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q318085f03

# q318085f03 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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18.085 Prof. Strang Quiz 3 December 3, 2003 Your name is: Grading 1 2 3 Total Thank you for taking 18.085, I hope you enjoyed it. 1) (35 pts.) Suppose the 2 π -periodic f ( x ) is a half-length square wave: f ( x ) = 1 for 0 < x < π/ 2 for π/ 2 < x < 0 1 0 elsewhere in [ π, π ] (a) Find the Fourier cosine and sine coeﬃcients a k and b k of f ( x ). π (b) Compute π ( f ( x )) 2 dx as a number and also as an in±nite series using 2 the a k and b 2 k . x (c) DRAW A GRAPH of the integral I ( x ) = 0 f ( t ) dt from π to π . What are the Fourier coeﬃcients A k and B k of I ( x )? df (d) DRAW A GRAPH of the derivative D ( x ) = dx from π to π . What are the Fourier coeﬃcients of D ( x )?
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q318085f03 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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