Rawitscher and Koltracht present a readily accessible introduction to the spectral method and its applications to solving boundary value problems. They proceed to demonstrate their ideas in the context of examples, first for approximating the exponential function using Chebyshev polynomials, and later by discussing the one-dimensional radial Schrödinger equation. The authors show how their ideas are related to the seminal work of Greengard and Rokhlin [1].

One of the strengths of this paper is its four readable appendices, which are available online. The MATLAB code in these appendices provides more than adequate guidance to the reader on the complexity of implementing the spectral method. The appendices are presented in such a way that I believe they will serve as excellent examples for advanced undergraduates and beginning graduate students interested in the subject.