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# Project1 - you are under 3 or 1 3 Sine and Cosine Series...

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Project 1: Basic Fourier Series The following items should be completed, and presented in an orderly and professional manner. The goal submission date it September 24. 1. Compute the Fourier series for the function f ( t ) = t , a) on [ - π, π ], and b) on [ - 2 π, 2 π ]. Plot the approximations using 5, 10, and 15 terms on [ - 4 π, 4 π ]. 2. Verify that the Fourier Isometry holds on [ - π, π ] for f ( t ) = t . To do this, a) calculate the coefficients of the orthogonal Fourier series from representation ?? , b) calculate the sum of the squared coefficients, and c) Calculate the norm of the function as π - π | f ( t ) | 2 dt. How many terms in the Fourier series are necessary to have the isometry be under 5%? How many until
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Unformatted text preview: you are under 3%, or 1%. 3. Sine and Cosine Series Calculate the sine and cosine series for f ( t ) = t on [0 , 1]. Plot the ±rst 30 terms of these series on [-3 , 3]. Estimate the error between both series and the function on [0 , 1] after 30 terms. How many more terms of the sine series are necessary to achieve the same error as was achieved with the cosine series and 30 terms? 4. Sine and Cosine Series Plot the ±rst 30 terms of the derivatives of both the sine and cosine series in the above problem. What do you observe? 1...
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