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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 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).
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. SingularitiesStudents will be able to evaluate definite integrals and calculate Laplace transforms using the calculus of residuesStudents 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.
MATH201 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval
General information for students
Domestic fee $749.00
International fee $3,788.00
* 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