Ancient Integrals and Modern Numerics - Where's the Physics?

It is proposed that engineering educators should carefully consider the use of modern numerical solution techniques as outright replacements for traditional analytical solutions in many applications. Examples are given from the field of aerodynamics, specifically thin airfoil and finite wing theory. It is shown that an arguably more useful solution can be obtained more easily, and with a more direct connection to the underlying physics of the problem, using numerical approaches.