Courses & Units

Applied Complex Variables and Transform Theory KMA382



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
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


Location Study period Attendance options Available to
Hobart Semester 1 On-Campus International Domestic


International students
Domestic students

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Key Dates

Study Period Start date Census date WW date End date
Semester 1 22/2/2021 23/3/2021 12/4/2021 30/5/2021

* 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).

About Census Dates


Field of Education Commencing Student Contribution 1 Grandfathered Student Contribution 1 Approved Pathway Course Student Contribution 2 Domestic Full Fee
010101 $493.00 $493.00 not applicable $2,402.00

1 Please refer here more information on student contribution amounts.
2 Information on eligibility and Approved Pathway courses can be found here
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Please note: international students should refer to this page to get an indicative course cost.



  • KMA252 or KME271


Teaching Pattern

3x 1hr lecture per week


End of semester 3-hr exam (70%), assignments (30%)

TimetableView the lecture timetable | View the full unit timetable



Information about any textbook requirements will be available from mid November.

Booktopia textbook links

The University reserves the right to amend or remove courses and unit availabilities, as appropriate.