Scientific computing, from the ground up
When the air fights back
A ball, a differential equation with no solution, and the numerical methods that get an answer anyway.
Everyone in the room already knows the range of a projectile: R = u² sin 2θ / g, with the maximum at 45 degrees. It is one of the first formulas anybody memorises, and it is wrong about every ball that has ever actually been thrown.
The talk works out why. Adding air resistance to the model takes one line. Solving the result takes a computer, because the equation that comes out has no closed-form solution, and neither does most of engineering.
The formula you memorised is a special case of an equation nobody can solve. Scientific computing is how engineers work in the general case, which is every case that has ever been built.