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II. Integration – 3. Generelle områder 202 3.2. 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] 3.3. Integralet i to variable Definition Givet rektanglet R = [a,b] × [c,d]. Dobbelt integralet af en funktion f : R → R er ☞ [S] 12.1 Double integrals over rect. . . 5 f(x,y)dA = lim m n R f(x m,n→∞ i=1 j=1 ∗ ij,y ∗ ij)∆A
II. Integration – 3. Generelle områder 203 Når grænseværdien eksisterer. 3.4. Fubini: Alle veje fører til Rom 4 Sætning (Fubinis sætning) ☞ [S] 12.2 Iterated integrals Lad R = [a,b] × [c,d] og antag f : R → R er kontinuert. Så er dobbeltintegralet lig de itererede integraler b d f(x,y)dA = f(x,y)dydx og R R a d b f(x,y)dA = f(x,y)dxdy 3.5. Generelle områder ☞ [S] 12.3 Double integrals over general regions Figur c c a
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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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1. Grafiske/numeriske metoder IV Di
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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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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