Show that if v is a harmonic conjugate for u, then -u is a harmonic conjugate for v.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 18EQ
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3. Show that if u is a harmonic conjugate for u, then -u is a harmonic conjugate for v.
4. Show that the following functions are harmonic, and find all harmonic conjugates:
a) u = x³ 3xy² + 2xy + x,
d) u = e(y cos y + x siny),
Transcribed Image Text:3. Show that if u is a harmonic conjugate for u, then -u is a harmonic conjugate for v. 4. Show that the following functions are harmonic, and find all harmonic conjugates: a) u = x³ 3xy² + 2xy + x, d) u = e(y cos y + x siny),
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