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I. Differentiation – 4. Kædereglen 80 er Jakobimatricen følgende m × n-matrix ⎛ du(g) = ⎜ ⎝ ∂g1 ∂u1 . ∂gm ∂u1 4.19. Kædereglen ☞ [LA] $ 2.2 Kædereglen i matrix-formulering Sætning For differentiable afbildninger er sammensætningen R n ... . .. ... ∂g1 ∂un . ∂gm ∂un ⎞ ⎟ ⎠ g −−−−→ Rm f −−−−→ Rp R n f◦g −−−−→ R p differentiabel og Jakobimatricen er matrixproduktet du(f ◦ g) = d g(u)(f)du(g) 4.20. Matricer er godt ☞ [S] 11.5 The chain rule Eksempel 5 (Matrixform) u = x 4 y + y 2 z 3 x = rse t , y = rs 2 e −t , z = r 2 ssin t
I. Differentiation – 4. Kædereglen 81 Beregn us. d(u) = ur us ut = ⎛ ux uy uz ⎝ xr xs xt yr ys yt zr zs zt 4.21. Matrixprodukt ☞ [S] 11.5 The chain rule Eksempel 5 (Matrixform) - fortsat Svaret er u = x 4 y + y 2 z 3 , x = rse t , y = rs 2 e −t , z = r 2 ssin t ur us ut ⎛ = 4x3y x4 + 2yz3 3y2z2 ⎝ ⎞ ⎠ set ret rset s2e−t 2rse−t −rs2e−t 2rssin t r2 sint r2scos t us = 4x 3 yre t + (x 4 + 2yz 3 )2rse −t + 3y 2 z 2 r 2 sin t 4.22. Test matrixform ☞ [S] 11.5 The chain rule ⎞ ⎠
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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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