Fritz Ursell was a singular and influential applied mathematician. He made seminal contributions to research in the mathematical analysis of linear water waves. This required the development of new techniques for the asymptotic evaluation of integrals, especially uniformly valid approximations. He made numerous contributions to the field; for example, he constructed a family of solutions for edge waves on a sloping beach that extended Stokes’s original result, he gave a detailed analysis of the Kelvin ship-wave pattern, and he was the first to prove the existence of trapped modes in water-wave problems.
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