- #1

- 464

- 0

## Homework Statement

My question involves the mid-point in deriving some of the equations to solve Laplace's equation in rectangular coordinates. The question may no make sense as it isn't problem specific. I can provide boundary values if necessary - just let me know.

## Homework Equations

I've included a photo of how the example problem is broken up. For my question we'll choose subproblem #1.

[tex]u(x,y)=\sum^{\infty}_{n=1} A_{n} sin \frac{n \pi x}{a}sinh\frac{n\pi(b-y)}{a}[/tex]

[tex]A_{n}= \frac{2}{a sinh \frac{n \pi b}{a}} \int^{a}_{0} f(x) sin \frac{n \pi x}{a} dx[/tex]

## The Attempt at a Solution

I don't understand how I get from the summation to the integral so I can solve for A

_{n}. I see the pattern and transform the four summations in the example, but I'd really like to know the how/why it's done.

Let me know if I need to include anymore information as I don't have much regarding the actual problem.