calculus of variations

English

Noun

the calculus of variations (uncountable)

1. (calculus) The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.
   • 1885, Lewis Buffett Carll, A Treatise on the Calculus of Variations, Macmillan and Co., page 550:

     The next advance was made by Cauchy in a memoir on the calculus of variations published in the third volume of his Exercices d'analyse et de Physique Mathématique, 1844, extending from page 50 to page 130.

   • 2004, Bernard Dacorogna, Introduction to the Calculus of Variations, 2nd Edition, Imperial College Press, page 2,

     In the nineteenth century and in parallel to some of the work that was mentioned above, probably, the most celebrated problem of the calculus of variations emerged, namely the study of the Dirichlet integral; a problem of multiple integrals.

   • 2023, Filippo Santambrogio, A Course in the Calculus of Variations, Springer, page 57:

     On the other hand, we can also consider that the calculus of variations includes all optimization problems where the unknown are functions […] .

Translations

form of calculus

• Arabic: please add this translation if you can
• Chinese:

  Mandarin: 變分法／变分法 (zh) (biànfēnfǎ)

• Czech: variační počet m
• Dutch: variatierekening f
• Estonian: please add this translation if you can
• Finnish: variaatiolaskenta
• French: calcul des variations m
• Georgian: please add this translation if you can
• German: Variationsrechnung f
• Greek: please add this translation if you can
• Hebrew: חשבון וריאציות (he)
• Hungarian: variációszámítás (hu)
• Icelandic: hnikareikningur m
• Indonesian: please add this translation if you can
• Irish: please add this translation if you can
• Italian: calcolo delle variazioni m
• Japanese: 変分法 (henbunhō)
• Kannada: please add this translation if you can
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• Maltese: Kalkulu tal-Varjazzjonijiet
• Persian: حسابان وردش‌ها
• Piedmontese: càlcol dle variassion
• Polish: rachunek wariacyjny m
• Portuguese: cálculo de variações m
• Russian: вариацио́нное исчисле́ние (variaciónnoje isčislénije)
• Scottish Gaelic: please add this translation if you can
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• Slovene: variacijski račun m
• Spanish: cálculo de variaciones m
• Swedish: variationskalkyl c
• Ukrainian: варіаційне числення (uk) (variacijne čyslennja)
• Vietnamese: phép tính biến phân (vi)

Further reading

• Fundamental lemma of calculus of variations on Wikipedia.Wikipedia
• Euler–Lagrange equation on Wikipedia.Wikipedia
• Functional (mathematics) on Wikipedia.Wikipedia
• Functional derivative on Wikipedia.Wikipedia