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# Class9OK - Read Hecht, Chapter 2: 2.1-2.6 Waves:...

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Waves: Mathematical preliminaries The gradient operator: (cartesian coordinates): k z j y i x r r r + + = When the gradient is applied to a scalar function U(x,y,z) the result is a vector called the gradient of U: k z U j y U i x U U r r r + + = (1) The components of the gradient on the axes of coordinates ) cos( | | | | θ = = r d U r d U dU r r Total differential of U : (2)
Waves: Mathematical preliminaries ) cos( | | | | θ = = r d U r d U dU r r Some important properties of the gradient: is directed along the steepest rate of increase of U (cos( )=1) is perpendicular to the any surface U(x,y,z) = const. 1. 2. U U

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Waves: Mathematical preliminaries The divergence of a vector function: (cartesian coordinates): k z y x E j z y x E i z y x E z y x E z y x r r r r ) , , ( ) , , ( ) , , ( ) , , ( + + = z E y E x E E z y x + + = r (3)
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## This note was uploaded on 10/19/2009 for the course PHY 31 taught by Professor Cebe during the Fall '08 term at Tufts.

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Class9OK - Read Hecht, Chapter 2: 2.1-2.6 Waves:...

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