6. Suppose that u is a harmonic function and that v is a harmonic conjugate of u. Show that Ә ди де ди ди 21 ( - ) - 2 ( = +u дг дг дх дх

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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6. Suppose that u is a harmonic function and that v is a harmonic conjugate of u. Show that
Ә ди ди
+u
( Эт) - 1 (
дх
ди du
дх ду Әх дх
7. Suppose that f = u +iv is analytic and not identically constant.
a) Show that ue is the real part of an analytic function.
b) Show that u2+2 cannot be the real part of any analytic function.
Transcribed Image Text:6. Suppose that u is a harmonic function and that v is a harmonic conjugate of u. Show that Ә ди ди +u ( Эт) - 1 ( дх ди du дх ду Әх дх 7. Suppose that f = u +iv is analytic and not identically constant. a) Show that ue is the real part of an analytic function. b) Show that u2+2 cannot be the real part of any analytic function.
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