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Meaning of "calculus of variations" in the English dictionary

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PRONUNCIATION OF CALCULUS OF VARIATIONS

calculus of variations play
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GRAMMATICAL CATEGORY OF CALCULUS OF VARIATIONS

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Calculus of variations is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES CALCULUS OF VARIATIONS MEAN IN ENGLISH?

Calculus of variations

Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. The interest is in extremal functions that make the functional attain a maximum or minimum value – or stationary functions – those where the rate of change of the functional is zero. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is obviously a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, where the optical length depends upon the material of the medium. One corresponding concept in mechanics is the principle of least action. Many important problems involve functions of several variables.

Definition of calculus of variations in the English dictionary

The definition of calculus of variations in the dictionary is a branch of calculus concerned with maxima and minima of definite integrals.

WORDS THAT BEGIN LIKE CALCULUS OF VARIATIONS

calculability
calculable
calculably
calcular
calculary
calculate
calculated
calculatedly
calculatedness
calculating
calculatingly
calculation
calculational
calculative
calculator
calculi
calculose
calculous
calculus

WORDS THAT END LIKE CALCULUS OF VARIATIONS

accommodations
alterations
combinations
communications
conditions
congratulations
connections
directions
foundations
frequently asked questions
go through the motions
instructions
limitations
millions
public relations
reflections
relations
representations
telecommunications
transactions
United Nations

Synonyms and antonyms of calculus of variations in the English dictionary of synonyms

SYNONYMS

Translation of «calculus of variations» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF CALCULUS OF VARIATIONS

Find out the translation of calculus of variations to 25 languages with our English multilingual translator.
The translations of calculus of variations from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «calculus of variations» in English.

Translator English - Chinese

变分法
1,325 millions of speakers

Translator English - Spanish

cálculo de variaciones
570 millions of speakers

English

calculus of variations
510 millions of speakers

Translator English - Hindi

पथरी की विविधताओं
380 millions of speakers
ar

Translator English - Arabic

حساب التفاضل والتكامل من الاختلافات
280 millions of speakers

Translator English - Russian

вариационное исчисление
278 millions of speakers

Translator English - Portuguese

cálculo das variações
270 millions of speakers

Translator English - Bengali

বৈচিত্র্যের ক্যালকুলাস
260 millions of speakers

Translator English - French

calcul des variations
220 millions of speakers

Translator English - Malay

Kalkulus variasi
190 millions of speakers

Translator English - German

Variationsrechnung
180 millions of speakers

Translator English - Japanese

変分法
130 millions of speakers

Translator English - Korean

변화 의 미적분
85 millions of speakers

Translator English - Javanese

Kalkulus variasi
85 millions of speakers
vi

Translator English - Vietnamese

tính toán của các biến thể
80 millions of speakers

Translator English - Tamil

வேறுபாடுகளின் கால்குலஸ்
75 millions of speakers

Translator English - Marathi

विविधतांचे गणनशास्त्र
75 millions of speakers

Translator English - Turkish

Varyasyon hesabı
70 millions of speakers

Translator English - Italian

calcolo delle variazioni
65 millions of speakers

Translator English - Polish

Rachunek zmian
50 millions of speakers

Translator English - Ukrainian

варіаційне числення
40 millions of speakers

Translator English - Romanian

calculul variațiilor
30 millions of speakers
el

Translator English - Greek

λογισμού των μεταβολών
15 millions of speakers
af

Translator English - Afrikaans

variasierekening
14 millions of speakers
sv

Translator English - Swedish

variationskalkyl
10 millions of speakers
no

Translator English - Norwegian

variasjonsregning
5 millions of speakers

Trends of use of calculus of variations

TRENDS

TENDENCIES OF USE OF THE TERM «CALCULUS OF VARIATIONS»

The term «calculus of variations» is regularly used and occupies the 81.876 position in our list of most widely used terms in the English dictionary.
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100%
FREQUENCY
Regularly used
62
/100
The map shown above gives the frequency of use of the term «calculus of variations» in the different countries.
Principal search tendencies and common uses of calculus of variations
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «calculus of variations».

FREQUENCY OF USE OF THE TERM «CALCULUS OF VARIATIONS» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «calculus of variations» during the past 500 years. Its implementation is based on analysing how often the term «calculus of variations» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about calculus of variations

EXAMPLES

10 ENGLISH BOOKS RELATING TO «CALCULUS OF VARIATIONS»

Discover the use of calculus of variations in the following bibliographical selection. Books relating to calculus of variations and brief extracts from same to provide context of its use in English literature.
1
Calculus of Variations
This textbook on the calculus of variations covers from the basics to the modern aspects of the theory.
Jürgen Jost, Xianqing Li-Jost, 1998
2
The Calculus of Variations
An authoritative text on the calculus of variations for first-year graduate students.
N.I. Akhiezer, 1988
3
The Calculus of Variations
Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate ...
Bruce van Brunt, 2004
4
Calculus of Variations
The brachistochrone problem was posed by John Bernoulli in 1 696, and played an important part in the development of the calculus of variations. The problem was solved by John Bernoulli, James Bernoulli, Newton, and L'Hospital.
I. M. Gelfand, S. V. Fomin, 2012
5
An Introduction to the Calculus of Variations
Highly regarded text for advanced undergraduate and graduate students explores first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.
Charles Fox, 1987
6
Multiple Integrals in the Calculus of Variations
Suitable for those concerned with multiple integral variational problems and with elliptic partial differential equations, this book presents a comprehensive treatise of the theory of multiple integral variational problems.
Charles Bradfield Morrey, 2009
7
The Calculus of Variations and Optimal Control
This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations.
George Leitmann, 1981
8
Introduction to the Calculus of Variations
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Hans Sagan, 1969
9
Calculus of Variations I: The Lagrangian Formalism
This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike.
Mariano Giaquinta, Stefan Hildebrandt, 1996
10
Calculus of Variations with Applications
Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers.
George McNaught Ewing, 1985

10 NEWS ITEMS WHICH INCLUDE THE TERM «CALCULUS OF VARIATIONS»

Find out what the national and international press are talking about and how the term calculus of variations is used in the context of the following news items.
1
Euler's Identity: 'The Most Beautiful Equation'
... every rotation has an axis), Euler's equations for motion of fluids, and the Euler-Lagrange equation (that comes from calculus of variations)." ... «Live Science, Jul 15»
2
Scientist provides new fluid dynamics insights
... physicists Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton refined these ideas using the Calculus of Variations. «Phys.Org, May 15»
3
Theory of Convergent Evolution Analyzed
In the language of the calculus of variations, these examples of convergent evolution -- if correctly identified as such -- imply that there is a ... «Discovery Institute, May 15»
4
Five faculty members and one graduate student are honored.
In fact, the "Mosco Convergence" is familiar to virtually all researchers and students working in the areas of analysis, calculus of variations, and ... «WPI News, Apr 15»
5
Why Minority Valedictorians Fail Calculus, Findings Of The Berkeley …
It's not hard to dazzle ten year olds with the calculus of variations on a white board or a stick laying in dirt by talking about the problem of a ... «Science 2.0, Apr 15»
6
From submarines to algorithms, nature's optimality hands …
Ants don't know the calculus of variations. They don't “know” anything. Yet the colony's collective behavior routinely finds the correct solution to ... «Ars Technica, Jan 15»
7
TCA Srinivasa-Raghavan: Fouling your own nest
To give you just one bizarre example, one of the problems they set out to solve in growth theory used the calculus of variations and geodesics! «Business Standard, Dec 14»
8
Controlling light with freeform optics
This approach is based on rigorous physical and geometric principles, combined with ideas from calculus of variations, as well as on novel, ... «SPIE Newsroom, Oct 14»
9
IU's newest mathematician receives Vietnam's highest honor in field …
His broad mathematical interests are in partial differential equations, geometric analysis and the calculus of variations. His specific areas of ... «Sigma Triton Chapter of Phi Sigma Kappa, Mar 14»
10
Sudden Progress on Prime Number Problem Has Mathematicians …
Finding the richest fishing grounds for prime numbers ended up being a problem in “calculus of variations,” a generalization of calculus. «Wired, Nov 13»

REFERENCE
« EDUCALINGO. Calculus of variations [online]. Available <https://educalingo.com/en/dic-en/calculus-of-variations>. May 2024 ».
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