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Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics
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Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education . Calculus has widespread applications in science , economics , and engineering and can solve many problems for which algebra alone is insufficient.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.
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[2] [3] [4] Keisler's student K. Sullivan, [5] as part of her PhD thesis, performed a controlled experiment involving 5 schools, which found Elementary Calculus to have advantages over the standard method of teaching calculus. [1] [6] Despite the benefits described by Sullivan, the vast majority of mathematicians have not adopted infinitesimal ...
Calculus focuses on rates of change (within functions), such as accelerations, curves, and slopes. The development of calculus is credited to Archimedes, Bhaskara, Madhava of Sangamagrama, Gottfried Leibniz and Isaac Newton; lesser credit is given to Isaac Barrow, René Descartes, Pierre de Fermat, Christiaan Huygens, and John Wallis.