MATH365-12S2 (C) Semester Two 2012

Applications of Complex Variables

15 points, 0.1250 EFTS
09 Jul 2012 - 11 Nov 2012


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 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:


MATH264, EMTH204, (MATH261 and MATH262), EMTH202, MATH243, MATH202 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval.



Streams Day Time Where Notes
Stream 01 Wednesday 11:00am-12:00pm Erskine 446 3 Sep - 14 Oct
Thursday 12:00pm-1:00pm Erskine 446 3 Sep - 14 Oct

Streams Day Time Where Notes
Stream 01 Wednesday 3:00pm-4:00pm Erskine 441 9 Jul - 19 Aug,
3 Sep - 14 Oct
Stream 02 Thursday 9:00am-10:00am Erskine 242 9 Jul - 19 Aug,
3 Sep - 14 Oct

Course Coordinator / Lecturer

Rick Beatson


Huy-Qui Bui


Assessment Due Date Percentage 
Internal Assessment - TBA 40%
Final Examination 60%

Examination and Formal Tests

Exam Wednesday 07 Nov 2012 9:30am-11:30am  
Test Tuesday 04 Sep 2012 7:00pm-8:30pm Erskine 101


Recommended reading (any of the following):

• James Ward Brown & Ruel V. Churchill, Complex variables and Applications, 8th ed., McGraw-Hill, 2009.
• Erwin Kreyszig, Advanced engineering mathematics, 8th ed., John Wiley & Sons, 1999 (or other edition).
• Jerrold E. Marsden & Michael J. Ho man, Basic complex analysis, 2nd ed., W.H. Freeman & Co, New York, 1987.

Course links

MATH365 Homepage

Indicative Fees

Domestic fee $622.00

International fee $3,200.00

* 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

  • MATH365-12S2 (C) Semester Two 2012