Topic Ideas for Electrodynamics Math Methods Course

AI Thread Summary
For a mathematical methods course focused on electrodynamics, suggestions include studying Fourier analysis, particularly Fourier series, which is suitable for undergraduate levels. Vector calculus concepts like divergence, gradient, and curl should be approached from a physics perspective to enhance understanding. Additionally, a basic introduction to tensor calculus may be beneficial. Resources such as Landau & Lifshitz can provide foundational knowledge in electrodynamics. Exploring these topics will prove useful for future studies in the field.
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For a mathematical methods course, the end of year assignment is to study and present a topic in mathematics of my choice. I'd like to pick something directly related to electrodynamics that will prove to be useful later. However, I have very little idea of what is used in electrodynamics! Does anyone have a suggestion?

This is a sophomore/junior level course. My mathematics background so far is Calc 1,2, multivariable, vector, and diff. eqs.

Thank you very much for your time!
 
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I'm not sure whether you are up to it, but Fourier analysis would fit right in.
 
Fourier series would probably be enough for an undergraduate level.
Vector calculus (div, grad, curl) from a physics, rather than a mathematical point of view would also be good.
 
Maybe some rudimental tensor calculus? Our electrodynamics course was based on Landau&Lifshitz.
First google result: link. This is fairly sufficient and not much for an undergraduate level course.
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
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Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
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