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IV. Differentialligninger – 1. Grafiske/numeriske metoder 320 n xn yn 1 0.1000 1.1000 2 0.2000 1.2200 3 0.3000 1.3620 4 0.4000 1.5282 5 0.5000 1.7210 x0 = 0, y0 = 1 n xn yn 6 0.6000 1.9431 7 0.7000 2.1974 8 0.8000 2.4872 9 0.9000 2.8159 10 1.0000 3.1875 1.17. Eulers metode ☞ [S] 7.2 Direction fields and Euler’s method Eulers metode For begyndelsesværdiproblemet y ′ = x 2 + y 2 − 1, y(0) = 1 prøver vi at tilnærme løsningen y(x) med differentialet i små intervaller. I et givet punkt (xn,yn) vil differentialet være og dy = (x 2 n + y 2 n − 1)dx y ≈ yn + (x 2 n + y 2 n − 1)(x − xn) 1.18. Eulers metode ☞ [S] 7.2 Direction fields and Euler’s method Eulers metode
IV. Differentialligninger – 1. Grafiske/numeriske metoder 321 Tabellæg løsning til y ′ = x 2 + y 2 − 1, y(0) = 1 n xn yn 1 0.1000 1.0000 2 0.2000 1.0010 3 0.3000 1.0052 4 0.4000 1.0152 5 0.5000 1.0343 n xn yn 6 0.6000 1.0663 7 0.7000 1.1160 8 0.8000 1.1895 9 0.9000 1.2950 10 1.0000 1.4438 1.19. Separabel ligning ☞ [S] 7.3 Separable equations Definition En 1. ordens differentialligning 1 kaldes separabel. Løsning Integration 2 Fastlægger løsninger optil en konstant. dy = g(x)f(y) dx dy f(y) = g(x)dx 1.20. Separabel ligning ☞ [S] 7.3 Separable equations
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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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Litteratur • Arnold, Ordinary dif
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