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.
Faculty
Organisational Unit
School of Mathematical Sciences
Chief examiner(s)
Coordinator(s)
Dr Zihua Guo
Professor Paul Cally
Unit guides
Synopsis
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.
Outcomes
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.
Assessment
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.
Workload requirements
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information