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
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
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.
Starting at point (1,0), you move along a distance t along a unit circle until you reach a terminal point at P(1213,513)P(1213,513). Find all six trignometric functions of t. Express your answer as a reduced fraction, NO DECIMALS!
Is the function u =
x3 – 3xy? harmonic? If your answer is yes, find a
corresponding analytic function.
NOTE: If the function is harmonic, use c as the arbitrary constant.
If the function is not harmonic, indicate that using the checkbox.
f(z) =
The function is not harmonic
The equation x²/3 + y²/3 = 4 describes an astroid:
a. Find an expression for in terms of x and y.
b. Find the equation of the tangent line to the astroid at the point (-3v3,1).
c. There are 4 points on the astroid where the tangent line is not defined. What are these 4 points?
What do you get if you evaluate at these points?
dx
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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