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 is essentially an extension of calculus to complex-valued functions of a complex variable. We will show that such an extension follows a fairly natural course. The mathematical rewards are tremendous and far-reaching, and beautiful results abound. There is a variety of applications of complex functions in Engineering and Science, and it also leads naturally to the field of special functions which itself has many applications. This course will cover the basic theory with an emphasis on some of these applications. It is strongly recommended for students in Mathematics, Engineering and Physics.

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


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



Course Coordinator / Lecturer

Ngin-Tee Koh


Rick Beatson


Tutorials 10%
Test 30%
Final Exam 60%

Notes on final grades
The Department reserves the right to adjust marks and consequent grades, up or down, in
order to achieve consistency of assessment standards.

Textbooks / Resources

Recommended Reading

Erwin Kreyszig; Advanced engineering mathematics; 8th Edition; John Wiley & Sons.

James Ward Brown & Ruel V. Churchill,; Complex variables and Applications; 8th Edition; McGraw-Hill,, 2009.

Jerrold E. Marsden & Michael J. Hoffman; Basic complex analysis; 2nd Edition; W.H. Freeman & Co, 1987.

Indicative Fees

Domestic fee $780.00

International fee $4,250.00

* 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

  • MATH365-20S2 (C) Semester Two 2020