4. (a) Define a harmonic function. (b) Prove whether u(x, y) = ² - 2xy + y² is a harmonic function on a set D={(x,y) |z

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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E
4. (a) Define a harmonic function.
(b) Prove whether u(x, y) = x² - 2xy + y² is a harmonic function on a set
D = {(x,y) | a <y}.
(c) If o andare harmonic functions, show that
V-Vo
is solenoidal. (Hint: replace solenoidal by incompressible)
Transcribed Image Text:E 4. (a) Define a harmonic function. (b) Prove whether u(x, y) = x² - 2xy + y² is a harmonic function on a set D = {(x,y) | a <y}. (c) If o andare harmonic functions, show that V-Vo is solenoidal. (Hint: replace solenoidal by incompressible)
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