maths

eigenvalues and eigenfunctions. who knows about such things?

also, how do you arive at bessel functions? are they derived from geometry like trig functions. I know bessel intersects with the horizontal axis every pi units, but that's about it.

uh, eigenvalues and eigenfunctions are generally an easy concept, with some hugely useful properties.

Bessel's functions, in the only manner I've come across them, are the result of an application of Sturm-Liouville Theory to the 2D wave equation.

Bessel functions are the solutions of Bessel's equation, and are defined as such I believe. Bessel's equation is generally solved using series methods.

I remember that they're used in NMR for something.

say we have a function u(x,t) and a differential equation such as u_tt=u_xx we now assume that u(x,t)=g(x)*h(t) gives us a solution to the equation.  Now we get g*h''=g''*h or h''/h=g''/g  Since h''/h depends only upon t and g''/g depends only upon x, for them to be equal, they must be constant, so we get h''/h=g''/g=λ.  λ will be your eigenvalues (which you will determine using the boundary conditions) solutions to the equation using eigenvalue λ are the eigenfunctions.

>>5
>λ

I think my other car may be a cdr, you guys.

The eigenvalues of a matrix A are defined to be the set of values m such that det(mI-A)=0. For an operator, this turns into the spectrum--the values of m such that (mI-A) is noninvertible.

Google it.

>>6
gb2/bed, Alonzo.