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IV. Differentialligninger – 1. Grafiske/numeriske metoder 322 Eksempel 1 dy dx = 6x2 2y + cos(y) er separabel. Løsning (2y + cos(y))dy = 6x 2 dx Giver løsning bestemt ved ligningen 3 y 2 + sin(y) = 2x 3 + C 1.21. Logistisk ligning ☞ [S] 7.5 The logistic equation Eksempel 1. ordens differentialligningen 1 kaldes den logistiske ligning. Løsning Ligningen er separabel 2 dP dt = kP(1 − P K ) dP P(1 − P/K) = kdt
IV. Differentialligninger – 1. Grafiske/numeriske metoder 323 1.22. Logistisk ligning ☞ [S] 7.5 The logistic equation Eksempel - fortsat 2 dP P(1 − P/K) = kdt integreres til løsninger 4 P(t) = hvor A = K 1 + Ae −kt K − P(0) P(0) 1.23. Vækst ☞ [S] 7.4 Exponential growth and decay Definition dy 1 = ky dt Vækstligningen er separabel med løsninger dy y = kdt ln |y| = kt + C y = Ae kt
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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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II. Integration - 1. Dobbelt integr
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III. Potensrækker - 2. Talfølger
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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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