A function (x, y, z) is said to be harmonic in a region D in space if
Question:
A function ƒ(x, y, z) is said to be harmonic in a region D in space if it satisfies the Laplace equation
throughout D.
a. Suppose that ƒ is harmonic throughout a bounded region D enclosed by a smooth surface S and that n is the chosen unit normal vector on S. Show that the integral over S of ∇ƒ · n, the derivative of ƒ in the direction of n, is zero.
b. Show that if ƒ is harmonic on D, then
Transcribed Image Text:
V²f = V.Vf= a²fa²fa²f + + dx² dy² dz² = 0
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a To show that the integral over S of n is zero we can use the divergence theorem The divergence the...View the full answer
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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