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Woodhouse was interested in the theoretical foundations of the calculus, the importance of notation, the nature of imaginary numbers and other similar topics. He wrote an important work Principles of Analytic Calculation in 1803 defending Lagrange's calculus method based on series expansions. This support of Continental methods was aimed at his fellow professors at Cambridge but it had little effect. Peacock, however, considered his work of major importance.
Woodhouse, therefore, failed to have much influence as a reformer in mathematical studies at Cambridge but he wrote several widely used elementary texts which, during his lifetime, brought him more fame.
Woodhouse's other works include History of the Calculus of Variations (1810), Treatise on Astronomy (1812) and a work on gravitation published in 1818.
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