calculus of variations


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calculus of variations

n.
Mathematical analysis of the maxima and minima of definite integrals, the integrands of which are functions of independent variables, dependent variables, and the derivatives of one or more dependent variables.

calculus of variations

n
(Mathematics) a branch of calculus concerned with maxima and minima of definite integrals
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.calculus of variations - the calculus of maxima and minima of definite integrals
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
infinitesimal calculus, calculus - the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
Translations
Variační počet
Variationsrechnung
cálculo de variaciones
حسابان وردش‌ها
Calcul des variations
חשבון וריאציות
Calcolo delle variazioni
変分法
Rachunek wariacyjny
Variacijski račun
Варіаційне числення
References in periodicals archive ?
In [3] Almeida studied certain problems of calculus of variations that are dependent upon a Lagrange function on a Caputo-type fractional derivative; sufficient and necessary conditions of the first- and second-order are presented.
Mathematically, formulated in the view of the equations of (1)-(2), this particularly given problem setting is stated as the simplest problem of the calculus of variations for the objective functionals likewise [25]:
In the discrete time setting (see e.g., [14]-[16], [18] and [26]) and in the time scale setting (see e.g., [17], [19], [20]), the question of characterizing the nonnegativity and positivity of F"([bar.x], [bar.u]; [eta], v) was intensively studied when F itself is symplectic (i.e., of the form (D) below), or when we are in the calculus of variations setting.
Saunders, "Thirty years of the inverse problem in the calculus of variations," Reports on Mathematical Physics, vol.
Li-Jost, Calculus of Variations, Cambridge University Press, Cambridge, UK, 2008.
Bohner, "Calculus of variations on time scales," Dynamic Systems and Applications, vol.
of Tokyo) introduces researchers and graduate students to the stochastic calculus of variation, also called Malliavin calculus, for processes with jumps--that is both pure jump processes and jump-diffusions.
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems.
Keywords: Calculus of variations, Euler-Lagrange equation, boundedness of the solution.
Results on differential equations and the calculus of variations with fractional operators of variable order can be found in [15, 16] and references therein.
Lions, The concentration-compactness principle in the calculus of variations. The locally compact case.