A good example would be the fluids class digging into the governing differential equations of fluid flows and how to use intuition to convert the physical problem into a series of mathematical statements that allow a student to simplify the equations to be more easily solvable.
Basically, in order to understand the “why” and not just the recipe for “how,” then many of the core engineering classes are completely inseparable from high-level mathematics, most typically differential equations. Most ET programs don’t even require differential equations.