# Workbook guide +problem in Math. Phys.

In summary, the conversation was about the search for good workbooks for practicing various mathematical problems in the field of theoretical physics, specifically special functions, Bessel, Legendre, Laplace, integral transforms, ODEs, PDEs, and complex variables. The conversation also included a request for help with a specific problem involving the heat equation and heat conductivity. Tips were given to practice by answering physics forums and searching for homework assignments and solutions on websites like ocw.mit.edu.

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.

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.
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.

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

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.

#### Attachments

• heat diffusion.pdf
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@jasonRF yes indeed I am just looking to solve a lot of problems to become more fluent in the mathematics.