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Verify that the following function is harmonic u(x, y) = -ey sin x - 2e siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.

Verify that the following function is harmonic u(x, y) = -ey sin x - 2e siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.

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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only part b please. thank you

(a) Express Log (34) in Cartesian form (x + iy). Justify all of your steps. (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e¯* siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.
Transcribed Image Text:(a) Express Log (34) in Cartesian form (x + iy). Justify all of your steps. (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e¯* siny. Find a harmonic conjugate v of u, namely a function v such that the function u(x, y) + iv(x, y) is an analytic function, such that v(0,0) = 4. Justify all of your steps.
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