Lab10 - Engineering 7 Introduction to Programming for...

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Engineering 7: Prof. Alexandre Bayen Introduction to Programming for Engineers Spring 2011 Lab 10: Numerical Differentiation and Integration Date Assigned: 5:00pm, Friday – April 15. Date Due: 5:00pm, Friday – April 22. Problem 1 : Write a function with header [dy, X] = myNumDiff(f, a, b, n, option) where f is handle to a function. The function myNumDiff should compute the derivative of f numerical for n evenly spaced points starting at a and ending at b according to the method defined by option . The input argument option is one of the following strings: ‘forward’ , ‘ backward’ , ‘central’ . Note that for the forward and backward method, the output argument, dy , should be 1x(n-1) , and for the central difference method dy should be 1x(n-2). The function should also output a row vector X that is the same size as dy and denotes the x-values for which dy is valid. Test Cases: >> x = linspace(0, 2*pi,100); >> f = @sin; >> [dyf, Xf] = myNumDiff(f, 0, 2*pi, 10, 'forward'); >> [dyb, Xb] = myNumDiff(f, 0, 2*pi, 10, 'backward'); >> [dyc, Xc] = myNumDiff(f, 0, 2*pi, 10, 'central'); >> plot(x, cos(x), Xf, dyf, Xb, dyb, Xc, dyc) >> title('Analytic and Numerical Derivatives of Sine') >> xlabel('x') >> ylabel('y') >> grid on >> legend('analytic', 'forward', 'backward', 'central') 0 1 2 3 4 5 6 7 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Analytic and Numerical Derivatives of Sine x y analytic forward backward central
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Engineering 7: Prof. Alexandre Bayen Introduction to Programming for Engineers Spring 2011 >> x = linspace(0, pi, 1000); >> f = @(x) sin(exp(x)); >> [dy10, X10] = myNumDiff(f, 0, pi, 10, 'central'); >> [dy20, X20] = myNumDiff(f, 0, pi, 20, 'central'); >> [dy100, X100] = myNumDiff(f, 0, pi, 100, 'central'); >> plot(x, cos(exp(x)).*exp(x), X10, dy10, X20, dy20, X100, dy100) >> xlabel('x') >> ylabel('y') >> title('Numerical Derivative of f(x) = sin(e^{x})') >> legend('Analytic', '10 points', '20 points', '100 points') 0 0.5 1 1.5 2 2.5 3 3.5 -25 -20 -15 -10 -5 0 5 10 15 20 x y Numerical Derivative of f(x) = sin(e x ) Analytic 10 points 20 points 100 points
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Engineering 7: Prof. Alexandre Bayen
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