MATH365-14S2 (C) Semester Two 2014

Applications of Complex Variables

15 points

Details:
Start Date: Monday, 14 July 2014
End Date: Sunday, 16 November 2014
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 25 July 2014
  • Without academic penalty (including no fee refund): Friday, 10 October 2014

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 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.

Prerequisites

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

Restrictions

MATH342

Course Coordinator / Lecturer

Rick Beatson

Lecturer

Ngin-Tee Koh

Assessment

Assessment Due Date Percentage 
Tutorials 10%
Test 30%
Final Examination 60%

Textbooks / Resources

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.

Indicative Fees

Domestic fee $672.00

International fee $3,388.00

* 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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  • MATH365-14S2 (C) Semester Two 2014
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