Due 022009
Physics 132
Winter 2009
P. Kraus
HOMEWORK #5
Material covered: sections 4052. We are skipping section 43 and 47
Hand into box marked “132” outside 1707D 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 nonanalytic. In fact, this last statement as well as the CauchyGoursat theorem
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 Winter '06
 staff
 Physics, Work, Cauchy's integral theorem, Lists of integrals, AugustinLouis Cauchy

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