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Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics.
His A Course of Modern Analysis (1902) is important in the study of functions of a complex variable. It also studies special functions and their related differential equations.
One of his most important historical studies was A History of the Theories of Aether and Electricity, from the Age of Descartes to the Close of the Nineteenth Century (1910). In 1953 he produced a revised version including the work of the first 1900 to 1925.
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