Please show work. Let D be a region in C and let u(x, y) be a real-valued functi
ID: 3372648 • Letter: P
Question
Please show work.
Let D be a region in C and let u(x, y) be a real-valued function on D. We seek another real-valued function v(x, y) such that f(z) = u + iv is analytic, i.e. satisfies the Cauchy-Riemann equations. Equivalently, we want to find a function v such that which says that Vv is the vector field F = F satisfies the mixed partials condition exactly when u is harmonic. Conclude that, if D is simply connected, then F is a gradient vector field Delta v and hence that u is the real part of an analytic function.Explanation / Answer
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