Calculus, Part 1Predecessors 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 ofthem was theirad hoccharacter. It is possible to find examples from the time before Newtonand Leibniz which, when translated into modern mathematical language, show that differ-entiation and integration are inverse procedures; however, these examples are all related tospecific problems and not to general theories.”•Descartes’ Method for finding tangents•Fermat’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•Fermat’s “logarithmic” integrationNewton and Leibniz•Pedersen: “The special merit of Newton and Leibniz was that they both worked out a generaltheory of the infinitesimal calculus. However, it cannot be said that either Newton or Leibniz
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