Symmetric derivative

Symmetric derivative

In mathematics, the symmetric derivative is an operation related to the ordinary derivative.

It is defined as:

:lim_{h o 0}frac{f(x+h) - f(x-h)}{2h}.

A function is symmetrically differentiable at a point "x" if its symmetric derivative exists at that point. It can be shown that if a function is differentiable at a point, it is also symmetrically differentiable, but the converse is not true. The best known example is the absolute value function f(x) = |x|, which is not differentiable at x = 0, but is symmetrically differentiable here with symmetric derivative 0. It can also be shown that the symmetric derivative at a point is the mean of the one-sided derivatives at that point, if they both exist.

See also

* Symmetrically continuous function

References

* cite book
first= Brian S.
last= Thomson
year= 1994
title= Symmetric Properties of Real Functions
publisher= Marcel Dekker
id= ISBN 0-8247-9230-0


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Derivative — This article is an overview of the term as used in calculus. For a less technical overview of the subject, see Differential calculus. For other uses, see Derivative (disambiguation) …   Wikipedia

  • Symmetric space — In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to make this precise. In Riemannian… …   Wikipedia

  • Symmetric convolution — In mathematics, symmetric convolution is a special subset of convolution operations in which the convolution kernel is symmetric across its zero point. Many common convolution based processes such as Gaussian blur and taking the derivative of a… …   Wikipedia

  • Symmetric multiprocessing — In computing, symmetric multiprocessing (SMP) involves a multiprocessor computer hardware architecture where two or more identical processors are connected to a single shared main memory and are controlled by a single OS instance. Most common… …   Wikipedia

  • Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   Wikipedia

  • Particle in a spherically symmetric potential — In quantum mechanics, the particle in a spherically symmetric potential describes the dynamics of a particle in a potential which has spherical symmetry. The Hamiltonian for such a system has the form:hat{H} = frac{hat{p}^2}{2m 0} + V(r)where m 0 …   Wikipedia

  • Upper convected time derivative — In continuum mechanics, including fluid dynamics upper convected time derivative or Oldroyd derivative is the rate of change of some tensor property of a small parcel of fluid that is written in the coordinate system rotating and stretching with… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Saint-Venant's compatibility condition — In the mathematical theory of elasticity the strain varepsilon is related to a displacement field u by:varepsilon {ij} = frac{1}{2} left( frac{partial u i}{partial x j} + frac{partial u j}{partial x i} ight) Saint Venant derived the compatibility …   Wikipedia

  • Symmetrically continuous function — In mathematics, a function f: mathbb{R} o mathbb{R} is symmetrically continuous at a point x if:lim {h o 0} f(x+h) f(x h) = 0.The usual definition of continuity implies symmetric continuity, but the converse is not true. See also * Symmetric… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”