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Mathematics LibreTexts

2: Calculus in the 17th and 18th Centuries

 

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  • 2.1: Newton and Leibniz Get Started
    The rules for calculus were first laid out in Gottfried Wilhelm Leibniz’s 1684 paper Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales, quantitates moratur, et singulare pro illi calculi genus (A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional Nor by Irrational Quantities, and a Remarkable Type of Calculus for This).
  • 2.2: Power Series as Infinite Polynomials
    Applied to polynomials, the rules of differential and integral calculus are straightforward. Indeed, differentiating and integrating polynomials represent some of the easiest tasks in a calculus course. Unfortunately, not all functions can be expressed as a polynomial. A standard technique is to write such functions as an “infinite polynomial,” what we typically refer to as a power series. Such “infinite polynomials” are much more subtle object than mere polynomials, which by definition are finite.
  • 2.E: Calculus in the 17th and 18th Centuries (Exercises)

Thumbnail: Engraving of Gottfried Wilhelm Leibniz. Image used with permission (Public Domain; Pierre Savart)

Contributors

  • Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)