Recent content by bobcat817

Homework Statement Consider a traveling wave u(x,t) =f(x - at) where f is a given function of one variable. (a) If it is a solution of the wave equation, show that the speed must be a = \pm c (unless f is a linear function). (b) If it is a solution of the diffusion equation, find f and show...

Thanks for the tex advice. This does clarify things a bit, but I have a few more questions. To begin with, can you give me an example of "patching" together two different solutions to get a new one? I think I am following but I'm not entirely sure. Also, u(x,y)= constant because a function...

Homework Statement (a) Solve the equation yu_{x} + xu_{y} = 0 with the condition u(0,y) = e^{-y^{2}}. Okay. My tex has gone wrong. Those are supposed to be subscripts in the the equation. I'm not sure why they aren't. (b) In which region of the xy plane is the solution uniquely...

I suppose I should do a separate case for p=0.

Oh yes. I am quite certain that the inequality is right. Doing a few test cases shows that it is the correct inequality. So, basically, I end up with: -1<p\leq0 Then letting p=|p| and f'(x)=y\frac{1}{x^{p}}-\frac{1}{(1+x)^{p}}. And since x\geq0 for all x, and since x<x+1 for all x...

Homework Statement Let y be a fixed real number satisfying 0<y\leq1. Prove that (1+x)^{y}\leq1+ x^{y} for all x\geq0. Homework Equations I'm not sure. The Attempt at a Solution The hint given with the problem states that the derivative of x^{y} is yx^{y-1}. My first thought is...

Homework Statement Let {a_{n}}^{\infty}_{n=1} be a sequence of real numbers that satisfies |a_{n+1} - a_{n}| \leq \frac{1}{2}|a_{n} - a_{n-1}| for all n\geq2 Homework Equations The Attempt at a Solution So, I know that it suffices to show that the sequence is...

Thank you very much. That's what I did initially, but I wasn't sure if that was the right method.

Homework Statement An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube)...