Although in the physics department, Sneddon continued to be interest in applied mathematics. His next major text was Fourier Transforms which appeared in 1951. Remarkably the book was reprinted from the 1951 original in 1995, showing what a classic text Sneddon wrote. The book discusses applications of Fourier , Mellin , Laplace and Hankel transforms to the solution of problems in physics and engineering. It is a major text containing around 550 pages and is mainly concerned with applications which involve the solution of ordinary differential equations and boundary value and initial value problems for partial differential equations.
More unusual applications are to topics such as the theory of cosmic ray showers.
The book concludes with chapters which bring together many results from Sneddon's own papers on boundary value problems in elasticity. It does not confine itself merely to the Laplace transform, and many of the applications are of a more advanced nature than is usual - the later chapters are based almost entirely on work published within the last ten years. He enjoyed the challenge of building up a department in a new institution and now in a department of mathematics Sneddon made the small shift in attitude required to be an applied mathematician rather than a theoretical physicist. Each of Sneddon's previous two moves had preceded the publication of a major work by him and Sneddon's final move back to the University of Glasgow in 1956 followed a similar pattern. Glasgow established the Simson Chair of Mathematics to which Sneddon was appointed.