SJSU EE 140 - ch3_Vector_Calculus (9 pages)

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ch3_Vector_Calculus



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ch3_Vector_Calculus

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Pages:
9
School:
San Jose State University
Course:
Ee 140 - Principles of Electromagnetic Fields

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Chapter 3 Vector Calculus Dr Ray Kwok SJSU Vector Calculus Dr Ray Kwok Del operator Gradient Divergence Curl Laplacian f f f y z z x y r A A A A i Ai x y z x y z f e i i f x x r A e i ijk j Ak x Ax y y Ay z z Az 2 2 2 2 2 2 x y z 2 can operate on scalar or vector Vector Calculus Dr Ray Kwok 2 useful identities r A 0 f 0 for any vector function A for any scalar function f x1 x 2 r A x1 x 2 A1 A2 x 3 x 3 0 A3 e 1 e 2 f x1 x 2 f x1 f x 2 e 3 x 3 0 f x 3 r in static fields B 0 r E 0 r r B A r E V Vector Calculus Dr Ray Kwok Differential Cartesian Vector Calculus Dr Ray Kwok Differential Cylindrical Vector Calculus Dr Ray Kwok Differential Spherical Vector Calculus Dr Ray Kwok Homework Show that 1 2 3 4 5 r A 0 in spherical coordinates 2 fg f 2 g g 2 f 2 f g for any scalar function f g r r r 2 A A A for any vector function A r r r r r r r r r r A B B A A B B A A B Er Hr Also do Ch 3 4 9 12 15 18 Vector Calculus Dr Ray Kwok Group exercise 1 2 r r E H What are r r r r r r r r r r A B B A A B B A A B Vector Calculus Dr Ray Kwok Exercise 2 r A xy xyz r 2 2 B 3x 4 x y y r r B 2A r r A B r r A B r A r B r A r B



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