MATH365-16S2 (C) Semester Two 2016

Applications of Complex Variables

15 points

Start Date: Monday, 11 July 2016
End Date: Sunday, 13 November 2016
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 22 July 2016
  • Without academic penalty (including no fee refund): Friday, 7 October 2016


Applications of complex variable theory in the physical and engineering sciences. Contour integration. Conformal mappings.

Complex variables with applications and special functions are essential tools for pure and applied mathematicians, scientists and engineers.
The material covered is a mix of beautiful theory (e.g. Taylors theorem for functions of a complex variable),  applications and computational techniques (e.g. calculation of Laplace transforms via contour integration).

Learning Outcomes

At the end of the course the student will be familiar with the following topics:
 - complex numbers and functions of a complex variable
 - analytic functions and the Cauchy-Riemann equations
 - Cauchy's theorem.  Taylor and Laurent series.  Singularities

Students will be able to evaluate definite integrals and  calculate Laplace transforms using the calculus of residues

Students will also be familiar with:
 - conformal mappings and applications to electrostatics, heat and fluid flow
 - Legendre polynomials, properties of these, and applications to sphere in a  uniform electric field, potential of a ring of charge

Alternatively students will be familiar with the properties and applications of another family of special functions.


MATH201 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval



Course Coordinator / Lecturer

Rick Beatson


Christopher Price


Assessment Due Date Percentage 
Tutorials 10%
Test 30%
Final Examination 60%

Indicative Fees

Domestic fee $720.00

International fee $3,450.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH365 Occurrences

  • MATH365-16S2 (C) Semester Two 2016