Delta Function -- from Wolfram MathWorld

Delta Function -- from Wolfram MathWorld - Delta Function -...

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Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index Interactive Entries Random Entry New in MathWorld Classroom About Contribute to Send a Message to the Team Book 13,082 entries Last updated: Thu Sep 29 2011 Calculus and Analysis > Generalized Functions > Interactive Entries > Interactive Demonstrations > Delta Function The delta function is a generalized function that can be defined as the limit of a class of delta sequences . The delta function is sometimes called "Dirac's delta function" or the "impulse symbol" (Bracewell 1999). It is implemented in Mathematica as DiracDelta [ x ]. Formally, is a linear functional from a space (commonly taken as a Schwartz space or the space of all smooth functions of compact support ) of test functions . The action of on , commonly denoted or , then gives the value at 0 of for any function . In engineering contexts, the functional nature of the delta function is often suppressed. The delta function can be viewed as the derivative of the Heaviside step function , (1) (Bracewell 1999, p. 94). The delta function has the fundamental property that (2) and, in fact, (3) for . Additional identities include
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This note was uploaded on 03/01/2012 for the course EE 101 taught by Professor Munk during the Spring '12 term at Alaska Anch.

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Delta Function -- from Wolfram MathWorld - Delta Function -...

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