Related to Dirac delta function

Lebesgue integralMethod of mathematical integration The integral of a positive function can be interpreted as the area under a curve.

Measure (mathematics)In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.

Kronecker deltaIn mathematics, the Kronecker delta (named after Leopold Kronecker), is a function of two variables, usually non-negative integers.

IntegralOperation in calculus "Area under the curve" redirects here. For other uses, see Area under the curve (disambiguation).

Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.

Generalized functionIn mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful for treating discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.

Paul DiracPaul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for both quantum electrodynamics and quantum field theory, coining the former term. He was Lucasian Professor of Mathematics at the University of Cambridge from 1932 to 1969, and a professor of physics at Florida State University from 1970 to 1984.

Laurent SchwartzLaurent-Moïse Schwartz (French:; 5 March 1915 – 4 July 2002) was a French mathematician who received the Fields Medal in 1950 for pioneering the theory of distributions or generalized functions, giving a well-defined meaning to objects such as the Dirac delta function. For several years he taught at the École polytechnique.

Limit (mathematics)In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.

Distribution (mathematical analysis)In mathematical analysis, distributions are a type of generalized function that makes it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative.

Mathematical analysisMathematical analysis is the branch of mathematics that studies functions, spaces, and operators through methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities, and in the 19th century its foundations were reformulated with greater rigor. Basic objects of study in mathematical analysis include the real numbers, functions, sequences, series, and limits.

HeuristicA heuristic or heuristic technique (problem solving, mental shortcut, rule of thumb) is any approach to problem solving that employs a pragmatic method that is not necessarily optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution.