Fall2011-HW11

# Fall2011-HW11 - Homework 11 Math 371 Fall 2012 Assigned...

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Homework 11 Math 371, Fall 2012 Assigned: Friday, December 2, 2011 Due: Tuesday, December 13, 2011 Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, and section. Add 12 for page numbers in the international edition. (1) (Richardson Extrapolation) P. 454 #11 (2) (Newton–Cotes). Suppose that f is a function with four continuous derivatives on the interval [ a,b ]. Recall that the error bound for the composite trapezoidal rule T ( h ) with panel width h is T ( h ) - ˆ b a f ( x ) dx = ( b - a ) h 2 12 f Í ( ξ ) for some ξ [ a,b ]. The error in the composite Simpson’s rule S ( h ) with panel width h is S ( h ) - ˆ b a f ( x ) dx = ( b - a ) h 4 180 f (4) ( ξ ) for some (diﬀerent) ξ [ a,b ]. (a) Let f ( x ) = e - x sin x . For the composite trapezoidal rule and the composite Simpson’s rule, ﬁnd the number of panels n required to integrate
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