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Clayton First semester 2007 (Day)
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: sketch the evolution of the solutions of the system on a phase-plane diagram; appreciate some applications of phase-plane analysis; be familiar with the basic properties of complex numbers and functions; have developed skills in the evaluation of line integrals; understand Cauchy's integral theorem and its consequences; be able to determine and work with Laurent and Taylor series; understand the method of Laplace transforms and be able to 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; have developed skills in using a computer algebra package.
Examination (3 hours): 50%
Assignments and tests: 40%
Laboratory work: 10%
Three 1-hour lectures and an average of one 1-hour computer laboratory and one 1-hour support class per week