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II. Integration – 1. Dobbelt integral 170 1.11. Inddelinger i to retninger ☞ [S] 12.1 Double integrals over rectangles Figur y d c a b x (x ij , y ij ) Inddelt rektangel R = [a,b] × [c,d] 1.12. Gør det let Bemærkninger ☞ [S] 12.1 Double integrals over rectangles Med valg af brikhjørner som middelpunkter kan det bestemte integral af en funktion f : R → R skrives simplere 6 f(x,y)dA = lim m n f(xi,yj)∆A R m,n→∞ i=1 j=1
II. Integration – 1. Dobbelt integral 171 Hvis f(x,y) ≥ 0, så er volumen over rektanglet R og under grafen z = f(x,y) V = f(x,y)dA R 1.13. Riemann summer Definition ☞ [S] 12.1 Double integrals over rectangles Den dobbelte Riemann sum er m n R i=1 j=1 f(x ∗ ij,y ∗ ij)∆A Den bruges til at tilnærme dobbeltintegralet m n f(x,y)dA ≈ i=1 j=1 f(x ∗ ij,y ∗ ij)∆A 1.14. Riemann sum til beregning ☞ [S] 12.1 Double integrals over rect. . . Eksempel 1 R = [0,2] × [0,2], f(x,y) = 16 − x 2 − 2y 2 ≥ 0 Inddel hvert interval i halve og brug hjørner.
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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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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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