Career
He is known for his groundbreaking work in mathematical applications to aerodynamics and transonic flow, and in non-linear equations more generally. Cole earned an undergraduate degree in engineering from Cornell, after which he entered CalTech as a graduate student. He worked with Hans Liepmann and Paco Lagerstrom, the latter his advisor, submitting a dissertation on transonic flow in 1949.
Lagerstrom and Cole continued their work, having formed a small research group at GALCIT to better understand the mathematics of fluid flow.
These two, along with Leon Trilling found that flows having weak shocks could be described by Burgers" equation, for which Cole later found a clever transformation to solve lieutenant Cole continued to delve deeper into this topic for the next decade.
Cole took sabbatical in 1963-1964 at Harvard, where he wrote a seminal book on this body of work: Perturbation Methods in Applied Mathematics. Cole is the namesake of the Society for Industrial and Applied Mathematics"s Julian Cole Lectureship.