MATH365-24S2 (C) Semester Two 2024

Applications of Complex Variables

15 points

Start Date: Monday, 15 July 2024
End Date: Sunday, 10 November 2024
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 28 July 2024
  • Without academic penalty (including no fee refund): Sunday, 29 September 2024


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.
    • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.


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



Timetable 2024

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Thursday 13:00 - 14:00 Meremere 105 Lecture Theatre
15 Jul - 25 Aug
9 Sep - 20 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 12:00 - 13:00 E16 Lecture Theatre
15 Jul - 25 Aug
9 Sep - 20 Oct
Tutorial A
Activity Day Time Location Weeks
01 Friday 14:00 - 15:00 Rata 128 Tutorial Room
15 Jul - 25 Aug
9 Sep - 20 Oct
02 Friday 11:00 - 12:00 Rata 128 Tutorial Room
15 Jul - 25 Aug
9 Sep - 20 Oct
03 Friday 10:00 - 11:00 Rata 128 Tutorial Room
15 Jul - 25 Aug
9 Sep - 20 Oct

Course Coordinator

Ngin-Tee Koh

Indicative Fees

Domestic fee $847.00

International fee $4,988.00

* 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 .

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  • MATH365-24S2 (C) Semester Two 2024