Please show all steps, thank you:
Problem C: Does there exist an analytic function f(z) in...
Please show all steps, thank you:
Problem C: Does there exist an analytic function f(z) in some
domain D with the real part u(x,y)=x^2+y^2?
Problem D: Is the function f(z)=(x-iy)^2 analytic in any domain
in C? Are the real part u(x,y) and the imaginary pary v(x,y)
harmonic in C? Are u and v harmonic conjugates of each other in any
domain?
Are the following function harmonic? If your answer is yes, find
a corresponding analytic function f...
Are the following function harmonic? If your answer is yes, find
a corresponding analytic function f (z) =u(x, y) + iv(x, y). v = (
2x + 1)y
For the given function u(x, y) = cos(ax) sinh(3y),(a >
0);
(a) Find the value of...
For the given function u(x, y) = cos(ax) sinh(3y),(a >
0);
(a) Find the value of a such that u(x, y) is harmonic.
(b) Find the harmonic conjugate of u(x, y) as v(x, y).
(c) Find the analytic function f(z) = u(x, y) + iv(x, y) in
terms of z.
(d) Find f ′′( π 4 − i) =?
The real part of a f (z) complex function is given as
(x,y)=y^3-3x^2y. Show the harmonic...
The real part of a f (z) complex function is given as
(x,y)=y^3-3x^2y. Show the harmonic function u(x,y) and find the
expressions v(x,y) and f(z). Calculate f'(1+2i) and write x+iy
algebraically.
a)Prove that the function
u(x, y) = x -y÷x+y
is harmonic and obtain a conjugate function...
a)Prove that the function
u(x, y) = x -y÷x+y
is harmonic and obtain a conjugate function v(x, y) such that
f(z) = u + iv is analytic.
b)Convert the integral
from 0 to 5 of (25-t²)^3/2 dt
into a Beta Function and evaluate the resulting function.
c)Solve the first order PDE
sin(x) sin(y)
∂u
∂x + cos(x) cos(y)
∂u
∂y = 0
such that u(x, y) = cos(2x), on x + y =
π
2
Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2),
u=1/3,-2/3,2/3. (a) Find the gradient...
Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2),
u=1/3,-2/3,2/3. (a) Find the gradient of f. ∇f(x, y, z) = (b)
Evaluate the gradient at the point P. ∇f(1, 0, 2) = (c) Find the
rate of change of f at P in the direction of the vector u. Duf(1,
0, 2) =
Find the directional derivative of the function f(x, y, z) = 4xy
+ xy3z − x...
Find the directional derivative of the function f(x, y, z) = 4xy
+ xy3z − x z at the point P = (2, 0, −1) in the direction of the
vector v = 〈2, 9, −6〉.
Find directional derivative of the function f(x, y, z) =
5x2 + 2xy – 3y2z at...
Find directional derivative of the function f(x, y, z) =
5x2 + 2xy – 3y2z at
P(1, 0, 1) in the direction v = i +
j – k .