Most relevant math subjects for Astrophysics

[HossamCFD]

Hi all,

I have a B.Sc. and M.Eng. in Mechanical Engineering and I decided to switch to Astrophysics for my Ph.D. (for no reason other than following my passion). I still have a year or so before beginning the Ph.D program and I am willing to use this period to do some self study in Math to compensate my lack of mathematical background comparing to someone who did his undergrad in physics. what are the most important mathematical topics in astrophysics (or in theoretical physics in general) ? I understand that ALL fields of mathematics are important in theoretical physics, but I am hoping for some prioritization. Any info is most appreciated.

To elaborate more on my background, I had a fairly good introduction to various fields of mathematics in my undergrad but the emphasis was all about calculus. Also my Master thesis was in Computational Fluid Dynamics which is all about numerical techniques for PDE's. Sometimes I even forget that there is more to Math than just Calculus.

 

[nicksauce]

Any area of astrophysics in particular?

 

[HossamCFD]

Any area of astrophysics in particular?

Well I'm not 100% sure of that yet, but probably computational relativistic astrophysics.

 

[nicksauce]

Well I'm not 100% sure of that yet, but probably computational relativistic astrophysics.

Well, some obvious math to cover would be numerical analysis, pdes and odes, Fourier analysis, and tensor analysis. If by "computational relativistic" you mean "general relativistic", then some differential geometry would be good, though I suspect you just mean high-energy. Hmm, I can't think of anything else...

 

[HossamCFD]

That is very encouraging. I am very familiar with all these topics except for differential geometry. And I am not sure whether I am going to study a general relativistic astrophysical problem.

Thanks for your replies