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II. Integration – 4. Koordinatskift 226 Et polært koordinatsystem bestemmer et kartesisk koordinatsystem. Polen og punktet med polære koordinater (1,0) bestemmer x-aksen og polen og punktet med polære koordinater (1, π 2 ) bestemmer y-aksen. y 1 O 1 r P(r cos( ), r sin( )) 4.3. Polær-kartesisk ordbog ☞ [S] Appendix H.1 Polar coordinates Sætning Givet et polœrt og tilhørende kartesiske koordinatsystem. Et punkt med polœre koordinater (r,θ) har kartesiske koordinater 1 x = r cos(θ), y = r sin(θ) Et punkt med kartesiske koordinater (x,y),x > 0 har polœre koordinater 2 r = x 2 + y 2 , θ = tan −1 ( y x ) x
II. Integration – 4. Koordinatskift 227 4.4. Lagkageområde ☞ [S] 12.4 Double integrals in polar coordinates Polært rektangel y = r=a (b cos ,b sin ) = r=b {(r,θ)|a ≤ r ≤ b,α ≤ θ ≤ β} {(x,y) = (r cos θ,r sinθ)|a ≤ r ≤ b,α ≤ θ ≤ β} 4.5. Lagkageområde ☞ [S] 12.4 Double integrals in polar coordinates 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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III. Potensrækker - 2. Talfølger
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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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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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