Let F = u(x, y) i v(x, y) j be an incompressible, irrotational vector field of class C2
Chapter 3, Problem 39(choose chapter or problem)
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 CauchyRiemann equations u x = v y , and u y = v x .(b) Show that u and v are harmonic, that is, that 2u x 2 + 2u y2 = 0 and 2v x 2 + 2v y2 = 0.
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