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Verify that the given function u is harmonic. u(x, y) = x² - y² The function u(x, y) has the following second order partial derivatives. Thus and the function is harmonic. Find v, the harmonic conjugate function of u. (Give your answer in terms of an arbitrary constant C.) v(x, y) = Form the corresponding analytic function f(z) = u + iv. f(x + y) =

Verify that the given function u is harmonic. u(x, y) = x² - y² The function u(x, y) has the following second order partial derivatives. Thus and the function is harmonic. Find v, the harmonic conjugate function of u. (Give your answer in terms of an arbitrary constant C.) v(x, y) = Form the corresponding analytic function f(z) = u + iv. f(x + y) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Verify that the given function u is harmonic. u(x, y) = x² - y² The function u(x, y) has the following second order partial derivatives. 8²u 8²u 0²u 02u Thus + and the function is harmonic. 0x² Oy2 Find v, the harmonic conjugate function of u. (Give your answer in terms of an arbitrary constant C.) v(x, y) = Form the corresponding analytic function f(z) = u + iv. f(x + y) = Deal =
Transcribed Image Text:Verify that the given function u is harmonic. u(x, y) = x² - y² The function u(x, y) has the following second order partial derivatives. 8²u 8²u 0²u 02u Thus + and the function is harmonic. 0x² Oy2 Find v, the harmonic conjugate function of u. (Give your answer in terms of an arbitrary constant C.) v(x, y) = Form the corresponding analytic function f(z) = u + iv. f(x + y) = Deal =
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