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3.) Consider the function u(x, y) = x cosh(x) cos(y) - y sinh(x) sin(y). a.) Show that this function is harmonic over the entire xy-plane. b.) Find the harmonic conjugate, v(x, y), for this function satisfying v(0, 0) = 0. c.) Your function f(x, y) = u(x, y)+iv(x, y) should be an entire func- tion of z. Rewrite the function completely in terms of z. 1

3.) Consider the function u(x, y) = x cosh(x) cos(y) - y sinh(x) sin(y). a.) Show that this function is harmonic over the entire xy-plane. b.) Find the harmonic conjugate, v(x, y), for this function satisfying v(0, 0) = 0. c.) Your function f(x, y) = u(x, y)+iv(x, y) should be an entire func- tion of z. Rewrite the function completely in terms of z. 1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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3.) Consider the function u(x, y) = x cosh(x) cos(y) - y sinh(x) sin(y). a.) Show that this function is harmonic over the entire xy-plane. b.) Find the harmonic conjugate, v(x, y), for this function satisfying v(0, 0) = 0. c.) Your function f(x, y) = u(x, y)+iv(x, y) should be an entire func- tion of z. Rewrite the function completely in terms of z. 1
Transcribed Image Text:3.) Consider the function u(x, y) = x cosh(x) cos(y) - y sinh(x) sin(y). a.) Show that this function is harmonic over the entire xy-plane. b.) Find the harmonic conjugate, v(x, y), for this function satisfying v(0, 0) = 0. c.) Your function f(x, y) = u(x, y)+iv(x, y) should be an entire func- tion of z. Rewrite the function completely in terms of z. 1
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