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.

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.