Workbook guide +problem in Math. Phys.

1. Sep 29, 2013

Hey I have a degree robotics and moved to theoretical physics so am still struggling to keep up with the mathematics. I was wondering if there are any good workbooks out there where I can just practice a lot of problems, mainly (special functions: Bessel, Legendre, Laplace, Integral transforms, ODEs PDEs and complex variables)?
Also some help with the following problem would be helpful:

If a cube of side length a originally at temp. T$_{0}$ is placed in a reservoir at temp. T=0 K, show the subsequent temp. is :

$T(x,t)$ = $T_0$ $\Sigma_{l,m,n}$ $64 \over lmn \pi^3$ $sin[ {{l \pi} \over{a}} x]$ $sin[ {{m \pi} \over{a}} y]$ $sin[ {{n \pi} \over{a}} z]$ $e^{-(l^2 + m^2 + n^2)({\pi \over a})^2 \kappa t}$

where $\kappa$ is the heat conductivity.

Any help or guidance on how to approach the solution would be much appreciated.

2. Sep 30, 2013

Mandelbroth

I'm not really a physics guy, but my initial reaction is to start with the heat equation.

$$\frac{\partial T}{\partial t}-\frac{\kappa}{\rho c_p}\nabla^2T=0.$$

As an aside, am I the only one here who sees that mess and automatically imagines Steve Irwin yelling "Crikey! Look at the size of that thing!" ? :rofl:

Edit: If you really want to get good at the math, what I've done for practice is stalk the forums and try to answer whatever questions I deem worth answering. It's actually rather effective.

3. Oct 1, 2013

jasonRF

Are you just looking for a bunch of good problems with some answers to check your work? Many university classes post homework assignments and solutions. Try
ocw.mit.edu

jason

4. Oct 2, 2013

Thanks for the tips, yeah answering physics forums seems like a good idea. I tried the solution.. maybe its something like this (attached pdf). but not sure about the subsequent temperature.

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5. Oct 2, 2013