You are given a function f(x, z, y) of three variables, x, z, y. The following PDE
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According to this, in Laplace’s equation, the sum of second partials with respect to the variables in the function must equal zero.
Do the following equations satisfy Laplace’s equation?
fxx +fyy + fzz = 0
(a) f (x, y, z) = 4z2y – x2y – y3
(b) f (x, y) = x2 – y2
(c) f (x, y) = x3 – 3xy
(d) f (x, z, y) = x / (y + z)
Why is it that more than one function satisfies Laplace’s equation? Is it “good” to have many solutions to an equation in general?
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Related Book For
An Introduction to the Mathematics of financial Derivatives
ISBN: 978-0123846822
2nd Edition
Authors: Salih N. Neftci
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