All the difficult bits of
engineering, without the fun bits
Difficult bits: differential equations, vector fields, non-dimensional numbers, control theory, soil mechanics, fluid dynamics, conformal mapping, dynamics, analog circuit analysis, thermodynamics, entropy, enthalpy, heat engines...and these are just the names I can remember from finals. There's not a hope in hell of remembering the equations.
Fun bits Design, inventing, fiddling about with power supplies which chuck out large numbers of volts and amps, spinning up big rotating machines, making models and then applying very large forces to see what happens, Schlieren photography, welding, machining, dropping dry ice in your beer (don't try that one at home, folks), smashing large lumps of concrete and steel under very precise conditions. Taking the piss out of mathematicians (again, it's best not to try that one at home).
Engineering Science is the study of the mathematics that underpin the world of machines, buildings, sewage pipes and jet engines.
Successful completion of such a course requires a dedication to mathematics, an abilty to juggle vectors, matrices and many different types of differential equation. It also requires a firm grip on reality as you apply these powerful mathematical techniques to real-world issues, like calculating the destructive force of a broken dam, or figuring out the best time to join the queue for a rock concert. Most of these analyses are based on mathematical models of real world events, and the point of engineering science is to train people to build successful models, to enable all of us to better understand how stuff works.