Recent content by maddogtheman

Ok I think I realized my problem. My tutorial solved a slightly different DE for R(r) which resulted in the diffence of powers. Also for this problem I think the n=0 case takes on the solution A_0 + B_0*ln(r) which would give a final solution u(r,theta)=3+2ln(r)/ln(2). I'm going to bed, let me...

u(r,\vartheta) = A_0 + B_0 right?

Well n=0 has to be one right? I can't think of any others

Yeah I think you're right for some reason the -n-1 power is used in our class tutorial. Yes I understand how it was found and the principal of linear superposition. The second part of the expression is a constant because u is theta independent for the first set of boundary conditions.

Yeah I have and I think that leave's me with u(r,\vartheta) = \sum_{n=0}^\infty (A_n r^n + B_n r^{-n-1})(C_n cos(n\vartheta) + D_n sin(n\vartheta)) but I don't know how to apply the boundary conditions correctly

Homework Statement Solve Laplace's equation \nabla^2 u(r,\vartheta) =0 in an annulus with inner radius r_1 and outer radius r_2 . (a) For boundary conditions take u(1,\vartheta) = 3 and u(2,\vartheta) = 5. (b) What is the solution using this second set of boundary conditions...

Thanks can't believe I missed it

Homework Statement The Bessel function generating function is e^{\frac{t}{2}(z-\frac{1}{z})} = \sum_{n=-\infty}^\infty J_n(t)z^n Show J_n(t) = \frac{1}{\pi} \int_0^\pi cos(tsin(\vartheta)-n\vartheta)d\vartheta Homework Equations The Attempt at a Solution So far I...

doesn't make*

I assumed the basis to be orthogonal but I think it makes for a rigorous proof.

If you had an operator A-hat whose eigenvectors form a complete basis for the Hilbert space has only real eigenvalue how would you prove that is was Hermitian?

If x=cos(theta) how do you find what d/dx is in terms of d/d(theta)?

[SOLVED] Forth Order DiffEq I've recently come across the following differential equations. y''''+y=0 and y''''-y=0. Can differential equations such as these be solved with any technique other than guessing for the particular solutions? They seem very simular to trig's equation but are still...

Thanks Thanks I got it

Use the Fourier series technique to show that the following series sum to the quantities shown: 1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity I foudn the series to be: sum(1/(2n-1)^2,n,1,infinity) but I don't know how to prove the idenity. I don't know how to go about...