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2. Vector Calculus Chapter Summary

2. Vector Calculus Chapter Summary. • The grad, div, and curl in Cartesian coordinates are. • The coordinate-independent definitions of grad, div, and curl are.

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2. Vector Calculus Chapter Summary

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  1. 2. Vector Calculus Chapter Summary • The grad, div, and curl in Cartesian coordinates are G L Pollack and D R Stump Electromagnetism

  2. • The coordinate-independent definitions of grad, div, and curl are §In the second equation, dV is a small volume and the limit means dV shrinks to a point. The integral is the flux of F outward through the boundary of dV. The divergence is a scalar. § In the third equation, dA is a small surface area which shrinks to a point. The integral is the line integral around the boundary of dA. The curl is a vector, so it is implied by the equation that the right-hand side is the component of F normal to the surface.) G L Pollack and D R Stump Electromagnetism

  3. • The grad, div, and curl in cylindrical or spherical coordinates are not simple generalizations of the Cartesian equations, because of scale factors. The formulas for these operators are in Tables 2.3 and 2.4. • Two important integral identities are G L Pollack and D R Stump Electromagnetism

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