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

IEV ref102-05-06

Symbol
dA

en
scalar surface element
at a given point of a given surface, area of a surface element containing the point and contained in a sphere of infinitesimal radius

Note 1 to entry: For a surface defined by r = f(u, v) where (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , the scalar surface element is given by

| f u × f v |dudv MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaemaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamyDaaaacqGHxdaTdaWcaaqa aiabgkGi2kaahAgaaeaacqGHciITcaWG2baaaaGaay5bSlaawIa7ai abgwSixlGacsgacaWG1bGaciizaiaadAhaaaa@4A27@ .

Note 2 to entry: For a surface defined by the equation z = f(x, y), the scalar surface element is given by

1+ ( f x ) 2 + ( f y ) 2 dxdy MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaakaaabaGaaGymai abgUcaRmaabmaabaWaaSaaaeaacqGHciITcaWGMbaabaGaeyOaIyRa amiEaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccqGHRa WkdaqadaqaamaalaaabaGaeyOaIyRaamOzaaqaaiabgkGi2kaadMha aaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaGcciGGKb GaamiEaiGacsgacaWG5baaaa@4A2F@ .


fr
élément scalaire de surface, m
en un point donné d'une surface donnée, aire d'un élément de cette surface contenant le point et contenu dans une sphère de rayon infinitésimal

Note 1 à l'article: Pour une surface définie par r = f(u, v), où (u,v)U R 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWG1bGaai ilaiaadAhacaGGPaGaeyicI4CcLbuacaqGvbGccqGHgksZieqacaWF sbWaaWbaaSqabeaajugabiaabkdaaaaaaa@440F@ , l'élément scalaire de surface est

| f u × f v |dudv MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaemaabaWaaSaaae aacqGHciITcaWHMbaabaGaeyOaIyRaamyDaaaacqGHxdaTdaWcaaqa aiabgkGi2kaahAgaaeaacqGHciITcaWG2baaaaGaay5bSlaawIa7ai abgwSixlGacsgacaWG1bGaciizaiaadAhaaaa@4A27@ .

Note 2 à l'article: Pour une surface définie par l'équation z = f(x, y), l'élément scalaire de surface est

1+ ( f x ) 2 + ( f y ) 2 dxdy MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaakaaabaGaaGymai abgUcaRmaabmaabaWaaSaaaeaacqGHciITcaWGMbaabaGaeyOaIyRa amiEaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccqGHRa WkdaqadaqaamaalaaabaGaeyOaIyRaamOzaaqaaiabgkGi2kaadMha aaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaGcciGGKb GaamiEaiGacsgacaWG5baaaa@4A2F@ .


de
skalares Flächenelement, n

es
elemento escalar de superficie

ja
スカラ面積素

pl
element różniczkowy skalarny powierzchni

pt
elemento escalar de superfície

sr
скаларни елемент површи, м јд

sv
skalärt ytelement

zh
标量曲面元素

Publication date: 2008-08
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