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IV. Differentialligninger – 2. 1. ordens ligninger 344 2.39. Ingen egenværdier ☞ [LA] 15 Lineært system Eksempel 2 Betragt det lineære system Koefficientmatricen y ′ 1 = y1 − y2 y ′ 2 = y1 + y2 A = 1 −1 1 1 har karakteristisk polynomium λ 2 − 2λ + 2 med diskriminant −4 og dermed ingen egenværdier. 2.40. Ingen egenværdier ☞ [LA] 15 Lineært system Eksempel 2 - Løsning Ved brug af komplekse tal findes løsningen ved metoden med egenvektorer y(x) = C1e x cos x + C2e sin x x −sin x cos x Skrevet ud y1(x) = C1e x cos x − C2e x sin x y2(x) = C1e x sin x + C2e x cos x
IV. Differentialligninger – 2. 1. ordens ligninger 345 2.41. 1 egenværdi ☞ [LA] 15 Lineært system Eksempel 3 Betragt det lineære system y ′ 1 = 3y1 + y2 y ′ 2 = 3y2 Koefficientmatricen A = har egenværdi 3 og egenrum E3 = span(e1). 3 1 0 3 2.42. 1 egenværdi ☞ [LA] 15 Lineært system Eksempel 3 - Løsning Løsningen bestemmes ved metoden med egenvektorer y(x) = C1e 3x 1 + C2e 0 3x x 1 Skrevet ud Gør prøve! y1(x) = C1e 3x + C2e 3x x y2(x) = C2e 3x
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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 - 2. Lineære afbildnin
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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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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