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hw11 - ASE 311 Engineering computation Fall 2009 Homework...

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ASE 311 Engineering computation, Fall 2009, Homework 11 Due: Monday, November 30, 2:00 PM in the lecture room JGB 2.216 Report all work, including any m -files you have written. You may also find the command diary useful in recording your MATLAB session. Please write clearly and be sure to label for which problem each solution is. Please, staple Part I and Part II separately and make sure that your name is written on both parts. Part I 1. [Derivatives of unequally spaced data] Differentiate the second-order Lagrange polynomial fitted to the data points ( u1D465 0 ,u1D466 0 ), ( u1D465 1 ,u1D466 1 ) and ( u1D465 2 ,u1D466 2 ) to obtain an estimate of the derivative at any point u1D465 within the range of the prescribed data points. If the data points are equispaced, what formula do you get for the derivative approximation at u1D465 = u1D465 1 ? 2. Use the MATLAB built-in function gradient to estimate the derivative of the function u1D453 ( u1D465 ) = 2 u1D465 in the interval [0 , 1]. Use ten equally spaced points and plot the approximation and the true derivative in the same figure.
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