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Calculus, Part 1 Predecessors of Newton/Leibniz Area by Method of Exhaustion in antiquity Eudoxus Archimedes India Pedersen: “Many methods were developed to solve calculus problems; common to most of them was their ad hoc character. It is possible to Fnd examples from the time before Newton and Leibniz which, when translated into modern mathematical language, show that di±er- entiation and integration are inverse procedures; however, these examples are all related to speciFc problems and not to general theories.” Descartes’ Method for Fnding tangents ²ermat’s Method of Maxima and Minima Cavalieri’s Principle: If cross-sections are in a constant ratio, areas are in that same ratio. Roberval’s quadrature of the cycloid Wallis’s “arithmetic” integration ²ermat’s “logarithmic” integration Newton and Leibniz Pedersen: “The special merit of Newton and Leibniz was that they both worked out a general theory of the inFnitesimal calculus. However, it cannot be said that either Newton or Leibniz
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.

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