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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.
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
Keisler also published a companion book, Foundations of Infinitesimal Calculus, for instructors, which covers the foundational material in more depth. Keisler defines all basic notions of the calculus such as continuity, derivative, and integral using infinitesimals. The usual definitions in terms of ε–δ techniques are provided at the end ...
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.
A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends upon the material of the medium. One corresponding concept in mechanics is the principle of least/stationary action. Many important problems involve functions of several variables.
Elementary calculus may refer to: The elementary aspects of differential and integral calculus ; Elementary Calculus: An Infinitesimal Approach , a textbook by Jerome Keisler.
Is a subfield of calculus [30] concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. [31] differential equation Is a mathematical equation that relates some function with its derivatives. In applications ...
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