Section outline

  • In this topic we continue with the study of contour integrals. In particular we apply the Cauchy Integral Formula and The Cauchy Integral Formula for derivatives to solve complex integrals.

    We also have a brief study of Taylor series and Laurent Series of complex functions. 

    In computing Laurent series, in most cases the Laurent theorem is not applied but we do use the other easily available techniques to determine the coefficients of the series. These techniques are the binomial expansion and the Taylor series expansion. This is because of the simplicity of these techniques in comparison to Laurent theorem.

    Learning Objectives

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

    • Evaluate complex integrals using the Cauchy Integral Formula.
    • Compute the Taylor series of various functions.
    • Determine the radius of convergence of various  series.
    • Compute Laurent series of a function valid for a specific region.
    Learning Activities
    • Read section 5.5 of our course reference book and attempt the exercises.
    • Read sections 6.2 and 6.3 of our course reference book on Taylor series and Laurent series.
    • Download and read the attached lecture notes below.
    • Watch the video on Taylor and Laurent series for additional information.

    • Learning Resources

    • Students must
      Mark as done

    • MASTERY QUIZ 7
      Students must
      Mark as done
    • TIMED QUIZ 7
      Not available unless: You achieve higher than a certain score in MASTERY QUIZ 7
    • Computation of Laurent series Forum