Definition of calculus of variations in English:

calculus of variations

noun

  • A form of calculus applied to expressions or functions in which the law relating the quantities is liable to variation, especially to find what relation between the variables makes an integral a maximum or a minimum.

    • ‘He used Newton like iterations to solve the generalized Euler - Lagrange equation of the calculus of variations.’
    • ‘Pure mathematics became Clebsch's main research topic when he began to study the calculus of variations and partial differential equations.’
    • ‘There he very effectively applied methods from the calculus of variations to solve problems relating to correcting missile trajectories for the effects of wind, changes in air density, rotation of the Earth and other perturbations.’
    • ‘The four memoirs that Monge submitted to the Académie were on a generalisation of the calculus of variations, infinitesimal geometry, the theory of partial differential equations, and combinatorics.’
    • ‘Radon applied the calculus of variations to differential geometry which led to applications in number theory.’
    • ‘He also dealt with other fields of mathematics: group theory, calculus of variations, differential equations, Hilbert spaces.’
    • ‘He also made major contributions in other areas of mathematics, including topology, potential theory, the Dirichlet problem, the calculus of variations, set theory, the theory of surface area and dimension theory.’
    • ‘His papers are rather confused, and ignorant of the work of others, but do contain some very original ideas in the calculus of variations, differential equations and the theory of equations.’
    • ‘Mayer worked on differential equations, the calculus of variations and mechanics.’
    • ‘Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations.’
    • ‘There he taught courses on advanced algebra, the calculus of variations, mechanics, Fourier series, and synthetic geometry.’
    • ‘Bernoulli greatly advanced algebra, the infinitesimal calculus, the calculus of variations, mechanics, the theory of series, and the theory of probability.’
    • ‘Jacob Bernoulli and Johann Bernoulli invented the calculus of variations where the value of an integral is thought of as a function of the functions being integrated.’
    • ‘His steady stream of publications is testimonial to his authority in the fields of Riemannian geometry and the calculus of variations.’
    • ‘Immediately after his return Bolza continued teaching and research, in particular on function theory, integral equations and the calculus of variations.’
    • ‘Mason's research interests lay in differential equations, the calculus of variations and electromagnetic theory.’
    • ‘Osgood's main work was on the convergence of sequences of continuous functions, solutions of differential equations, the calculus of variations and space filling curves.’
    • ‘In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.’
    • ‘In particular he studied the role of these curves in the calculus of variations and in mechanics.’
    • ‘He has interests in differential equations, the calculus of variations, and functions of a real variable which he would work on for the rest of his life.’