5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x, y), the harmonic conjugate of u. Form the corresponding analytic function f(z) = u + iv: (ii) u(x, y) = x³ – 3xy2 %3D

5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x, y), the harmonic conjugate of u. Form the corresponding analytic function f(z) = u + iv: (ii) u(x, y) = x³ – 3xy2 %3D

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.3: Implicit Differentiation

Problem 2E

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Question

5- Verify that the given function u is harmonic in an appropriate domain D. Find
v(x,y), the harmonic conjugate of u. Form the corresponding analytic function
f(z) = u + iv:
(ii) u(x, y) = x³ – 3xy?
(i..

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