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II. Integration – 4. Koordinatskift 232 4.13. Cirkelring ☞ [S] 12.4 Double integrals in polar coordinates Eksempel 1 - figur y 2 {(r,θ)|1 ≤ r ≤ 2,0 ≤ θ ≤ π} 1 2 4.14. Integral over en cirkelring ☞ [S] 12.4 Double integrals in polar . . . Eksempel 1 - fortsat x
II. Integration – 4. Koordinatskift 233 Givet funktionen på halvcirkelringen I polære koordinater er f(x,y) = 3x + 4y 2 R = {(x,y)|0 ≤ y, 1 ≤ x 2 + y 2 ≤ 4} f(r cos θ,r sinθ) = 3r cos θ + 4(r sin θ) 2 4.15. Integral over en cirkelring ☞ [S] 12.4 Double integrals in polar . . . Eksempel 1 - fortsat Dobbeltintegralet over {(r,θ)|1 ≤ r ≤ 2,0 ≤ θ ≤ π} beregnes ved polært koordinatskift β b f(x,y)dA = f(r cos θ,r sinθ)rdr dθ Det itererede integral R R π f(x,y)dA = 0 α a 2 (3r cos θ + 4r 1 2 sin 2 θ)rdr dθ 4.16. Integral over en cirkelring ☞ [S] 12.4 Double integrals in polar . . .
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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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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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