[analog31]

This isn't an answer, but an observation. I taught an EE course many years ago -- the second semester of electrodynamics. This was after being a college math major, and getting a physics degree.

It doesn't shock me that there are holes. I noticed that some math topics are very important to engineering and physics coursework, but given short shrift in the math department. Examples are the way that complex numbers are used, and specific kinds of differential equations such as the general harmonic oscillator.

My college physics coursework actually had its own "math methods" class, intended to fill some of those gaps, and to get us prepared for the higher level physics courses.

[throwawayjava]

You'll find the complementary opinion in Mathematics departments -- a general chagrin about the type of mathematics that they have to teach in their service courses for engineers.

Mathematics is a very general tool. As with any very general tool, a lot of the devil is in the details of how to use it in any particular domain.

For this reason, in-sourcing mathematics service courses is best for everyone. The very best math-adjacent departments in every field tend to do this either directly or indirectly. E.g., in the direct model, many CS departments internalize the Discrete Mathematics course and some combinatorics. And an example of the indirect model is Mathematics departments that hire Math Finance professors to cover the service load for econ/fin/bus depts.

I think this in-sourcing (either directly or indirectly) is best for everyone -- mathematics depts don't do a good job at teaching those service courses and often don't do a great job of it in any case. Unfortunately, most departments don't have the headcount (in students or faculty) for a specialized mathematics curriculum, so they have to share the math faculty with N other majors to predictable effect.