(a) Show that if v(x, y) is harmonic, so is u(x, y)= v(x2
Chapter 7, Problem 15(choose chapter or problem)
(a) Show that if v(x, y) is harmonic, so is u(x, y)= v(x2 y2,2xy). (b) Show that the transformation (x, y)(x2 y2,2xy) maps the rst quadrant onto the half-plane {y > 0}.(Hint: Use either polar coordinates or complex variables.)
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