2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation, and find for each a function f(z) of which the given function is the real part. Show that the function v(x, y) (which you find) also satisfies Laplace's equation. 3 a. 3x²y - y³ b. e cos y

2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation, and find for each a function f(z) of which the given function is the real part. Show that the function v(x, y) (which you find) also satisfies Laplace's equation. 3 a. 3x²y - y³ b. e cos y

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 68PQ

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2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation,
and find for each a function f(z) of which the given function is the real part. Show that the function
v(x, y) (which you find) also satisfies Laplace's equation.
a. 3x²y - y³
b. e cos y

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