Lotka-Volterra systemet, a,b,k,r > 0, dR = kR − aRW er der to ligevægtsløsninger dt dW dt = −rW + bRW (R,W) = (0,0), (R,W) = (r/b,k/a) 3.30. Lotka-Volterra stabilitet ☞ [LA] 18 Stabilitet Eksempel 2 - fortsat I (R,W) = (0,0) er den lineære approximation som giver en ustabil ligevægt. dR = kR dt dW = −rW dt 3.31. Lotka-Volterra stabilitet ☞ [LA] 18 Stabilitet
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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 - 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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VII. Skalarprodukt og projektion -
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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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