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- Thread starter kent davidge
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Vanadium 50

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Concerning the math you can do this in parallel, because a lot of concepts of math have their origin in physics anyway (it's not by chance that Newton discovered calculus when thinking about mechanics; on the other hand Leibniz discovered it by pure mathematical interest). In classical mechanics you need first of all Euclidean vectors, derivatives, integrals, and then some ordinary differential equations. Mathwise, I think the most challenging step is to learn the full 3D Euclidean vector calculus with div, grad, curl, as well as line, surface, and volume integrals and their various interrelations (Gauss's and Stokes's Theorems), which you need in full glory for classical electrodynamics. At the same time electrodynamics is the best subject to learn its use, together with the most important physically relevant partial differential equations, since a loarge part of classical electrodynamics is mathematically a linear field theory.

Concerning special relativity, I think the optimal order is to split it in two parts. You can already learn a part of special relativity after learning Newtonian mechanics, introducing 4D vector algebra (Minkowski space) on the same level as 3D Euclidean vector algebra. The second part then comes into the game when you have learnt classical electromagnetism in the usual 3D vector-calculus way. After this you can extend your knowledge about 4D Minkowski space to full 4D vector calculus.

Before dealing with quantum mechanics, I'd also recommend to learn about "the action principle" and together with it calculus of variations and some elementary (Lie) group theory, because that's the best way to understand the heuristics of quantum mechanics.

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I wouldn't spend too long on just the mathematics. But, if you take a look at "Paul's online maths", I'd say you need everything in his Calculus courses. You may be able to learn it from there, or you may need some textbooks.

For QM you also need a good introduction to Linear Algebra and Complex Numbers.

As others have said, there are physics prerequisites as well. Classical mechanics, Lagrangian and Hamiltonian mechanics, EM (field theory).

But also, it's experience and familiarity with the various physical and mathematical concepts.

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