Complex Analysis

Description

Complex analysis forms a basis for not only advanced mathematical topics (including differential equations, number theory, operator theory and others) but also for special functions of mathematical and quantum physics - subjects used to understand the world in which we live. The course covers fundamental knowledge in the theory of analytical functions with applications to definite integration and culminates with study of harmonic and special functions.

Availability

Callaghan Campus

  • Semester 2 - 2015

Learning Outcomes

1. Use analytical functions and conformal mappings;

2. Compute definite integrals using residue calculus;

3. Appreciate the existance of special functions and their use in a range of contexts.

Content

  • Functions of complex variable.
  • Differentiation of functions.
  • Cauchy's integral theorem.
  • The calculus of residues. Series expansions.
  • Contour integration.
  • Conformal mappings and further results on analytic functions.
  • Harmonic functions.
  • Entire functions and infinite products.
  • Special functions.

Assumed Knowledge

MATH2310

Assessment Items

Written Assignment: Written Assignments

Quiz: Quiz - Class

Formal Examination: Examination: Formal

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

Tutorial work will be integrated with the lecture material.