Question: I'm currently working on my MS in CS and have developed an interest in astrophysics. Luckily one of my professors is a astrophysicist and is currently doing research through computational physics and he agreed to help me get started.

I'm currently reading through Tao Pang's "An Introduction to Computational Physics" ([TOC](http://www.physics.unlv.edu/~pang/cp2_cont.html)), but the book's lack of detail on the mathematical methods used leaves me pretty lost at times.

My question is, are there any books that cover the topics in a more in-depth fashion or any books that I could use as a reference for the mathematical methods?

EDIT: The best way to describe my mathematical background is that I've studied calculus, linear algebra and differential equations, but remember very little.

Answer: 
**Short answer**: No, at least not that I know of.

I'm a Computer Scientist who, for the past year and a half, has been working with Astrophysicists on writing faster simulation codes. I spent quite a bit of time looking for books on the topic to provide some sort of overview, and found nothing convincing.

Most of what I now know about Astrophysics, I learnt from asking Astrophysicists directly. There are a number of good review papers on specific topics, e.g. Daniel Price's papers on [SPH](http://en.wikipedia.org/wiki/Smoothed-particle_hydrodynamics), e.g. [here](http://scholar.google.ch/scholar?cluster=15225120919672653172&hl=en&as_sdt=0,5), or [Walter Dehnen's papers](http://scholar.google.ch/scholar?cluster=5726569702248161437&hl=en&as_sdt=0,5) on N-body solvers, e.g. [here](http://en.wikipedia.org/wiki/N-body_simulation), but I still rely on my colleagues in that field for the details.

What I think you should keep in mind, though, is that most of the interesting computational problems don't involve that much physics or even maths, but algorithms and data structures. Keep in mind that most physics codes (or books on physics codes) were written not by Computer Scientists, but by Physicists. That doesn't necessarily mean they are bad, but given the choice, would you rather buy a physics book written by a Computer Scientist, or by a Physicist?

As a Computer Scientist, you have an edge with regards to algorithms and data structures, and there are loads of low-hanging fruit there. In most of my own work in this area, I have not had to tweak the physics of any problem at all, just the algorithms implementing them. Simply getting the algorithms right can already lead to [massive speedups](https://www.dur.ac.uk/pedro.gonnet/?p=290).

**In summary**: If you have close collaborators who are Astrophysicists, rely on them to get the physics right, but keep in mind that you will probably be able to make the largest contributions in the *algorithms and data structures* used to implement said physics.
You might try: Bertil Gustafsson: *Fundamentals of Scientific Computing* to get an overview, and for a more encyclopaedic treatment of the mathematical methods Gander, Gander, Kwok: *Scientific Computing.*