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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

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

Advanced Engineering Mathematics
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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Subject : Mathematical Physics 2 Topic : Functions of a Complex Variable
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
Transcribed Image Text: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
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