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Intuitive Infinitesimal Calculus

Intuitive Infinitesimal Calculus

Intuitive Infinitesimal Calculus

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Year:2015
Publisher:Universiteit Utrecht
Pages:109 pages
Language:english
Since:10/02/2016
Size:7.95 MB
License:Pending review

Content:

In mathematics, infinitesimals are things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as angle or slope, even though these entities were quantitatively small. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a sequence. It was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz. Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective, "infinitesimal" means "extremely small". To give it a meaning, it usually must be compared to another infinitesimal object in the same context (as in a derivative). Infinitely many infinitesimals are summed to produce an integral.

Summary:

  • Differentiation
  • Integration
  • Power series
  • Differential equations
  • Polar and parametric curves
  • Vectors
  • Multivariable differential calculus
  • Multivariable integral calculus
  • Vector calculus
  • Precalculus review
  • Linear algebra

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