(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples




IEVref:102-05-19ID:
Language:enStatus: Standard
Term: gradient
Synonym1:
Synonym2:
Synonym3:
Symbol:
Definition: vector grad f associated at each point of a given space region with a scalar f, having a direction normal to the surface on which the scalar field has a constant value, in the sense of increasing value of f, and a magnitude equal to the absolute value of the derivative of f with respect to distance in this normal direction

Note 1 to entry: The gradient expresses the variation of the scalar field quantity from the given point to a point at an infinitesimal distance ds MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaWGZbaaaa@3732@ in the direction of a given unit vector e by the scalar product df = grad fe ds.

Note 2 to entry: In orthonormal Cartesian coordinates, the three coordinates of the gradient are:

f x , f y , f z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaeyOaIy RaaGPaVlaadAgaaeaacqGHciITcaaMc8UaamiEaaaacaaMe8UaaGjb VlaaysW7caGGSaGaaGjbVlaaysW7caaMe8UaaGjbVpaalaaabaGaey OaIyRaaGPaVlaadAgaaeaacqGHciITcaaMc8UaamyEaaaacaaMe8Ua aGjbVlaaysW7caGGSaGaaGjbVlaaysW7caaMe8UaaGjbVpaalaaaba GaeyOaIyRaaGPaVlaadAgaaeaacqGHciITcaaMc8UaamOEaaaaaaa@6774@ .

Note 3 to entry: The gradient of the scalar field f is denoted grad f or f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGWabiab=DGirlaayI W7caWGMbaaaa@3CD4@ .


Publication date:2008-08
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
2017-08-24: Order of <i> and <b> tags corrected. LMO
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: