# Search results

1. ### Estimating Rotational Temperature

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

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...
3. ### Use the Fourier transform directly to solve the heat equation

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...
4. ### Solve the Dirichlet problem for the heat equation

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?
5. ### Solve the Dirichlet problem for the heat equation

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...
6. ### Solve the Dirichlet problem for the heat equation

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...
7. ### Solve the Dirichlet problem for the heat equation

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...
8. ### Solve the Dirichlet problem for the heat equation

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...
9. ### Can someone explain this equality to me (complex variables)

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...
10. ### Need help finding a Laurent Series

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}
11. ### Need help finding a Laurent Series

so just f(z)=\sum_{n=0}^{\infty}\frac{(-1)^{n}(z-1)^{n-1}}{2^{n+1}},\: |z-1|<2
12. ### Need help finding a Laurent Series

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}}
13. ### Need help finding a Laurent Series

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...
14. ### Leibniz rule for differentiating an integral w.r.t a parameter

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.
15. ### Leibniz rule for differentiating an integral w.r.t a parameter

wait. am I messing up the chain rule here?
16. ### Leibniz rule for differentiating an integral w.r.t a parameter

sorry. I can type stuff out from now on. I'm confused by your primed notation now. what does that mean? even accounting for the negative sign I missed, I do not see how these can be equal, because one I am differentiating wrt x and the other one I am differentiating wrt t. u_{tt}=\frac{c^2}{2c}...
17. ### Leibniz rule for differentiating an integral w.r.t a parameter

see on the last two lines, I don't think I have an equality here? also the denominator in the last line is a typo. I know it should be c^2/2c

19. ### Leibniz rule for differentiating an integral w.r.t a parameter

ok, so first of all, how can you say the integral in the general formula is zero? because F is a function of y only? second, working this all out, I get something that looks like the wave equation kinda, but I don't see how I exactly haveu_{tt}=c^2u_{xx} Is it okay if I just upload an image...
20. ### Leibniz rule for differentiating an integral w.r.t a parameter

so the y still didn't do much for me. If I have g(y only), then how all of a sudden I have g(b(t),t)?
21. ### Leibniz rule for differentiating an integral w.r.t a parameter

Homework Statement I have the functionu(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xiwhere g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation. Homework Equations My prof gave me the...
22. ### Having trouble with CSC assignment. Trying to make an array of Strings

Homework Statement I need to write a program that takes a text file, and looks for how many unique words it has, as well as the number of times they occur in the file. Homework Equations None The Attempt at a Solution public static void main(String[] args) throws FileNotFoundException...
23. ### Having trouble with this definition of a connected set

I am not self-studying. I agree that this book is horrible. It used no formatting whatsoever up until the current edition, which bolds theorems. It has virtually no whitespace between different concepts. It is basically a collection of formulas. I have had to manually box the important ones to...
24. ### Having trouble with this definition of a connected set

Homework Statement My textbook gives me this definition of a connected set. http://media.newschoolers.com/uploads/images/17/00/69/80/76/698076.png [Broken] I have been working through my practice problems and I got to one that asked me to sketch the set given by|z+2-i|=2and note whether it is...
25. ### Is there any symmetry I can use to find this Fourier sine series?

Homework Statement I am going over a practice exam, and I need to find the FSS of f(x)=x(\pi^2-x^2) Homework Equations f(x) \sim \sum^\infty_{n=1}a_n sin\left(\frac{n \pi x}{L}\right) a_n=\frac{2}{L}\int^L_0 f(x)sin\left(\frac{n\pi x}{L}\right)dx The Attempt at a Solution I think I...
26. ### Insulated boundary for circular laplace equation?

so I was initially wrong about the time derivative, but have since corrected it to the formula above. Now I think that in this situation, whatever the normal unit vector to the boundary is, it would be perpendicular to the radial vector. if \hat{n}=\hat{\theta} then I would get\frac{\partial...
27. ### Insulated boundary for circular laplace equation?

u is temperature here. also that lambda is supposed to be the gradient operator. on a sidenote, what is the latex syntax for that? anyways in this situation insulated would mean the heat flux across the boundary = 0
28. ### Insulated boundary for circular laplace equation?

ok I now know that\Lambda u(r,\theta)\cdot \hat{n}=0where \hat{n} is an outward pointing unit normal vector. how do I determine \hat{n}?
29. ### Insulated boundary for circular laplace equation?

Homework Statement Consider the Laplace’s equation, ∆u(r,θ) = 0, inside the quarter-circle of radius 2 (0 ≤ θ < π, 0 ≤ r ≤ 2), where the boundary θ is insulated, and u(r,\theta/2)=0 Show that the insulated boundary condition can mathematically be expressed as \frac{\partial u}{\partial...
30. ### Using a Fourier Cosine Series to evaluate a sum

ok. I don't really have time to show my work, but I ended up with π^2/6. Is this the correct answer? the trick I didn't get was that part with the s/4