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IV. Differentialligninger – 3. Generelle metoder 360 Der er en oplagt udvidelse til differentialligningsystemer. 3.24. Ligevægt og stabilitet ☞ [LA] 18 Stabilitet Bemærkning 1 I en omegn af en ligevægt y(x) = b,F(b) = 0 kan det autonome begyndelsesværdiproblem tilnærmes med den lineære ligning hvor y(x) ≈ b + z(x). dy dx = F(y),y(x0) = b + ǫ dz dx = F ′ (b)z,z(x0) = ǫ 3.25. Ligevægt og stabilitet ☞ [LA] 18 Stabilitet Bemærkning 2 For en ligevœgt y(x) = b,F(b) = 0 for det autonome system gœlder F ′ (b) < 0: Stabil ligevœgt. F ′ (b) > 0: Ustabil ligevœgt. F ′ (b) = 0: Ingen konklusion. dy = F(y) dx
IV. Differentialligninger – 3. Generelle metoder 361 3.26. Ligevægt og stabilitet ☞ [LA] 18 Stabilitet Bemærkning 2 - figur y ′ Fasediagram y ′ = F(y) 3.27. Logistisk stabilitet ☞ [LA] 18 Stabilitet Eksempel 1 Den logistiske ligning har ligevægts løsninger dP dt = kP(1 − P K ) P(t) = 0, P(t) = K y
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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 - 7. Lagrangemet
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III. Potensrækker - 1. l’Hospita
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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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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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