Let C be a positively oriented smooth curve with interior D. A function f : R² → R Pf, Pf dy? is called harmonic on D if it satisfies the partial differential equation dx? %3D for all points (, y) E D. If ƒ is harmonic on D, show that d.x fe dy = 0 he
Let C be a positively oriented smooth curve with interior D. A function f : R² → R Pf, Pf dy? is called harmonic on D if it satisfies the partial differential equation dx? %3D for all points (, y) E D. If ƒ is harmonic on D, show that d.x fe dy = 0 he
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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Let C be a positively oriented smooth curve with interior D. A function f : R? → R
is called harmonic on D if it satisfies the partial differential equation
= 0
dy?
for all points (, y) E D. If ƒ is harmonic on D, show that
fe,
dx
fe
= 0
dy
-
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