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Analytic Functions; Harmonic Functions; Laplace's Equation

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5. Let the function ... be analytic in a domain D that does not include the origin ...

13. ... state why the functions ... are harmonic in D and why ... is in face, a harmonic conjugate

11. ... Why must this satisfy Laplace's equation?

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Harmonic Functions and Cauchy-Riemann Equations

15. Determine whether or not the given function u is harmonic and, if So, in what region. If it is, find the most general conjugate function v and corresponding analytic function f (z). Express f in terms of z.

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