While I agree that electrodynamics are generally more interesting, there are a number of interesting problems in modern physics that can be accurately modeled using electrostatics. So it's not all boring.
Think about the spacing of the slides at the opposite edge... what is the form of the spacing across the slide? So what is the condition for each minima? (hint: your equation is incomplete). Once you understand that it should be fairly straightforward.
The result given by Matlab will be correct, assuming you have adopted the same sign conventions when setting up the analytic FT. In particular the antisymmetry of X results in imaginary x.
Also, this looks like a QM problem, and as far as I know there's no reason you can't have an imaginary...
I'm not sure why you'd want the hollow shell case...
The way I'd do it is to use Gauss' law to work out the vector E for a uniformly charged sphere (it is a very simple expression)
Then do the superposition of the two spheres at a given point r, remembering to allow for change of coordinates...
You question is still a bit broad, but I'll bite.
Firstly I don't think the central difference is defined correctly... it should be
f'(x_0) = [f(x_0+h/2) - f(x_0-h/2)] / h
You're being asked to compute the convergence of the error of forward and central differentials, by comparing to the best...
Also, the original integral can alternatively be expressed in terms of Lommel functions, but again more complication and much less obvious from the outset.
Firstly I do not work directly with radar/sonar so I'm shooting off the cuff here, and very much depends on the details.
If you are going to be working on new techniques three things you will need to be familiar with are Fourier transforms, wave propagation and wave scattering. Fourier is a...