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Jan 02, 21 · Exercise 1571 Let a transformation T be defined as T(u, v) = (x, y) where x = u v, y = 3v Find the image of the rectangle G = {(u, v) 0 ≤ u ≤ 1, 0 ≤ v ≤ 2} from the uv plane after the transformation into a region R in the xy plane Show that T is a onetoone transformation and find T − 1(x, y) Hint%' %' W & % Ym^% V Y\ \%W\T % %' %' W vu}XVX& %DY v W T %^ ( W kY\ ^% y%D %D W £Y\ gT V Ym D ú^ g_ 0 yVX \W &(%DY0VX %e W Y VXW Ï úi =ÏX_ 1 »____ ~ _ _ _ , "_ _ t in J __,__ _ 92_~ ˘,__ ˝

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6 @ " aWhere Φ is the fundamental solution of Laplace's equation and for each x 2 Ω, hx is a solution of (45) We leave it as an exercise to verify that G(x;y) satisfies (42) in the sense of distributions Conclusion If u is a (smooth) solution of (41) and G(x;y) is the Green's function for ΩSep 23, 15 · Penyajian Dalam Koordinat Kartesius z = f(x,y) atau g(x,y,z) = 0 Misalnya z = 222 zyx atau x2 y2 z2 a2 = 0 x2 y2 z2 = a2 merupakan luasan dari bola dengan jarijari a dan berpusat di titik O(0,0,0) z a a y a x b Penyajian dalam bentuk fungsi vektor r(u,v) = x(u,v) i y(u,v) j z(u,v) k , (u,v) ∈ R CONTOH 1

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