1 x 120-minute lecture-1 weekly
1 x 60-minute lecture-2 weekly
1 x 1-hour tutorial weekly
1 of MATH2711, ENGR2711
Enrolment not permitted
1 of MATH8711, MATH9711 has been successfully completed
Assumed knowledge
Knowledge and skills such as can be obtained from completing MATH2711 Several Variable Calculus.
Topic description
Elementary mappings and transcendental functions in the complex domain; branch of argument; branch of logarithm. Complex power series, domain of convergence. Analytic functions; Cauchy-Riemann equations. Möbius transformation; conformal mapping; Schwarz-Christoffel transformations and applications. Taylor and Laurent series. Applications of the calculus of residues. Rouche's theorem. Infinite products.
Educational aims
The topic aims to ensure that the students have a basic understanding of the following:

  1. Functions of a complex variable
  2. Differentiation and integration of complex valued functions
  3. Solving Laplace's equation
  4. Evaluating real valued integrals and infinite products using complex analysis
Expected learning outcomes
At the completion of the topic, students are expected to be able to:

  1. Find detailed maps of complex valued functions
  2. Find derivatives and understand the concept of analytic functions
  3. Evaluate simple integrals of complex valued functions
  4. Solve Laplace's equation in bounded and unbounded domains through conformal mapping
  5. Test infinite series for convergence and divergence
  6. Find Taylor and Laurent series
  7. Apply the residue theorem to evaluate real integrals
  8. Apply Rouche's theorem to find the number of zeros of polynomials
  9. Evaluate infinite products