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IV. Differentialligninger – 1. Grafiske/numeriske metoder 316 Skitsen kaldes et retningsfelt. 1.10. Grafisk løsning ☞ [S] 7.2 Direction fields and Euler’s method Retningsfelt y 0 1 I punktet (x,y) tegnes et kort linjestykke med hældning y ′ (x) = x + y. En graf skitseres. 1 1.11. Grafisk løsning ☞ [S] 7.2 Direction fields. . . Eksempel - Retningsfelt dy dx = x3 y + e xy x
IV. Differentialligninger – 1. Grafiske/numeriske metoder 317 y 1 0 1 1.12. Grafisk løsning ☞ [S] 7.2 Direction fields and Euler’s method Retningsfelt For ligningen y ′ = x 2 + y 2 − 1 prøver vi at tilnærme grafen for løsningerne y(x) med små tangentstykker. I et givet punkt (x1,y1) vil en tangent have ligning y = y1 + (x 2 1 + y 2 1 − 1)(x − x1) 1.13. Grafisk løsning ☞ [S] 7.2 Direction fields and Euler’s method 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 - 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 - 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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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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