Chapter 3Vector CalculusDr. Ray KwokSJSUVector Calculus - Dr. Ray KwokDel - operator∇2222222ˆˆˆˆˆˆˆˆzyxAAAzyxzyxAeAzAyAxAAAzfzyfyxfxfefzyxkjijkizyxiiii∂∂+∂∂+∂∂=∇⋅∇=∇∂∂∂∂∂∂=∂=×∇∂∂+∂∂+∂∂=∂=⋅∇∂∂+∂∂+∂∂=∂=∇εrrGradientDivergenceCurlLaplaciancan operate on scalar or vectorVector Calculus - Dr. Ray Kwok2 useful identities0f0A=∇×∇=×∇⋅∇r0x/fx/fx/fx/x/x/eˆeˆeˆf0AAAx/x/x/x/x/x/A321321321321321321=∂∂∂∂∂∂∂∂∂∂∂∂=∇×∇=∂∂∂∂∂∂∂∂∂∂∂∂=×∇⋅∇rVEAB−∇=×∇=rrrfor any vector function Afor any scalar function fin static fields… 0E0B=×∇=⋅∇rr→Vector Calculus - Dr. Ray KwokDifferential - CartesianVector Calculus - Dr. Ray KwokDifferential - CylindricalVector Calculus - Dr. Ray KwokDifferential - SphericalVector Calculus - Dr. Ray KwokHomeworkShow that:1..2..3..4..5..A)A()A(gf2fggf)fg(0A2222rrrr∇−⋅∇∇=×∇×∇∇⋅∇+∇+∇=∇=×∇⋅∇in spherical coordinates.for any scalar function f & g.for any vector function A.()?=×⋅∇ HErrBAABBAABBArrrrrrrrrr)()()()()( ∇⋅−⋅∇−⋅∇+∇⋅=××∇Also, do Ch. 3 # 4, 9, 12, 15, 18Vector Calculus - Dr. Ray KwokGroup exercise()?=×⋅∇ HErr(1)(2)What are α & β??BAABBAABBArrrrrrrrrr)()()()()( ∇⋅−⋅∇−⋅∇+∇⋅=××∇Vector Calculus - Dr. Ray KwokExercise
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