ASE 311 Engineering computation, Fall 2009, Homework 11Due: Monday, November 30, 2:00 PM in the lecture room JGB 2.216Report all work, including anym-files you have written. You may also find the commanddiaryuseful in recording yourMATLABsession. Please write clearly and be sure to label for which problemeach solution is.Please, staple Part I and Part II separately and make sure that your name is written on both parts.Part I1. [Derivatives of unequally spaced data] Differentiate the second-order Lagrange polynomialfitted to the data points (u1D4650,u1D4660), (u1D4651,u1D4661) and (u1D4652,u1D4662) to obtain an estimate of the derivativeat any pointu1D465within the range of the prescribed data points. If the data points are equispaced,what formula do you get for the derivative approximation atu1D465=u1D4651?2. Use theMATLABbuilt-in functiongradientto estimate the derivative of the functionu1D453(u1D465) = 2u1D465in the interval [0,1]. Use ten equally spaced points and plot the approximation and the truederivative in the same figure.
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