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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.
Quadratrix as a plane curve for side length =, as given by the parametric formula for −∞ < t < ∞, with singularities when t is a nonzero integer multiple of π. If one places such a square with side length in a (Cartesian) coordinate system with the side ¯ on the -axis and with vertex at the origin, then the quadratrix is described by a parametric equation that gives the coordinates of ...
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
Envelope theorem (calculus of variations) Equal incircles theorem (Euclidean geometry) Equidistribution theorem (ergodic theory) Equipartition theorem (ergodic theory) Erdős–Anning theorem (discrete geometry) Erdős–Dushnik–Miller theorem ; Erdős–Gallai theorem (graph theory) Erdős–Ginzburg–Ziv theorem (number theory)
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function. The first part of the theorem, sometimes called the first fundamental theorem of calculus , states that one of the antiderivatives (also called indefinite integral ), say F , of some function f may be ...
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...
In calculus, interchange of the order of integration is a methodology that transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed. In some cases, the order of integration can be validly ...
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals. The book is available freely online and is currently published by Dover. [1]