Ee1038aS10

Ee1038aS10 - Overview of Numerical Integration, as an...

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Overview of Numerical Integration, as an Application of Polynomial Interpolation Newton-Cotes Rules bb f x dx P x dx  () 1 m aa 1 _ m f x dx P x dx error term  1 1 2 [,] , , . m m P x interpolates f at m equall ys p a c e d points in a b m P x a polynomial EE103 Slides 8A (SEJ) 1 " 1" The m case Rectangular Approximation a zero degree approximation, P 1 0 ab Pf 0 P x f a 0 P xf b EE103 Slides 8A (SEJ) 2
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Trapezoid Rule (m = 2) b a b 1 () a Px 1 2 b m a mP x  :( ) 1 b fa fb b a  ( () ) ( ) 1 2 a EE103 Slides 8A (SEJ) 3 Simpson’s Rule (m=3) bb 1 m aa f xdx P xdx a b c=(a+b)/2 2 P xdx e r ro r te rm  _ 2 P x interpolates afa cfc bfb ( , ( )),( , ( )) EE103 Slides 8A (SEJ) 4
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3 rd Degree Polynomial EE103 Slides 8A (SEJ) 5 Third degree polynomial (red), interpolating at the m=4 points, 0,1,2,3 Trapezoid, Simpson Trapezoid Approximation ab Simpson’s Approximation EE103 Slides 8A (SEJ) 6
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Summary 2 0 ( ) ( ) ( ) ,rectangular, bb f xdx P xdx Oh h b a   aa 3 () ( ) , f x dx P x dx O h Trapezoid h b a  1 4 ( ) /2 f x dx P x dx O h Simpson h b a 2 5 , / 2 or O h EE103 Slides 8A (SEJ) 7
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This note was uploaded on 06/01/2010 for the course EE EE 103 taught by Professor Jacobsen during the Spring '09 term at UCLA.

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Ee1038aS10 - Overview of Numerical Integration, as an...

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