Do you know PDEs? FEM? FIT? Differential Geometry? Alain Bossavit?

Your children will know them™.

Computers changed so many areas in science. We can now design things, making virtual prototypes using CAD systems. We do not form devices to make analytical calculations easier, but we make numerical calculations to be able to give devices any form.

Think for a moment! How many cars have you seen that had a reflector not shaped like a paraboloid 15 years ago (You know, round lamps behind some nice prisms)? Do you see any now?

Surprise! Eucledian space, differential equations are not quite good for numerical calculations. The whole CAD thing is hard, because we form our equations based on mathematics used for analytical calculations. Vectors, tensors are not the right thing. Period.

I would like to make teaching physics easier with using differential geometry. I would like to build a consistent system from elementary physics to engineers designing maglev trains.