I agree with Mr Krause here. All of the engineering majors I knew in undergrad would have been more than prepared for an MFE program.
Then again, everybody at my school was required (regardless of major) to take...
1) Calculus, Lin Al, Multivar Calculus
2) ODE, Probability/Statistics
3) Mechanics, E&M, Quantum Mechanics, Statistical Mechanics
In addition, all engineering majors were required to take
1) Complex Analysis
2) Advanced ODE
3) PDE
in addition to their specific engineering courses.
If you get that done, I'd say you'd be sufficiently prepared.
