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 x 2 y − y 3
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 x 2 y − y 3
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.
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.
UNIT 1
1.Show that the function u=4xy-3x+2 is Harmonic. Construct the corresponding
analytic function
f (z) = u+iv in terms of z.
Find the domain of the following function.
X-2
/+1
f(x,y) = cos
Select the correct choice below and fill in any answer boxes within your choice.
A. {(x,y): x*
(Use a comma to separate answers as needed.)
B. {(x,y): y *}
(Use a comma to separate answers as needed.)
C. {(x,y): x* and y*|
(Use a comma to separate answers as needed.)
OD. R²
College Algebra with Modeling & Visualization (5th Edition)
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