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1. * Consider the function f(t) = left{egin{array}{ll}1, & 0 < t < frac{pi}{2} \ 0, & -frac{pi}{2} < t < 0end{array} ight., f(t+pi) = f(t). Perform the following tasks: (a) Sketch the given function over exactly 3 periods. (b) Write out the form of Fourier series for f(t). (c) Write out integral expressions for a_n and b_n. (d) Evaluate the integrals in (c) using MATLAB. (e) Use the results in (d) to write out the Fourier series of f(t). (f) Write out the first few terms of the Fourier series in (e). (g) Plot the graphs of finite sums of the Fourier series of f(t) by using MATLAB, and thus figure out roughly how many terms are needed to get a good approximation of f(t). (h) Is f(t) continuous at t = frac{pi}{2}? What value does the Fourier series converge to at this point?

          1. * Consider the function f(t) = left{egin{array}{ll}1, & 0 < t < frac{pi}{2} \ 0, & -frac{pi}{2} < t < 0end{array}
ight., f(t+pi) = f(t). Perform the following tasks:
(a) Sketch the given function over exactly 3 periods.
(b) Write out the form of Fourier series for f(t).
(c) Write out integral expressions for a_n and b_n.
(d) Evaluate the integrals in (c) using MATLAB.
(e) Use the results in (d) to write out the Fourier series of f(t).
(f) Write out the first few terms of the Fourier series in (e).
(g) Plot the graphs of finite sums of the Fourier series of f(t) by using MATLAB, and thus figure out roughly how many terms are needed to get a good approximation of f(t).
(h) Is f(t) continuous at t = frac{pi}{2}? What value does the Fourier series converge to at this point?

$1. * Consider the function f(t) = lefteginarrayll1, 0 < t < fracpi2 0, -fracpi2 < t < 0endarray ight., f(t+pi) = f(t). Perform the following tasks: (a) Sketch the given function over exactly 3 periods. (b) Write out the form of Fourier series for f(t). (c) Write out integral expressions for an and bn. (d) Evaluate the integrals in (c) using MATLAB. (e) Use the results in (d) to write out the Fourier series of f(t). (f) Write out the first few terms of the Fourier series in (e). (g) Plot the graphs of finite sums of the Fourier series of f(t) by using MATLAB, and thus figure out roughly how many terms are needed to get a good approximation of f(t). (h) Is f(t) continuous at t = fracpi2? What value does the Fourier series converge to at this point?$

Added by Susan V.

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