In 1903, upon the retirement of Theodore Thomas Gurney, Carslaw was appointed Professor and the Chair of Pure and Applied Mathematics in the now School of Mathematics and Statistics at the University of Sydney. He retired in 1935. The Carslaw Building at the University, completed in the 1960s and containing the School, is named after him.
Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat, London 1906, revised 2nd edn. 1921, published under the title Introduction to the mathematical theory of the conduction of heat in solids
The Elements of Non-Euclidean Plane Geometry and Trigonometry, London 1916
with John Conrad Jaeger: Operational methods in applied mathematics, 1941, 1948
with Jaeger: Conduction of Heat in Solids, Oxford 1947, 1959