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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. [1] Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity.
However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields.
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
Nonlinear dimensionality reduction is a simplification that assumes that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. Nonlinear element, or nonlinear device, is an electrical element which does not have a linear relationship between current and voltage, e.g. a diode.
The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...
The following formula shows that a 4-ary function is bent when its nonlinearity is 6: = = In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables.
In multivariable calculus, in the context of differential equations defined by a vector valued function R n to R m, the Fréchet derivative A is a linear operator on R considered as a vector space over itself, and corresponds to the best linear approximation of a function.