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. x + y
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. x + y
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.
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
x
b. e cos y
Q. 2 Apply Cauchy Riemann's equations to check whether the following function of a complex 10
CLO2
C4
number z is differentiable or not:
f(2) = : +7
If yes, find the derivative.
B.Verify that the real and imaginary parts of the following function satisfy the
equation and that deduce the analyticity of function
Caushy-Riemann
•f(z) = e*cosy+ie siny
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY