Integral Transforms & Asymptotics

Subject 620-332 (2009)

Note: This is an archived Handbook entry from 2009. Search for this in the current handbook

Credit Points: 12.50
Level: 3 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2009:

Semester 2, - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period not applicable
Assessment Period End not applicable
Last date to Self-Enrol not applicable
Census Date not applicable
Last date to Withdraw without fail not applicable

Lectures and practice classes.

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 one-hour lectures (three per week) and up to 12 one-hour practice classes (one per week)
Total Time Commitment: 120 hours total time commitment.
Prerequisites:

One of

  • Mathematical Methods
  • 620-234 (prior to 2009)

and one of

  • 620-221 (prior to 2009)
  • Analysis
Corequisites: None
Recommended Background Knowledge: None
Non Allowed Subjects: None
Core Participation Requirements: It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit.

Coordinator

Prof Paul Anthony Pearce
Subject Overview:

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.
Objectives: .
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.
Prescribed Texts: None
Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Notes: This subject is available for science credit to students enrolled in the BSc (pre-2008 degree only), BASc or a combined BSc course.
Related Majors/Minors/Specialisations: Mathematics && Statistics Major
Mathematics and Statistics (Applied Mathematics specialisation)
Mathematics and Statistics (Mathematical Physics specialisation)

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