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# HW7 - Z 6-2 x-3 x 2 4 x 4-x 5 dx(a[1pt analytically(b[1pt...

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EMAE 250: Homework 7 March 17, 2011 1. [3pt] We derived a 0 and a k from the following equation in the class. Find b k by using the cosine and sine lows and the facts that R T 0 cos( αt ) dt = R T 0 sin( βt ) dt = 0. Note that w 0 = 2 π/T . f ( t ) = a 0 + X k =1 [ a k cos( kw 0 t ) + b k sin( kw 0 t )] Hint: Begin by multiplying ‘ sin( mw 0 t ) ’ to both sides of the equation and integrate over (0, T). 2. [3pts] Use a continuous Fourier series to approximate the wave form shown below. 3. Evaluate the following integral:
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Unformatted text preview: Z 6 (-2 + x-3 x 2 + 4 x 4-x 5 ) dx (a) [1pt] analytically; (b) [1pt] single application of the trapezoidal rule and calculate the true error, E t = | I true-I approx | where I true is the analytical solution obtained from (a) and I approx is an approximated value; (c) [2pt] composite trapezoidal rule with n = 2 and n = 4 and calculate E t for each case. 1...
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