EE103 Section8 - EE103 Winter 2009 Lecture Notes(SEJ...

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EE103 Winter 2009 Lecture Notes (SEJ) Section 8 SECTION 8: INTRODUCTION TO NUMERICAL INTEGRATION (An Application of Polynomial Interpolation) ............................................................................................................................................ 143 Background Information: .................................................................................................................... 143 Newton-Cotes Quadrature: ................................................................................................................. 144 Basic Idea: ............................................................................................................................................. 145 Rectangular Rule ( 1 m = ): .............................................................................................................. 145 Trapezoid Rule ( 2 m = ): ................................................................................................................ 145 Simpson’s Rule ( 3 m = ): ................................................................................................................. 147 Simpson’s is Actually ( ) 5 h Ο : (This subsection is a digression and may be omitted) ........... 148 Basic Newton-Cotes Error Bounds on [ , ] a b : ................................................................................... 150 Composite Integration .......................................................................................................................... 151 Composite Trapezoid Rule .............................................................................................................. 151 Composite Simpson’s Rule .............................................................................................................. 153 Composite Newton-Cotes Error Bounds : .......................................................................................... 155 Usage of Error Bounds ..................................................................................................................... 155 Trapezoid Rule: ............................................................................................................................ 156 Simpson’s Rule: ............................................................................................................................ 157
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