Problem

Let F = u(x, y) i − v(x, y) j be an incompressible, irrotational vector field of class C...

Let F = u(x, y) i − v(x, y) j be an incompressible, irrotational vector field of class C².

(a) Show that the functions u and v (which determine the component functions of F) satisfy the Cauchy–Riemann equations

(b) Show that u and v are harmonic, that is, that

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Solutions For Problems in Chapter 3.4

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