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IV. Differentialligninger – 1. Grafiske/numeriske metoder 318 Retningsfelt y 1 0 1 1.14. Eulers metode ☞ [S] 7.2 Direction fields and Euler’s method Eulers metode For begyndelsesværdiproblemet y ′ = x + y, y(0) = 1 prøver vi at tilnærme løsningen y(x) med differentialet i små intervaller. I et givet punkt (xn,yn) vil differentialet være dy = (xn + yn)dx x
IV. Differentialligninger – 1. Grafiske/numeriske metoder 319 og y ≈ yn + (xn + yn)(x − xn) 1.15. Eulers metode ☞ [S] 7.2 Direction fields and Euler’s method Eulers metode y ≈ yn + (xn + yn)(x − xn) giver rekursionen For en inddeling på x-aksen tabellægges tilnærmelser til funktionsværdierne yn+1 = yn + (xn + yn)(xn+1 − xn) x0,x1,...,xn,xn+1,... yn ≈ y(xn) 1.16. Eulers metode ☞ [S] 7.2 Direction fields and Euler’s method Eulers metode Tabellæg løsning til y ′ = x + y, y(0) = 1
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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 - 2. Partielle a
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I. Differentiation - 3. Tangentplan
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 5. Gradient 88
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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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II. Integration - 2. Itereret integ
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II. Integration - 3. Generelle omr
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II. Integration - 4. Koordinatskift
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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III. Potensrækker - 2. Talfølger
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V. Matricer - 1. Vektorer og matric
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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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IX. Opgaver - 1. August 2002 524 1.
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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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