Recent content by richyw

thanks! I think initially I forgot to square the internuclear distance which gave me a really weird result. Good luck with your studying!

Homework Statement An R-branch of a band of a ^1\Sigma - ^1\Sigma of CO has its maximum intensity at J'=11. The internuclear distance is 1.1 Ǻ. Estimate the rotational temperature. Homework Equations My notes don't even really define what rotational temperature is. They say that the...

Homework Statement Use the Fourier transform directly to solve the heat equation with a convection term u_t =ku_{xx} +\mu u_x,\quad −infty<x<\infty,\: u(x,0)=\phi(x), assuming that u is bounded and k > 0. Homework Equations fourier transform inverse Fourier transform convolution thm The...

so if I can solve the equation with u(x,0)=0 and u(0,t)=u(2\pi,t)=e^{0t} and solve u(x,0)=cos(x) and u(0,t)=u(2\pi,t)=0 and add the solutions together?

ok I am completely and utterly lost on using the eigenfunction expansion method. to solve this problem. I get the equation. I'm going to type out everything I have done. Keep in mind I have never seen the eigenfunction expansion being used, there are no worked examples in my textbook as far as I...

Thanks, I did do up to the eigenfunction expansion (and attempted that) before I posted here. Of course I want to do the work, but I was not sure if I was even on the right track!:smile: could you explain to me why I don't have eigenfunction \phi_n(x) =\sin\left( \frac{n x}{2} \right)and...

yes it's supposed to be a ut I don't know what I have learned about this type of question. I don't think I can use a general formula like I could when I had homogenous BC and a homogenous PDE. There is a chapter in my book which shows how to switch a PDE with time-dependent non-homogenous BC...

Homework Statement Solve the Dirichlet problem for the heat equation u_y=u_{xx}\quad 0<x<2\pi, \: t>0u(x,0)=\cos xu(0,t)=u(2\pi,t)=e^{-t} Homework Equations The Attempt at a Solution I have no idea what to do here. It seems to me like it's a mix of the solutions we learned. I...

Homework Statement I hate to upload the whole problem, but I am trying to evaluate an indefinite integral, and I can follow the solution until right near the end. The example says that for a point on C_R|e^{-3z}|=e^{-3y}\leq 1. I don't understand how they can say this. Below is the question...

is this correct? for 2 < |x-1|< ∞ I got \sum^\infty_{n=0}\frac{2^n(-1)^n}{(z-1)^{n+2}} and for 0 <|z| < 1 I got \sum^\infty_{n=0}-z^{2n}

so just f(z)=\sum_{n=0}^{\infty}\frac{(-1)^{n}(z-1)^{n-1}}{2^{n+1}},\: |z-1|<2

i'm still quite confused. I don't really remember from calculus how to get series expansions that aren't around z=0. I tried \frac{1}{2}\sum_{n=0}^{\infty}(-1)^n\left(\frac{z-1}{2}\right)^n=\sum_{n=0}^{\infty}\frac{(-1)^n(z-1)^n}{2^{n+1}}

Homework Statement Let f(z) = \frac{1}{z^2-1}. Find Laurent Series valid for the following regions. • 0<|z−1|<2 • 2<|z−1|<∞ • 0<|z|<1 Homework Equations \frac{1}{1-z}=\sum^{\infty}_{n=0}z^n,\: |z|<1 f(z)=\sum^{\infty}_{n=0}a_n(z-z_0)^n+\sum^{\infty}_{n=1}b_n(z-z_0)^{-n} The Attempt at a...

ok. I see where I went wrong with the chain rule now, I had to write the chain rule in leibniz notation (with ANOTHER dummy variable) and now I think I have the answer. Thanks a lot for your help.It seems so easy now. Although I guess it's always easy once you have figured it out haha.

wait. am I messing up the chain rule here?