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Advanced Methods: Transforms (MAST90067)

Graduate courseworkPoints: 12.5Dual-Delivery (Parkville)

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Overview

Availability
Semester 1 - Dual-Delivery
FeesLook up fees

This subject develops the mathematical methods of applied mathematics and mathematical physics with an emphasis on integral transform and related techniques. An introduction is given to the calculus of variations and the Euler-Lagrange equation. Advanced complex contour integration techniques are used to evaluate and invert Fourier and Laplace transforms. The general theory includes convolutions, Green’s functions and generalized functions. The methods of Laplace, stationary phase, steepest descents and Watson’s lemma are used to asymptotically approximate integrals. Throughout, the theory is set in the context of examples from applied mathematics and mathematical physics such as the brachistochrone problem, Fraunhofer diffraction, Dirac delta function, heat equation and diffusion.

Intended learning outcomes

After completing this subject students should:



  • have learned how the calculus of variations, transform methods and associated asymptotic analysis apply in a variety of areas in applied mathematics and mathematical physics;
  • appreciate the role of advanced contour integration techniques of complex analysis and to be able to use these techniques to calculate transform integrals;
  • understand the basic concepts of asymptotic evaluation of integrals, know how to implement Laplace’s method, stationary phase and steepest descents and appreciate their applicability and limitations;
  • be familiar with the basic properties of generalized functions and Green’s functions in applied mathematics and mathematical physics and their applications;
  • have the ability to pursue further studies in these and related areas.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 12 November 2022

Eligibility and requirements

Prerequisites

Code Name Teaching period Credit Points
MAST30021 Complex Analysis
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
 12.5

AND

One of

Code Name Teaching period Credit Points
MAST20030 Differential Equations
Semester 2 (Dual-Delivery - Parkville)
 12.5

MAST30029 Partial Differential Equations (pre-2014)

Corequisites

None

Non-allowed subjects

No disallowed subject combinations among new-generation subjects.

Recommended background knowledge

It is recommended that students have completed at least one of the following:

Code Name Teaching period Credit Points
MAST30030 Applied Mathematical Modelling
Semester 1 (Dual-Delivery - Parkville)
 12.5
MAST30031 Methods of Mathematical Physics
Semester 2 (Dual-Delivery - Parkville)
 12.5

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 12 November 2022

Assessment

DescriptionTimingPercentage

Up to 50 pages of written assignments (two assignments worth 20% each, due mid and late in semester)

  • 50 pages
Second half of the teaching period40%

A written examination

  • 3 hours
During the examination period60%

Last updated: 12 November 2022

Dates & times

  • Semester 1
    CoordinatorThomas Quella
    Mode of deliveryDual-Delivery (Parkville)
    Contact hours36 hours comprising two 1-hour lectures and one 1-hour practice class per week.
    Total time commitment170 hours
    Teaching period28 February 2022 to 29 May 2022
    Last self-enrol date11 March 2022
    Census date31 March 2022
    Last date to withdraw without fail 6 May 2022
    Assessment period ends24 June 2022

Time commitment details

170 hours

Last updated: 12 November 2022

Further information

  • Texts

    Prescribed texts

    None

    Recommended texts and other resources

    Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers: Asymptotic methods and perturbation theory. Springer. (1999).
    George F. Carrier, Max Krook, and Carl E. Pearson, Functions of a Complex Variable: Theory and Technique, SIAM (2005).

  • Related Handbook entries

    This subject contributes to the following:

    TypeName
    CourseDoctor of Philosophy - Engineering
    CourseMaster of Philosophy - Engineering
    CoursePh.D.- Engineering
    CourseMaster of Science (Mathematics and Statistics)
    Informal specialisationMathematics and Statistics
  • Available through the Community Access Program

    About the Community Access Program (CAP)

    This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

    Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.

  • Available to Study Abroad and/or Study Exchange Students

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 12 November 2022