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Solved: Harmonic functions A scalar-valued function is
Chapter 14, Problem 53AE(choose chapter or problem)
Harmonic functions A scalar-valued function \(\varphi\) is harmonic on a region D if \(\nabla^{2} \varphi=\nabla \cdot \nabla \varphi=0\) at ull points of D.
Show that if 4) is harmonic on a region D enclosed by a surface S. then \(\iint_{S} \nabla \varphi \cdot \mathbf{n} d S=0\).
Text Transcription:
nabla^2varphi = nabla cdot nabla_varphi = 0
iint_S nabla_varphi cdot n dS = 0
Questions & Answers
QUESTION:
Harmonic functions A scalar-valued function \(\varphi\) is harmonic on a region D if \(\nabla^{2} \varphi=\nabla \cdot \nabla \varphi=0\) at ull points of D.
Show that if 4) is harmonic on a region D enclosed by a surface S. then \(\iint_{S} \nabla \varphi \cdot \mathbf{n} d S=0\).
Text Transcription:
nabla^2varphi = nabla cdot nabla_varphi = 0
iint_S nabla_varphi cdot n dS = 0
ANSWER:Solu