MATH365-22S2 (C) Semester Two 2022

Applications of Complex Variables

15 points

Details:
Start Date: Monday, 18 July 2022
End Date: Sunday, 13 November 2022
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 31 July 2022
  • Without academic penalty (including no fee refund): Sunday, 2 October 2022

Description

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.

Pre-requisites

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

Restrictions

MATH342

Timetable 2022

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Thursday 12:00 - 13:00 Ernest Rutherford 465
18 Jul - 28 Aug
12 Sep - 23 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 16:00 - 17:00 Beatrice Tinsley 111
18 Jul - 28 Aug
12 Sep - 23 Oct
Tutorial A
Activity Day Time Location Weeks
01 Monday 15:00 - 16:00 Jack Erskine 239
18 Jul - 28 Aug
12 Sep - 23 Oct
02 Wednesday 09:00 - 10:00 Jack Erskine 239
18 Jul - 28 Aug
12 Sep - 23 Oct
03 Wednesday 11:00 - 12:00 Jack Erskine 239
18 Jul - 28 Aug
12 Sep - 23 Oct

Course Coordinator / Lecturer

Ngin-Tee Koh

Indicative Fees

Domestic fee $802.00

International fee $4,563.00

* 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

  • MATH365-22S2 (C) Semester Two 2022