Maths needed for a plasma physics and astrophysics module

AI Thread Summary
The discussion centers on a student pursuing a Master of Engineering in Electrical and Mechanical Engineering in the UK, who is taking an additional module in plasma and astrophysics for personal interest. The student seeks guidance on the necessary mathematical foundations for this advanced module, specifically mentioning their current focus on wave and heat equations, vector calculus, and the mathematics of electromagnetism and fluid dynamics. Key areas of mathematics highlighted include the need to understand and solve simultaneous partial differential equations, such as the Navier-Stokes equations related to fluid dynamics and conservation laws in physics. The discussion also points to available learning materials for further study in physics topics, emphasizing the importance of mastering these mathematical concepts for future coursework.
jemb
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Hi,

i'm studying a MEng Electrical and Mechanical engineering course in the UK. I've just started second year and have been approved by my advisor to take on an extra module next semester in plasma and astro physics.

This module is intended for 4th year physics students and won't count towards my actual degree credits. Its purely for my own interest in the subject.

My question is what maths am I going to need to be familiar with before I start? I've started looking at solutions to wave and heat equations, and covering vector calculus for electromagnetism and fluid dynamics.

Any thoughts on where I should go from there?
 
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Look at the mathematics of electromagnetic theory and hydrodynamics.

Ultimately one must be able to understand and solve sets of simultaneous partial differential equations, e.g., Navier-Stokes set (continuity - mass, momentum and energy), and conservation of charge. And one should be comfortable with time-depenedent, non-linear PDEs.

See our Learning Materials forum for tutorials in physics, including EM and plasma physics.
 
That sounds like plenty to be getting on with!

Hopefully if I learn the maths well it'll all stand me in good stead for later on in my course. It all seems pretty transferable.

Thanks for the recommendations!
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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