Section outline

  • This week we start on the study of integration in the complex plane. There are some similarities with integration involving real variables, but as you will find out, the integrals here cover a much wider class of functions. We will also introduce (and use) techniques and formulas for integrating in the complex plane.

    Students are encouraged to read section 5.1 of the course lecture notes to review on Real integrals.

    The main theme in integration in the complex plane is contour integrals (integrating over a curve). Techniques for evaluating the integral will depend on the nature of the curve, and the function being integrated with respect to the said curve.

    • Learning Objectives

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

      1. Evaluate contour integrals by reparameterization of curves.
      2. Use properties of contour integrals in calculating integrals.
      3. Evaluate integrals over piecewise smooth curves.
      4. Determine bounds of contour integrals.
      5. Apply the Cauchy Goursat theorem in calculating contour integrals.
      Learning activities
      1. Read section 5.1 of the course lecture notes to review on Real integrals
      2. Read section 5.2 of the lecture notes on contour integrals
      3. Read on section 5.3 of the lecture notes on Cauchy Goursat theorem and its application in solving contour integrals.
      4. Download and read additional lecture notes provided below.
      5. Attempt exercises in the course reference book and thee weekly quizzes. 

      Watch the videos below for an in-depth explanation of contour integrals.

    • Learning Resources

    • Topic 6 Lecture Notes File
    • Extra material File
    • Discussion forum
    • MASTERY QUIZ 6
      Students must
      Mark as done
    • TIMED QUIZ 6
      Not available unless: You achieve higher than a certain score in MASTERY QUIZ 6