Education

Abstract

Extolling laziness as a virtue is likely to produce a frown from most of the SIREV readership, but, in fact, most applied mathematicians strive to produce solutions that economize the effort needed to understand them. This aesthetic of finding just the right set of keys to unlock a problem concisely, yielding clarity and insight, is part of our heritage. Our paper this issue, “The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems,” provides an elegant illustration of this philosophy. Blasius's eponymous function describes the flow in the narrow transition region (a boundary layer) of a fluid encountering a solid surface, such as air over an airplane wing. Amazingly, the solution to this problem was well understood in the early 1900s, well before the age of serious computation. The historical development of our understanding of this problem is a fascinating story which illustrates that clever use of analysis, symmetry, and asymptotics can yield insights with an economy rarely associated with numerical computation. This paper uses a knowledge of differential equations as a springboard to introduce the reader to similarity solutions, asymptotic methods, and complex analysis. It is a great starting point for students looking to dig deeper into this area, and the author both suggests a set of projects suitable for undergraduates and summarizes some open research problems associated with the Blasius function. Moreover, encouraging your students to read this paper may help them find the right balance of industriousness and laziness needed to succeed in applied mathematics.