Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S1 / 1 / b

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- Solution b

Solution

The coefficient of

z^{- 1}

in the Laurent series is

- 1

. The residue theorem therefore gives, for the standard positive orientation,

\oint_{C} e^{- 1/ z} d z = 2 πi Res_{z = 0} e^{- 1/ z} = - 2 πi .

The residue theorem applies to an isolated essential singularity as well as to a pole.

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