Abstract

This subject allows you to appreciate how complex analysis extends the ideas of calculus to the complex plane, and throws light on real number problems. It generalises the concepts of calculus (limits, derivatives, Taylor series and integrals) to functions of complex variables. The subject culminates with residue theory and its … For more content click the Read More button below.

Syllabus

Complex numbers and their properties.Complex functions, limits and continuity.Derivatives, the Cauchy-Riemann equations, analytic functions.Elementary functions.Integration of complex functions.Power series methods.Residue theory.Applications.

Learning outcomes

Upon successful completion of this subject, students should:
1.
be able to explain the nature of complex numbers, and their representation in the complex plane;
2.
be able to explain the concept of function as applied to complex numbers, and the ideas of limit, continuity, and differentiation of complex functions;
3.
be able to identify elementary functions defined in terms of complex numbers;
4.
be able to apply the techniques of integration in the complex plane;
5.
be able to write complex functions as Taylor and Laurent series and
6.
be able to apply residue theory to evaluate closed contour integrals.

Enrolment restrictions

Available to undergraduate students only. Not available to students who have completed MTH406.