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homework5

# homework5 - HOMEWORK#5 Due Physics 132 Winter 2009 P Kraus...

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Due 02-20-09 Physics 132 Winter 2009 P. Kraus HOMEWORK #5 Material covered: sections 40-52. We are skipping section 43 and 47 Hand into box marked “132” outside 1-707D PAB by 3pm Fri. —————————————————————————————————————————— Key points: The integrals in this problem set involving integrating around closed contours various func- tions that are analytic except at isolated points. For such integrals the key points to know are the following: Cauchy - Goursat theorem : I C f ( z ) dz = 0 if f ( z ) analytic in C Cauchy integral formula : I C f ( z ) ( z - z 0 ) n +1 dz = 2 πif ( n ) ( z 0 ) n ! if f ( z ) analytic in C and z 0 in C In the Cauchy integral formula the contour is taken to go counterclockwise around z 0 (if it goes clockwise you should ﬂip the sign of the answer). Also, the shape of C can be altered without changing the value of the integral as long as the contour never crosses a point where the integrand is non-analytic. In fact, this last statement as well as the Cauchy-Goursat theorem

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homework5 - HOMEWORK#5 Due Physics 132 Winter 2009 P Kraus...

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