Year
2021
Units
4.5
Contact
1 x 120-minute lecture-1 weekly
1 x 60-minute lecture-2 weekly
1 x 1-hour tutorial weekly
1 x 60-minute lecture-2 weekly
1 x 1-hour tutorial weekly
Prerequisites
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
This topic includes: 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.
Educational aims
This topic aims to ensure that the students have a basic understanding of the following:
- Functions of a complex variable
- Differentiation and integration of complex valued functions
- Solving Laplace's equation
- Evaluating real valued integrals and infinite products using complex analysis
Expected learning outcomes
- Find detailed maps of complex valued functions
- Find derivatives and understand the concept of analytic functions
- Evaluate simple integrals of complex valued functions
- Test infinite series for convergence and divergence
- Find Taylor and Laurent series
- Apply the residue theorem to evaluate real integrals
- Apply Rouche's theorem to find the number of zeros of polynomials
Key dates and timetable
Timetable details for 2021 are no longer published.
Sturt Rd, Bedford Park
South Australia 5042
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