MATH365-20S2 (C) Semester Two 2020

Applications of Complex Variables

15 points

Start Date: Monday, 13 July 2020
End Date: Sunday, 8 November 2020
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 24 July 2020
  • Without academic penalty (including no fee refund): Friday, 25 September 2020


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



Timetable 2020

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 11:00 - 12:00 A9 Lecture Theatre 13 Jul - 23 Aug
7 Sep - 18 Oct
Lecture B
Activity Day Time Location Weeks
01 Thursday 09:00 - 10:00 A8 Lecture Theatre 13 Jul - 23 Aug
7 Sep - 18 Oct
Tutorial A
Activity Day Time Location Weeks
01 Friday 11:00 - 12:00 Rehua 427 Technology Workshop 13 Jul - 23 Aug
7 Sep - 18 Oct
02 Thursday 11:00 - 12:00 John Britten 117 HP Seminar Room 13 Jul - 23 Aug
7 Sep - 18 Oct

Course Coordinator

Ngin-Tee Koh


Ngin-Tee Koh

Indicative Fees

Domestic fee $780.00

International fee $4,250.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

All MATH365 Occurrences

  • MATH365-20S2 (C) Semester Two 2020