A lot of good physics students here!
When I was a student of physics and math for physics, the math was solid but often the physics had to be just swallowed whole. This thread has some explanations missing from the physics sources I had!
I'm busy with my startup, but I'd like to see how the physics of Lagrange, Hamilton, Schrödinger, etc., e.g., least action, quantum mechanics, really work and to compare them with Newton's calculus of variations (the shape of the wire that would let a bead slide down in least time), deterministic optimal control (e.g., the book by Athans and Falb), Kuhn-Tucker optimization conditions, Lagrangians in optimization, etc.