Hi,
This is my first post here. I am preparing for an exam which is tomorrow and I am stuck on this one question that I don't even know how to start because I don't understand the method of images. Can someone please help?
The question is:
Apply the method of images to derive the solution
\(\displaystyle \displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0\)
from
\(\displaystyle \displaystyle \bigtriangledown^2 \phi (x,y,z) = 0\)
\(\displaystyle \phi(x,y,0) = f(x,y)\)
from the region \(\displaystyle - \infty < x < \infty, - \infty < y < \infty, 0 < z < \infty\)
Its hard for me to start because I dont really understand the method of images.
This is my first post here. I am preparing for an exam which is tomorrow and I am stuck on this one question that I don't even know how to start because I don't understand the method of images. Can someone please help?
The question is:
Apply the method of images to derive the solution
\(\displaystyle \displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0\)
from
\(\displaystyle \displaystyle \bigtriangledown^2 \phi (x,y,z) = 0\)
\(\displaystyle \phi(x,y,0) = f(x,y)\)
from the region \(\displaystyle - \infty < x < \infty, - \infty < y < \infty, 0 < z < \infty\)
Its hard for me to start because I dont really understand the method of images.