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IV. Differentialligninger – 3. Generelle metoder 348 Differentialligningen dy dx = x3y + e xy har løsningskurver igennem ethvert (x0,y0) ∈ R × R. Løsninger kan ikke umiddelbart udtrykkes ved kendte elementære funktioner. 3.6. Elementære funktioner ☞ [LA] 17 Generel ligning Eksempel 2 Den entydigt bestemte løsning til begyndelsesværdiproblemet er eksponentialfunktionen dy = y, y(0) = 1 dx y(x) = e x 3.7. Elementære funktioner ☞ [LA] 17 Generel ligning Eksempel 2 - fortsat Den entydigt bestemte løsning til begyndelsesværdiproblemet dy1 dx dy2 dx = −y2 = y1 y1(0) = 1, y2(0) = 0
IV. Differentialligninger – 3. Generelle metoder 349 er de trigonometriske funktioner y1(x) = cos x y2(x) = sinx 3.8. Grafisk løsning ☞ [S] 7.2 Direction fields. . . ; [LA] 17 Generel ligning Eksempel 1 - Retningsfelt dy dx = x3 y + e xy y 1 0 1 3.9. Logistisk ligning grafisk ☞ [S] 7.5 The logistic equation Eksempel x
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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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II. Integration - 3. Generelle omr
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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V. Matricer - 2. Lineære afbildnin
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V. Matricer - 2. Lineære afbildnin
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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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