Find the second-order partial derivatives of f(x,y,z) with respect to x, y, and z, respectively.
Find the second-order partial derivatives of f(x,y,z) with respect to x, y, and z, respectively.
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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Question
Transcribed Image Text:The three-dimensional Laplace equation -
-1/6
Z f F f F f
=0 is satisfied by steady-state temperature distributions T=f(x,y,z) in space, by gravitational potentials, and by electrostatic potentials. Show that the function satisfies the three-dimensional Laplace equation.
f(x,y,z)= (x² + y² +z²)¯
Transcribed Image Text:Find the second-order partial derivatives of f(x,y,z) with respect to x, y, and z, respectively.
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