It looks as if the EM drive might work. A NASA Eagleworks paper has appeared now on November 17. The drive produces a thrust apparently violating momentum conservation. However, as the effect appears to be quantum mechanical this is not necessarily a contradiction. The drive could make use of the fact that vaccum is not really empty.
As for applications, NASA is interested in that since the drive could be used for deep space missions.

From the paper: "Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum", published on November 17, 2016, by Harold White, Paul March, James Lawrence, Jerry Vera, Andre Sylvester, David Brady, and Paul Bailey.
It was previously reported that radio-frequency (RF) resonant cavities generated anomalous thrust on a low-thrust torsion pendulum [1,2] in spite of the apparent lack of a propellant or other medium with which to exchange momentum. It is shown here that a dielectrically loaded, tapered RF test article excited in the transverse magnetic 212 (TM212) mode (see Fig. 1) at 1937 MHz is capable of consistently generating force at a thrust-to-power level of 1.2 +/i 0.1 mN/kW with the force directed to the narrow end under vacuum conditions.

As for multivariable calculus: look at the paper. Here is a graph from that paper featuring some vector fields: