After receiving my PhD in applied mathematics from the Courant Institute of Mathematical Sciences (NYU) in 1966, I chose a career in industry rather than academia because I thought that I might have a better chance to observe the development of new areas of applied mathematics, physics, and engineering before the “big guns” at the great universities had a chance to completely investigate and generalize them. I found that I have been able to do this in areas such as computational fluid dynamics, laser optics, device physics, process modeling, acoustics, physical chemistry, and electromagnetics. However, in most cases my major publications have been in physics and engineering journals rather than those in applied mathematics.

My basic task as an applied mathematician has been to model and solve equations in mathematical physics which simulate actual processes, and then let the computer be the experimenter by changing various parameters and studying the effects. In computational fluid dynamics, I solved the transonic potential equation, which is a mixed elliptic-hyperbolic nonlinear partial differential equation. The output is the pressure distribution and lift and drag coefficients for a given airfoil or airplane. The semiconductor device equations are a system of nonlinear mixed parabolic and elliptic partial differential equations. Their output describes the behavior of the semiconductor as a function of time. In electromagnetics, we are interested in minimizing the scattering from coated conductors to make airplanes “invisible” to radar.