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Variational Theory
Variational may refer to: *Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals *Variational method (quantum mechanics), a way of finding approximations to the lowest energy eigenstate or ground state in quantum physics *Variational Bayesian methods, a family of techniques for approximating integrals in Bayesian inference and machine learning *Variational properties, properties of an organism relating to the production of variation among its offspring in evolutionary biology *Variationist sociolinguistics or variational sociolinguistics, the study of variation in language use among speakers or groups of speakers See also *List of variational topics in mathematics and physics *Variation (other) * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as '' geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |