Advanced Methods: Transforms
Subject MAST90067 (2015)
Note: This is an archived Handbook entry from 2015.
Credit Points:  12.5 

Level:  9 (Graduate/Postgraduate) 
Dates & Locations:  This subject is not offered in 2015. 
Time Commitment:  Contact Hours: 36 hours comprising two 1hour lectures and one 1hour practice class per week. Total Time Commitment: 170 hours 
Prerequisites:  Subject Study Period Commencement: Credit Points: Plus one of: Subject Study Period Commencement: Credit Points: MAST30029 Partial Differential Equations (pre2014) 
Corequisites:  None 
Recommended Background Knowledge:  It is recommended that students have completed at least one of the following: Subject Study Period Commencement: Credit Points: 
Non Allowed Subjects:  No disallowed subject combinations among newgeneration subjects. 
Core Participation Requirements: 
For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry. The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/ 
Subject Overview: 
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 EulerLagrange 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. 

Learning Outcomes: 
After completing this subject students should:

Assessment: 
Up to 50 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3 hour written examination (60%, in the examination period). 
Prescribed Texts:  None 
Recommended Texts: 
Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers: Asymptotic methods and perturbation theory. Springer. (1999). 
Breadth Options:  This subject is not available as a breadth subject. 
Fees Information:  Subject EFTSL, Level, Discipline & Census Date 
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:

Related Course(s): 
Master of Philosophy  Engineering Master of Science (Mathematics and Statistics) Ph.D. Engineering 
Related Majors/Minors/Specialisations: 
Mathematics and Statistics 
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