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IV. Differentialligninger – 1. Grafiske/numeriske metoder 314 1.6. Pendul ☞ [S] 7.1 Modelling with differential equations Pendul tilnærmet • t tid og x(t) udsving 3 Løsninger • x ′ hastighed • x ′′ = −k m x acceleration d2x k = − dt2 m x k x(t) = C1 cos( m t) + C2 k sin( m t) 1.7. Differentialligning ☞ [S] 7.1 Modelling with differential equations Generel ligning 4 y ′ = xy eller 4 Løsning dy = xy dx y = f(x) f ′ (x) = xf(x)
IV. Differentialligninger – 1. Grafiske/numeriske metoder 315 1.8. Differentier funktion ☞ [S] 7.1 Modelling with differential equations Eksempel 1 1 + cet y = 1 − cet er løsning til 4 y ′ = 1 2 (y2 − 1) Gør prøve y ′ = cet (1 − cet ) + (1 + cet )cet (1 − cet ) 2 2ce = t (1 − cet ) 2 1 2 (y2 − 1) = 1 2 (1 + ce t ) 2 − (1 − ce t ) 2 (1 − ce t ) 2 = 2ce t (1 − ce t ) 2 1.9. Grafisk løsning ☞ [S] 7.2 Direction fields and Euler’s method Retningsfelt For ligningen y ′ = x + y prøver vi at tilnærme graferne for løsningerne y(x) med små tangentstykker. I et givet punkt (x1,y1) vil en tangent have ligning I dette tilfælde y = y1 + y ′ (x1)(x − x1) y = y1 + (x1 + y1)(x − x1)
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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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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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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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