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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 де ди ди 21 ( - ) - 2 ( = +u дг дг дх дх

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

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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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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