3 x 50-minute lectures weekly
1 x 50-minute tutorial weekly
Enrolment not permitted
MATH3711 has been successfully completed
Assumed knowledge
Several Variable Calculus, integration of fucntions of a single variable.
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. Mobius transformation; conformal mapping; Schwarz-Christoffel transformations and applications. Taylor and Laurent series. Applications of the calculus of residues. Rouche's theorem. Infinite products. Iteration of complex valued functions and their Julia and Fatou sets
Educational aims
  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
  5. Julia and Fatou sets
Expected learning outcomes
At the completion of this 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
  10. Iteration of complex valued functions and their Julia and Fatou sets