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34. Consider a two-dimensional Cartesian coordinate system and a two-dimensional uv-system with t...
34. Consider a two-dimensional Cartesian coordinate system and a two-dimensional uv-system with the coordinates related by y = (1/2)(112-U2). In general, Laplace's equation in two dimensions can be written as with ох ду Zi (a) In the xy-plane, sketch lines of constant u and constant v. (b) Express Laplace's equation using the uw-coordinates. (c) Use the method of separation of variables to separate Laplace's equation in the v-system and obtain the general solution for ų'(u, u).
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E liminaing : If y is censhank is An en レ2 (A Ir i canstant, it 's an e probela →え u, v) o = av2 Laplace e in this werdinate gstam i same ar that in Cartetian coordinaterahan of vari doles Ψ(u,v): f(n) g(v) uu 2 du 3 du 2 & he goneral soln. r(u,v)
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