LAPLACE OPERATOR

WHAT DOES LAPLACE OPERATOR MEAN IN ENGLISH?

In mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2 or ∆. The Laplacian ∆f of a function f at a point p, up to a constant depending on the dimension, is the rate at which the average value of f over spheres centered at p, deviates from f as the radius of the sphere grows. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems such as cylindrical and spherical coordinates, the Laplacian also has a useful form. The Laplace operator is named after the French mathematician Pierre-Simon de Laplace, who first applied the operator to the study of celestial mechanics, where the operator gives a constant multiple of the mass density when it is applied to a given gravitational potential.

Definition of Laplace operator in the English dictionary

The definition of Laplace operator in the dictionary is the operator ∂²/∂x² + ∂²/∂ y² + ∂²/∂ z², ∇² Also called: Laplacian,.

WORDS THAT RHYME WITH LAPLACE OPERATOR

æmˈfɪʃɪən

ænˈtɪʃɪən

ˌæpəˈleɪtʃɪən

sɪˈlɪʃɪən

ˌsaɪbənɛˈtɪʃɪən

ɡəˈlɪʃɪən

ˈɡreɪʃɪən

ˈheɪʃɪən

ˈheɪʃɪən

ˈlaʊʃɪən

ləˈpleɪʃɪən

ˌlɪlɪˈpjuːʃɪən

luːˈseɪʃɪən

ˈniːtʃɪən

ˌɔːdəʊˈvɪʃɪən

pænˈkreɪʃɪən

pəˈrɪʃɪən

ˈprɪʃɪən

sɑːˈmeɪʃɪən

ˈθreɪʃɪən

WORDS THAT BEGIN LIKE LAPLACE OPERATOR

WORDS THAT END LIKE LAPLACE OPERATOR

WORDS RELATING TO «LAPLACE OPERATOR»

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TRANSLATION OF LAPLACE OPERATOR

Find out the translation of Laplace operator to 25 languages with our English multilingual translator.

The translations of Laplace operator from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «Laplace operator» in English.

Translator English - Chinese

拉普拉斯算子

1,325 millions of speakers

Translator English - Spanish

operador de Laplace

570 millions of speakers

English

Laplace operator

510 millions of speakers

Translator English - Hindi

लाप्लास ऑपरेटर

380 millions of speakers

Translator English - Arabic

المشغل لابلاس

280 millions of speakers

Translator English - Russian

оператор Лапласа

278 millions of speakers

Translator English - Portuguese

operador de Laplace

270 millions of speakers

Translator English - Bengali

ল্যাপলেস অপারেটর

260 millions of speakers

Translator English - French

opérateur de Laplace

220 millions of speakers

Translator English - Malay

Pengendali Laplace

190 millions of speakers

Translator English - German

Laplace-Operator

180 millions of speakers

Translator English - Japanese

ラプラス演算子

130 millions of speakers

Translator English - Korean

라플라스 연산자

85 millions of speakers

Translator English - Javanese

Operator Laplace

85 millions of speakers

Translator English - Vietnamese

Laplace điều hành

80 millions of speakers

Translator English - Tamil

லாப்ளேஸ் ஆபரேட்டர்

75 millions of speakers

Translator English - Marathi

Laplace ऑपरेटर

75 millions of speakers

Translator English - Turkish

Laplace operatörü

70 millions of speakers

Translator English - Italian

operatore di Laplace

65 millions of speakers

Translator English - Polish

operator Laplace´a

50 millions of speakers

Translator English - Ukrainian

оператор Лапласа

40 millions of speakers

Translator English - Romanian

operatorul Laplace

30 millions of speakers

Translator English - Greek

Laplace χειριστή

15 millions of speakers

Translator English - Afrikaans

Laplace operateur

14 millions of speakers

Translator English - Swedish

Laplace-operatorn

10 millions of speakers

Translator English - Norwegian

Laplace operatør

5 millions of speakers

TENDENCIES OF USE OF THE TERM «LAPLACE OPERATOR»

The term «Laplace operator» is normally little used and occupies the 116.843 position in our list of most widely used terms in the English dictionary.

100%

FREQUENCY

Little used

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The map shown above gives the frequency of use of the term «Laplace operator» in the different countries.

Principal search tendencies and common uses of Laplace operator

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List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «Laplace operator».

FREQUENCY OF USE OF THE TERM «LAPLACE OPERATOR» OVER TIME

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

10 ENGLISH BOOKS RELATING TO «LAPLACE OPERATOR»

Discover the use of Laplace operator in the following bibliographical selection. Books relating to Laplace operator and brief extracts from same to provide context of its use in English literature.

Partial Differential Equations I: Basic Theory

In §8 we consider the Laplace operator on A:-forms, and derive the Hodge theorem. When n has a boundary, there arise natural boundary conditions, which we treat in F. The Hodge decomposition is extended to the case of manifolds with ...

Michael Eugene Taylor, 1996

Extremum Problems for Eigenvalues of Elliptic Operators: ...

For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues.

Antoine Henrot, 2006

Transmission Problems for Elliptic Second-Order Equations in ...

R. Kellogg [35, 36, 37, 38], Ben M'Barek and M. Merigot [3], K. Lemrabet [45], M. Dobrowolski [24] investigated the behavior of solutions of the transmission Dirichlet and Neumann problems for the Laplace operator in a neighborhood of an ...

Mikhail Borsuk, 2010

Conformal, Riemannian and Lagrangian Geometry: The 2000 ...

A basic tool in our study is the partial differential equations associated with conformally covariant operators. On a Riemannian manifold (M ", g) of dimension n, the Laplace operator is the natural geometric operator. Under conformal change of ...

Sun-Yung A. Chang, Alexandre S. Freire

Functional Fractional Calculus for System Identification and ...

In this book not only mathematical abstractions are discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls.

Shantanu Das, 2007

Differential Operators: Partial Derivative, Del, Laplace ...

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.

Source Wikipedia, Books Llc, 2010

Riemannian Geometry and Geometric Analysis: Riemannian ...

3.1 The Laplace Operator on Functions A fundamental topic in geometric analysis and an important tool for studying Riemannian manifolds is given by harmonic objects. Such objects are defined as the minimizers, or more generally, the ...

Jürgen Jost, 2011

Microlocal Analysis and Precise Spectral Asymptotics

The problem originated in 1911 when H. Weyl published a paper devoted to eigenvalue asymptotics for the Laplace operator in a bounded domain with regular boundary. After this article a huge number of different papers devoted to spectral ...

Victor Ivrii, 1998

Stochastic Spectral Theory for Selfadjoint Feller Operators: ...

The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

Michael Demuth, Jan A. van Casteren, 2000

New Developments in Differential Geometry, Budapest 1996: ...

The Laplace operator is an elliptic second order differential operator. By general elliptic theory it has a discrete eigenvalue spectrum. Since A is nonnegative so are the eigenvalues. If one changes the Riemannian metric the eigenvalues of A ...

J. Szenthe, 1998

Meaning of "Laplace operator" in the English dictionary

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