Section outline

  • This week we continue with the study of analytic functions. Our focus will be on the theorem

    Theorem: A complex valued function f(z)=u(x,y) + i v(x,y) is analytic if and only if it satisfies the Cauchy-Riemann equations.

    We also study Harmonic functions and how they relate to analytic functions. A function u(x,y) of real variables is said to be harmonic if it satisfies the Laplace's equation.

    Recall our previous encounter with Laplace's equations in MMA 202: Vector Analysis?

    • Students must
      Mark as done

      Learning Objectives

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

      1. Determine whether a function is analytic or not.
      2. Determine the domain of analyticity of an analytic function.
      3. State and use the Cauchy Riemann equations to determine whether a function is analytic.
      4. State the Laplace's equation and use it to determine whether a function is harmonic.
      5. Evaluate the harmonic conjugate of a harmonic function.

      Learning activities

      1. Read Chapter 3 sections 3.1 and 3.2 on analytic functions and attempt exercises.
      2. Read section 3.3 of the course reference book on harmonic functions and attempt exercises.
      3. Read additional uploaded notes below.
      4. Attempt the Mastery and Timed quizzes.

      Below is a video on how to deal with the complex exponential function.

    • Harmonic functions File
      Students must
      View
    • Laplace equation and harmonic functions File
      Students must
      View
    • Discussion forum 5
      Students must
      Mark as done
    • MASTERY QUIZ 5
      Students must
      Receive a grade
    • TIMED QUIZ 5
      Not available unless: You achieve higher than a certain score in MASTERY QUIZ 5