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. y ( 1 − x ) 2 + y 2 B
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. y ( 1 − x ) 2 + y 2 B
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
Complex Variables
as:
Given the following complex function expressed
w = f(z) = 6z² + 8z + 20-j22
a. Determine u and v
b. Calculate f(1-15). Express your answer in rectangular form.
c. Determine the derivative of f(z) at z = (1 + j2). Express your
answer in rectangular form.
d. Determine if the complex function f(z) is analytic or not analytic.
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