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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
In mathematics, the Fox derivative is an algebraic construction in the theory of free groups which bears many similarities to the conventional derivative of calculus.The Fox derivative and related concepts are often referred to as the Fox calculus, or (Fox's original term) the free differential calculus.
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 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.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
There are many alternatives to the classical calculus of Newton and Leibniz; for example, each of the infinitely many non-Newtonian calculi. [1] Occasionally an alternative calculus is more suited than the classical calculus for expressing a given scientific or mathematical idea. [2] [3] [4]
[4] [5] automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, [6] [7] is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no ...
This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. In general, the problem for three given circles has eight solutions, which can be seen as 2 3, each tangency condition imposing a quadratic condition on the space of circles. However, for special arrangements of the given ...
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