# vec_calc - Vector Calculus and Conservation Laws uses"del...

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Vector Calculus Electromagnetic Waves and Optics 1 Vector Calculus and Conservation Laws uses “del” or “nabla” operator components are derivatives simplifies many expressions boundary theorems (Stokes, Gauss) convert integral eqs. to differential eqs. particularly helpful for conservation laws reference: “Div, Grad, Curl, and All That”, H. M. Schey, (Norton, New York), 1997. z k y j x i + + = ˆ ˆ ˆ r Vector Calculus Electromagnetic Waves and Optics 2 Vector Calculus ( ) ( ) ( ) 0 , , 2 2 2 2 2 2 2 2 = × = × = × × + + = = f F F F F z f y f x f f z y x f r r r r r r r r r r r r r r gradient curl divergence double derivatives: ( ) z F y F x F F y F x F k x F z F j z F y F i F z f k y f j x f i z y x f z y x x y z x y z + + = + + = × + + = r r r r r ˆ ˆ ˆ ˆ ˆ ˆ , ,

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Vector Calculus Electromagnetic Waves and Optics 3 Gradient directed “uphill” , toward most rapid increase of f
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