2007 Undergraduate Handbook Entry with Annotations

The official handbook entry without annotations is available here.

620-332 Integral Transforms and Asymptotics (semester 2, 12.5 credit points)

Coordinator: A/Prof BD Hughes (not A/Prof P Pearce as shown in the 2007 Handbook)

Prerequisites: One of 620-232 or 620-234; and one of 620-221 or 620-252.

The prerequisites are quite essential. Your are expected to have passed 620-232 (or 620234), and one of 620-221, 620-252. If this is not so, you must contact the coordinator as soon as possible.

Students with a poor grasp of both the techniques and concepts of 620232/234, or with a poor grasp of complex analysis up to elementary techniques in contour integration covered in 620221/252 will find 620332 very hard.

Students who have previously failed the subject should note that teaching material from previous years that you may have may not be sufficient for the study of this year's version of 620-332 as notation and emphasis may be different. Attendance at all lectures and practice classes is strongly advised.

Contact: 36 lectures (three per week) and up to 12 practice classes (one per week)

The practice class will run in the first week and essential prerequisite material may be reviewed then.

Subject Description: This subject introduces methods of evaluating real integrals using complex analysis; and develops methods for evaluating and inverting Fourier, Laplace and Mellin transforms, with selected applications including summing series and computing asymptotic series.
   Students should learn what an asymptotic expansion is and how it provides approximations; how to use Watson's lemma and the methods of Laplace, stationary phase and steepest descents to evaluate asymptotic expressions; and how to find asymptotic solutions to ordinary differential equations.
   This subject demonstrates a range of important and useful techniques and their power in solving problems in applied mathematics.
   Complex analysis covers advanced applications of contour integration. Integral transforms covers Fourier, Laplace and Mellin transforms; inversion by contour integration; convolution; and applications.
   Asymptotic expansions covers convergence and divergence; integrals with a large parameter, Watson's Lemma, Laplace's method, steepest descent, stationary phase; and WKB method for ordinary differential equations.

Assessment: A 45-minute written test held mid-semester (either 0% or 20%); a 3-hour written examination in the examination period (80% or 100%). The relative weighting of the examination and the mid-semester test will be chosen so as to maximise the student's final mark.

The midsemester test replaces the 9.00 a.m. lecture on Tuesday 4 September. The test is held in WILSON HALL.

There are no assignments.

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