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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