Offered in odd numbered years only
Offered subject to student demand/lecturer availability
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.
|Unit name||Applied Complex Variables and Transform Theory|
|Faculty/School||College of Sciences and Engineering
School of Natural Sciences
Prof L Forbes
|Available as student elective?||Yes|
This unit is currently unavailable.
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|Band||Field of Education|
Fees for next year will be published in October. The fees above only apply for the year shown.
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3x 1hr lecture per week
End of semester 3-hr exam(70%), assignments (30%)
|Timetable||View the lecture timetable | View the full unit timetable|
Information about any textbook requirements will be available from mid November.
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