Define a harmonic function. (b)Prove whether u(x, y) = x² - 2xy + y² is a harmonic function on a set D = {(x, y) | x

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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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) | x
<y}.
(c)If and are harmonic functions, show
that
66
-
is solenoidal. (Hint: replace solenoidal by
incompressible)
Transcribed Image Text: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) | x <y}. (c)If and are harmonic functions, show that 66 - is solenoidal. (Hint: replace solenoidal by incompressible)
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