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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…

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Overview

History

Extrema

Euler–Lagrange equation

Beltrami's identity

Lavrentiev phenomenon

Functions of several variables

Eigenvalue problems

Applications

Variations and sufficient condition for a minimum

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Calculus of variations

Nodes123
Edges122
Triples168
Avg. degree1.98
Density0.01626
Components1

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Calculus of variations

Top relations

related to Further reading · 78
Calculus of variations → Albert Einstein, An Introduction, Applications, Applied Mathematics, Archived, Benesova, Bernard, Bolza, Calculus, Cambridge University Press, Cassel, Chap, Chapter, Charles, Chelsea Publishing Company, Clegg, Cloud, Cornelius, Courant, Dacorogna
related to history · 41
Calculus of variations → Adrien-Marie Legendre, After Euler, Alfred Clebsch, An, Augustin-Louis Cauchy, Bernoulli, Carl Friedrich Gauss, Carl Jacobi, Elementa Calculi Variationum, Euler, Euler's, Galileo Galilei, Gottfried Leibniz, Hilbert, His, Hôpital, In, Isaac Newton, Jacob Bernoulli, Johann Bernoulli
related to External links · 15
Calculus of variations → Calculus, Encyclopedia, Example, Geodesic Fields, Integral Equations, Lectures, Mathematics, MathWorld, Part, Part II, PlanetMath, Selected, Variational, Variations, YouTube
has application · 13
Calculus of variations → Bayesian, Einstein's, Finite, Further, Geometric, Hamiltonian, Lagrangian, Newton's, Plateau's, The, Total, Variational, Variational Bayesian
related to Extrema · 10
Calculus of variations → An, Both, Delta, Euler, Finding, For, Functionals, Lagrange, The, Thus
see also · 8
Calculus of variations → Bayesian, Donder, First, Lagrangian, MedalFermat PrizeConvenient, Variational, Washizu, Weyl
related to Variations and sufficient condition for a minimum · 3
Calculus of variations → Calculus, For, The

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displaystyle frac variations equation calculus function dx problem functions first euler lagrange int left partial boundary functional may right variation

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SubjectPredicateObjectConfidenceSrc
Calculus of variationshas applicationFurther0.60section
Calculus of variationshas applicationThe0.60section
Calculus of variationshas applicationNewton's0.60section
Calculus of variationshas applicationPlateau's0.60section
Calculus of variationshas applicationLagrangian0.60section
Calculus of variationshas applicationHamiltonian0.60section
Calculus of variationshas applicationGeometric0.60section
Calculus of variationshas applicationVariational0.60section
Calculus of variationshas applicationVariational Bayesian0.60section
Calculus of variationshas applicationBayesian0.60section
Calculus of variationshas applicationEinstein's0.60section
Calculus of variationshas applicationFinite0.60section

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