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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).
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 chargeAlternatively students will be familiar with the properties and applications of another family of special functions.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
MATH264, EMTH204, (MATH261 and MATH262), EMTH202, MATH243, MATH202 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval.
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. Homan, Basic complex analysis, 2nd ed., W.H. Freeman & Co, New York, 1987.
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.