Section outline

  • Highlighted

    We start by the study of singularities of complex integrals. We classify the three types of singularities from the Laurent series expansion of the complex function.

    For a case when the singularities are poles, we use the Laurent series expansion of the complex function to determine the residue of the function at that particular point. The residues are then used to evaluate the integral of the complex function. This is the study of the residue theorem.

    • Learning Objectives

      By the end of this topic you should be able to:

      1. Compute the residue of analytic functions with finite number of poles of various orders.
      2. State the Residue theorem.
      3. Use the Residue theorem to evaluate integrals.

    • Learning Activities

      1. Read sections 6.4 and 6.5 of the course reference book.
      2. Attempt exercises in sections 6.4 and 6.5 of the course reference book.
      3. Watch additional videos on the Residue theorem..
      4. Attempt the weekly homework.

    • Topic Summary

      When analytic function has more than one pole in a certain closed curve then the best way to find its integral over that curve is to use Residue theorem since it will be easy to compute the function's residue at each and every pole.

    • Learning Resources

    • Topic 8 Lecture Notes File
    • Extra Notes File
    • Residue theorem Forum
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