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Area Mathematics - General concepts and linear algebra / Scalar and vector fields

IEV ref102-05-28

en
Laplacian, <of a scalar field>
scalar Δf associated at each point of a given space region with a scalar f, equal to the divergence of the gradient of the scalar field

Δf = div grad f

Note 1 to entry: In orthonormal Cartesian coordinates, the Laplacian of a scalar field quantity is:

Δf= 2 f x 2 + 2 f y 2 + 2 f z 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGWaaiab=r5aejaayI W7caWGMbGaeyypa0ZaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadIhadaahaaWcbeqaaiaaik daaaaaaOGaey4kaSYaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadMhadaahaaWcbeqaaiaaik daaaaaaOGaey4kaSYaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadQhadaahaaWcbeqaaiaaik daaaaaaaaa@5816@ .

Note 2 to entry: The Laplacian of the scalar field f is denoted Δf or ∇2f, where Δ is the Laplacian operator.


fr
laplacien scalaire, m
scalaire Δf associé en chaque point d'un domaine déterminé de l'espace à un scalaire f, défini par la divergence du gradient du champ scalaire

Δf = div grad f

Note 1 à l'article: En coordonnées cartésiennes orthonormées, le laplacien scalaire est:

Δf= 2 f x 2 + 2 f y 2 + 2 f z 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGWaaiab=r5aejaayI W7caWGMbGaeyypa0ZaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadIhadaahaaWcbeqaaiaaik daaaaaaOGaey4kaSYaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadMhadaahaaWcbeqaaiaaik daaaaaaOGaey4kaSYaaSaaaeaacqGHciITdaahaaWcbeqaaiaaikda aaGccaWGMbaabaGaeyOaIyRaaGPaVlaadQhadaahaaWcbeqaaiaaik daaaaaaaaa@5816@ .

Note 2 à l'article: Le laplacien scalaire du champ scalaire f est noté Δf ou ∇2f, où Δ est l'opérateur laplacien.


de
Laplace-Operator (angewandt auf eine skalare Feldgröße), m
skalarer Laplace-Operator, m

es
laplaciana escalar
laplaciana de un campo escalar

ja
ラプラシアン, <スカラ場の>

pl
laplasjan skalarny

pt
laplaciano escalar

sr
лапласијан, <скаларног поља> м јд

sv
Laplaceoperator (på ett skalärfält)

zh
拉普拉斯算子, <标量场的>

Publication date: 2008-08
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