calculus of variations

noun

The form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.

Meanings

nounthe calculus of variations (uncountable)
  1. uncountablecalculusThe form of calculus that deals with the maxima and minima of definite integrals of functions of many variables.

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

    2023, Filippo Santambrogio, A Course in the Calculus of Variations, Springer, page 57
    2 more examples

    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.

    1885, Lewis Buffett Carll, A Treatise on the Calculus of Variations, Macmillan and Co., page 550

    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.

Synonyms & antonyms

Translations

Chinese Mandarin 變分法 /变分法
  • 變分法 /变分法 (biànfēnfǎ)form of calculus
Czech variační počet
  • variační početform of calculus
Dutch variatierekening
  • variatierekeningform of calculus
Estonian variatsioonarvutus
  • variatsioonarvutusform of calculus
Finnish variaatiolaskenta
  • variaatiolaskentaform of calculus
French calcul des variations
  • calcul des variationsform of calculus
German Variationsrechnung
  • Variationsrechnungform of calculus
Greek λογισμός των μεταβολών, μεταβολικός λογισμός
  • λογισμός των μεταβολών (logismós ton metavolón)form of calculus
  • μεταβολικός λογισμός (metavolikós logismós)form of calculus
Hebrew חשבון וריאציות
  • חשבון וריאציותform of calculus
Hungarian variációszámítás
  • variációszámításform of calculus
Icelandic hnikareikningur
  • hnikareikningurform of calculus
Italian calcolo delle variazioni
  • calcolo delle variazioniform of calculus
Japanese 変分法
  • 変分法 (henbunhō)form of calculus
Korean 변분법
  • 변분법 (byeonbunbeop)form of calculus
Persian حسابان وردشها
  • حسابان وردشهاform of calculus
Polish rachunek wariacyjny
  • rachunek wariacyjnyform of calculus
Portuguese cálculo de variações
  • cálculo de variaçõesform of calculus
Russian вариацио́нное исчисле́ние
  • вариацио́нное исчисле́ние (variaciónnoje isčislénije)form of calculus
Spanish cálculo de variaciones
  • cálculo de variacionesform of calculus
Swedish variationskalkyl
  • variationskalkylform of calculus
Ukrainian варіаційне числення
  • варіаційне числення (variacijne čyslennja)form of calculus
Vietnamese phép tính biến phân
  • phép tính biến phânform of calculus
Cite this entry
APA

calculus of variations. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/calculus%20of%20variations

MLA

“calculus of variations.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/calculus%20of%20variations. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “calculus of variations,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/calculus%20of%20variations.

Source: calculus of variations on Wiktionary, CC BY-SA 4.0.