Section outline

  • In this topic, we use the concept of the limit of a complex function to define continuity of a complex function. We also introduce the concept of complex differentiation. Cauchy Riemann equations will be introduced and used to prove analyticity of complex functions.

    • Students must
      Mark as done

      Objectives

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

      1. Determine whether a complex function is continuous in a region or not.
      2. State the Cauchy Riemann equations.
      3. Determine whether a certain complex valued function is analytic or not.
      4. Compute the derivatives of complex functions.
      5. Determine whether a function is harmonic or not.
      6. Calculate harmonic conjugates of harmonic functions.

      Learning activities

      1. Read section 2.6 and chapter 3 of the course reference book.
      2. Read additional lecture notes provided below.
      3. Watch tutorial videos to enhance your understanding of concepts covered in this topic.
      4. Attempt weekly quizzes for this topic within the time limits.
      5. Engage in discussions with colleagues on the forum.
    • Students must
      Mark as done

      Learning Activities

      1. Download Topic 3 Lecture Notes and also the extra material and read.
      2. Solve exercises in Topic 3 Lecture Notes and submit your results.
      3. Read pages 69-73 of Course Book 1 and 32-36 of Course Book 2 and make short notes.
      4. Browse web page en.wikipedia.org/wiki/Harmonic_function.
      5. Engage your colleagues in discussion.
    • Students must
      Mark as done

      Learning Resources

      Analytic functions

    • Discussion forum 4
      Students must
      Make forum posts: 1
    • MASTERY QUIZ 4
      Students must
      Receive a grade
    • TIMED QUIZ 4
      Not available unless: You achieve higher than a certain score in MASTERY QUIZ 4