6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
- Second semester 2018 (On-campus)
Complex numbers and functions; domains and curves in the complex plane; differentiation; integration; Cauchy's integral theorem and its consequences; Taylor and Laurent series; Laplace and Fourier transforms; complex inversion formula; branch points and branch cuts; applications to initial value problems.
On completion of this unit students will be able to:
- Understand the basic properties of complex numbers and functions, including differentiability;
- Evaluate line integrals in the complex plane;
- Understand Cauchy's integral theorem and its consequences;
- Determine and work with Laurent and Taylor series;
- Understand the method of Laplace transforms and evaluate the inverse transform;
- Appreciate the importance of complex analysis for other mathematical units, as well as for physics and engineering, through seeing applications of the theory;
- Use a computer algebra package to assist in the application of complex analysis.
Examination (3 hours): 60% (Hurdle)
Continuous assessment: 40%
Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information