The difficulty of learning Electromagnetism vs Classical Mechanics

[vco]

There was an old thread comparing the difficulty of classical mechanics and electromagnetism. The consensus was that electromagnetism is more difficult, and substantially so according to some. The thread was no longer open for replies, but it got me suspecting that we're comparing apples to oranges here.

Comparing the difficulty of classical mechanics to that of electromagnetism is a bit unfair if we limit ourselves to particle mechanics (point masses, springs, etc.), which is often the scope of mechanics courses for undergraduate physics students. The electrical counterpart of particle mechanics is circuit theory, not electromagnetism. Electromagnetism is a field theory and therefore its mechanical counterpart is continuum mechanics (elasticity, fluid dynamics).

While electromagnetism certainly is conceptually more difficult than continuum mechanics, I believe the mathematics and application of continuum mechanics are more difficult. Richard Feynman appeared to agree (The Feynman Lectures on Physics, Volume II, Chapter 39. Elastic Materials):

... somewhat more difficult to do than the corresponding problems in electromagnetism. It is more difficult, first, because the equations are a little more difficult to handle, and second, because the shape of the elastic bodies we are likely to be interested in are usually much more complicated. In electromagnetism, we are often interested in solving Maxwell’s equations around relatively simple geometric shapes such as cylinders, spheres, and so on, since these are convenient shapes for electrical devices. In elasticity, the objects we would like to analyze may have quite complicated shapes—like a crane hook, or an automobile crankshaft, or the rotor of a gas turbine.

 

[vanhees71]

Indeed, continuum mechanics is more difficult than electrodynamics, because it's at the start a non-linear theory already for the most simple case of perfect fluid dynamics, while you get pretty far in electrodynamics as a linear theory since linear-response theory for the constitutive relations of matter ($\epsilon$, $\mu$, $\sigma$ as material constants or functions of frequency in Fourier space of the matter).