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About this episode

We explored isolated singularities that have finite negative parts of their Laurent series, called poles. We defined the order of a pole and a simple pole as a pole of order 1. We proved a lemma saying that a functions norm goes to infinity near a pole, but when multiplied by a certain power of (z - z_0), the pole turns into a removable singularity. We finished by showing that all singularities of rational functions are removable or poles.

• Release Date

  Jan 6, 2011

• Runtime

  01:09:06