374bhw10 - HW#10 Phys374Spring 2007 Prof. Ted Jacobson Due...

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Unformatted text preview: HW#10 Phys374Spring 2007 Prof. Ted Jacobson Due before class, Friday, April 20, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374b/ jacobson@physics.umd.edu 1. The relation between the real Fourier coefficients for the sine and cosine terms are obtained with the help of the following identities: Z - cos( m ) cos( n ) d = mn (1) Z - sin( m ) sin( n ) d = mn (2) Z - cos( m ) sin( n ) d = 0 , (3) where m and n are assumed to be positive integers. Prove these identities by express- ing the cosine and sine in terms of complex exponentials, and using R - e ik d = 2 k . (These are equivalent to eqns (15.3-6) in the textbook. 2. Consider the rectified cosine function defined by f ( x ) = cos( x/ 2 L ) , L x L, (4) and continued periodically so that f ( x + 2 L ) = f ( x ). (a) Sketch the function f ( x ) over several periods....
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374bhw10 - HW#10 Phys374Spring 2007 Prof. Ted Jacobson Due...

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