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ECE-305-Lecture2 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 2 Dennis McCaughey, Ph.D. 21 January, 2010
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01/21/2010 Dennis McCaughey, ECE305, Spring 2010 2 Homework Homework Problems 1.5, 1.23, 1.29 Due Jan 26
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01/21/2010 Dennis McCaughey, ECE305, Spring 2010 3 Rectangular Coordinates Rectangular Coordinates ( 29 ( 29 ( 29 2 2 2 Unit vectors: 1 0 0 0 , 1 , 0 0 0 1 Differential Length: Differential Volume: Differential areas: r x y z x y z x y z x r x y z y z v v a v a v a a a a v v a a a v v dL dx dy dz dV dxdydz dx = + +             = = =                   = = + + = , , dy dxdz dydz
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01/21/2010 Dennis McCaughey, ECE305, Spring 2010 4 Cylindrical Coordinates Cylindrical Coordinates ( 29 1 2 2 , , Rectangular to cylindrical tan , , Cylindrical to Rectangular cos , sin , Unit vectors at cos sin 0 sin , cos , 0 0 0 1 r P x y z y x y z z x x y z z P a a a ρ φ φ ρ ρ φ ρ φ φ φ φ φ - = = = + = = = = -     = = =       Differential Volume: Differential areas: , d , dV d d dz d d dz d dz ρ ρ φ ρ ρ φ ρ ρ φ =
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01/21/2010 Dennis McCaughey, ECE305, Spring 2010 5 Transformations Transformations Reisz Representation Theoerm: Every linear transformation on a finite dimension vector space has a matrix representation. Thus Table 1.1 has a matrix representation , x x y z y r c z f f a a a f f a f ρ = = ( 29 1 Unit vectors at tan , cos sin 0 sin cos sin 0 sin cos 0 0 0 1 , cos , 0 0 0 1 ' z z z x x y z y z z f a a f f P y x a a a f f f T a T a a a a a f f f ρ φ φ ρ θ ρ ρ φ φ
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