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lec12

# lec12 - b h n a h n a h n a h a h a h a a dx x f dx x f dx...

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Lecture Notes for C-term 2009 Lecture 12 Prof. R. Ludwig Department of Electrical and Computer Engineering Worcester Polytechnic Institute Worcester, MA ECE 2112 Electromagnetic Theory Copyright, 2000 © R. Ludwig

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ECE2112_12 2 Lecture 12 Objectives • What is numerical integration? • How can the potential be numerically integrated? • Critical issues involve discretization and singularities?
ECE2112_12 3 ECE 2112 - Lecture 12 Trapezoidal evaluation of integral: b a dx ) x ( f trapezoid of Area dx x f b a ) ( ) )( ( 2 1 height panels of Sum   ) a b ( ) a ( f ) b ( f 2 1 2 ) b ( f ) a ( f ) a b ( b a x y=f(x)

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ECE2112_12 4 ECE 2112 Lecture 12 • Multi-segment configuration • Summing up segments
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Unformatted text preview: b h ) n ( a h ) n ( a h ) n ( a h a h a h a a dx ) x ( f dx ) x ( f ... dx ) x ( f dx ) x ( f 1 1 2 2 b a dx ) x ( f b a dx ) x ( f ) b ( f ) ih a ( f ) a ( f n a b n i 1 1 2 2 f(x) a b y x 4 a b a 4 2 a b a 4 3 a b a ECE2112_12 5 ECE 2112- Lecture 12 • Complex field distributions • Numerical Evaluation S S z y y x x dS z y x z y x V 2 2 2 ) ' ( ) ' ( ' ) ' , ' , ' ( 4 1 ) , , (...
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lec12 - b h n a h n a h n a h a h a h a a dx x f dx x f dx...

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