Physics 225 Formula Sheet - ! ! f " d ! l ! a ! b # =...

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Unformatted text preview: ! ! f " d ! l ! a ! b # = f ( ! b ) $ f ( ! a ) ( ! ! " ! E ) # d ! A Surf $ = ! E # d ! l % Surf " $ ( ! ! " ! E ) dV Vol # = ! E " d ! A $ Vol " # d ! ! " = ! # ! " GGS ! 1 : ! 2 : ! 3 : d ! l = ( h i dr i ) r i i = 1 3 ! ! ! f = r i h i " f " r i i = 1 3 # ! ! " ! E = 1 h 1 h 2 h 3 # # r i ( h j h k E i ) i = 1 3 $ ! ! " ! E = r i i = 1 3 # 1 h j h k $ $ r j ( h k E k ) % $ $ r k ( h j E j ) & ( ( ) * + + r i = h i ! ! r i " h i = 1 ! ! r i r 1 r 2 r 3 h 1 h 2 h 3 x y z pos vec r Cartes x y z 1 1 1 x y z x x + y y + z z Spher r 1 r r sin r sin cos r sin sin r cos r r Cylind s z 1 s 1 s cos s sin z s s + z z Line Element: Coordinate Systems Unit Vectors: Complex #s e i ! = cos ! + i sin ! imag x ! z = re i ! = x + iy r real y ! z * ! x " iy | ! z | ! ! z * ! z = r Switch to polar for multiplic n , divis n , powers Switch to Cartesian for addition, subtraction If ( x + iy ) in denominator, multiply by ( x iy )/(x iy ) Physical observable =...
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This note was uploaded on 10/06/2011 for the course PHYS 225 taught by Professor Makins during the Spring '10 term at University of Illinois, Urbana Champaign.

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Physics 225 Formula Sheet - ! ! f " d ! l ! a ! b # =...

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