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 in the direction of a given unit vector e by the scalar product df = grad f ⋅ e ds.
Note 2 to entry: In orthonormal Cartesian coordinates, the three coordinates of the gradient are:
∂ f∂ x , ∂ f∂ y , ∂ f∂ z.
Note 3 to entry: The gradient of the scalar field f is denoted grad f or ∇ f.
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 f ⋅ e ds.
∂ 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@ .