Pitfalls of E&M or QM without classical mechanics

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I'm an EE major doing a minor in physics. I have to take a standard intermediate electromagnetism course from the engineering department (which is just a more applied version of the physics department course). To get my minor, I was thinking about getting permission to use this course as a prereq to take the second E&M course (electrodynamics). In addition, I'd also like to take the introductory quantum mechanics course out of my own personal interests.

The prereq for the first E&M course in the physics department is a course in classicalc mechanics. Assuming I can, in a special case, get into the electrodynamics course, would I face any difficulties not having taken classical mechanics? What about for the quantum mechanics course?

Also: will I be at a major disadvantage taking a physics electrodynamics course after an engineering first course in electromagnetism? Our EE department does not have more than one E&M course, and so the physics department is my only option for more.

For reference: I've taken the standard freshman-level E&M course already.
 
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It always depends on the courses, their focus, the knowledge the lecturer takes as granted and so on.
Quantum mechanic courses will probably require some knowledge of Lagrange- and Hamilton formalism, the concept of phase space and related topics. It is possible to learn those topics with books, lectures are not necessary (but can be useful).
For electrodynamics, mathematical knowledge is probably more important than classical mechanics - vectors, tensors, concepts like the gradient, curl and other things in 3 or 3+1 dimensions.
 
But aside from the pure prerequisities which mfb describes, there are also problem-solving techniques which are important. It happens occasionally that techniques used in classical mechanics are used in E&M. This might be a problem since the professor might assume that people know these techniques from a previous course.
 
George Jones said:
Do you know what texts are being used now, or have been used in the past, for these courses?
The department uses Taylor for classical mechanics and Griffiths for E&M.

The engineering E&M course uses "Fundamentals of Applied Electromagnetics" by Ulaby.
 
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