This unit has been discontinued.
Offered in odd numbered years only
Offered subject to student demand/lecturer availability
Introduction
This unit provides the basic tools in the use of complex variables to solve practical problems in Applied Mathematics and Physics. It continues the use of integral transform methods to solve ordinary and partial differential equations. Analytic functions. The elementary functions. Contour integrals, Cauchy's integral theorem and the integral formula. Taylor and Laurent series. The residue theorem. Evaluating real integrals using complex methods. Conformal mapping and applications. Differential equations with regular singular points and the Frobenius method. Special functions. The Fourier transform and inverse. Evaluating Fourier transform using complex variable theory. Convolution theorem. Solving PDE's using Fourier transforms. Fourier transform of generalized functions. The Laplace transform and its inversion formula (the Bromwich integral). The convolution theorem. Solving ODE's and PDE's using Laplace transforms. Integral Equations. Fredholm and Volterra integral equations. Fredholm integral equations with degenerate kernels. Integral equations with convolution kernels. Asymptotic Approximation Methods. Method of steepest descent. Method of stationary phase.
Summary 2020
Unit name | Applied Complex Variables and Transform Theory |
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Unit code | KMA382 |
Credit points | 12.5 |
Faculty/School | College of Sciences and Engineering School of Natural Sciences |
Discipline | Mathematics |
Teaching staff | Prof L Forbes |
Level | Advanced |
Available as student elective? | Yes |
Breadth Unit? | No |
Availability
Note
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TNE Program units special approval requirements.
* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see withdrawal dates explained for more information).
Fees
Requisites
Prerequisites
Teaching
Teaching Pattern | 3x 1hr lecture per week |
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Assessment | End of semester 3-hr exam(70%), assignments (30%) |
Timetable | View the lecture timetable | View the full unit timetable |
Textbooks
Required | Information about any textbook requirements will be available from mid November. |
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The University reserves the right to amend or remove courses and unit availabilities, as appropriate.