MATH365-21S2 (C) Semester Two 2021

Applications of Complex Variables

15 points

Details:
Start Date: Monday, 19 July 2021
End Date: Sunday, 14 November 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 1 August 2021
  • Without academic penalty (including no fee refund): Friday, 1 October 2021

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 2021

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 13:00 - 14:00 F3 Lecture Theatre
19 Jul - 22 Aug
13 Sep - 24 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 13:00 - 14:00 Rehua 003 Music
19 Jul - 29 Aug
13 Sep - 24 Oct
Tutorial A
Activity Day Time Location Weeks
01 Friday 10:00 - 11:00 E13
19 Jul - 29 Aug
13 Sep - 24 Oct
02 Friday 13:00 - 14:00 Jack Erskine 441
19 Jul - 29 Aug
13 Sep - 24 Oct
03 Friday 09:00 - 10:00 Jack Erskine 241
19 Jul - 29 Aug
13 Sep - 24 Oct
04 Friday 15:00 - 16:00 Jack Erskine 446
19 Jul - 29 Aug
13 Sep - 24 Oct

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Tuesday 13:00 - 14:00 Ernest Rutherford 140
23 Aug - 29 Aug

Course Coordinator / Lecturer

Ngin-Tee Koh

Indicative Fees

Domestic fee $788.00

International fee $4,438.00

* 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

  • MATH365-21S2 (C) Semester Two 2021