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.
If F = (2x +y?)i + (3y - 4x)j, evaluate
F.dr around the triangle C of Figure 1, (a) in the indicated
direction, (b) opposite to the indicated direction.
Ans. (a) – 14/3 (b) 14/3
(1,1)
(2,1)
(2,0)
Fig. 1
Fig. 2
Determine whether the functions y, and y, are linearly dependent on the interval (0,1)
y=1-2 sint, y, = 12 cos 2t
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. Since y, = ( )y½ on (0,1), the functions are linearly dependent on (0, 1).
(Simplify your answer.)
O B. Since y,= ( )y½ on (0,1), the functions are linearly independent on (0,1).
(Simplify your answer ).
OC. Since y, is not a constant multiple of y, on (0,1), the functions are linearly independent on (0, 1)
O D. Since y, is not a constant multiple of y, on (0,1), the functions are linearly dependent on (0,1).
Find the first partlal derivatives of the function.
w = -
u + v6
aw
au
aw
av
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
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