Handbook 1996 : Faculty of Science (Volume 4 page 213)
Mathematics subject : Next:618-332 | Prev:618-322 | Search | Help
618-331 "Mathematical Methods A" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p213) : Next:618-332 | Prev:618-322
Note: To enter 618-331 using 618-252 or 618-202 (1995 Handbook) a grade of H3 or better will normally be required.
Credit points: 15.0
Coordinator: Dr R Brak
Prerequisite: Mathematics 618-202 or 618-252 (See Note below), 231 and 232.
Contact: 39 lectures ( three a week)
Timetable: First semester
Objectives:
On completion of this subject, students should:Comprehend:
- how to evaluate real integrals using complex analysis;
- how to evaluate and invert Fourier, Laplace and Mellin transforms, and how these can be applied to solve differential and integral equations, to sum series and to compute asymptotic series;
- 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;
- how to find asymptotic solutions to ordinary differential equations.
Have developed:
- the necessary mathematical skills and knowledge to apply a range of mathematical techniques to correctly solve applied mathematics problems.
Appreciate:
- the power of these techniques to solve mathematical problems.
Content:
Complex analysis: contour integration, branch cuts, evaluation of integrals. Integral transforms: wave equation, Fourier series; Fourier transform, Fourier integral theorem, convolution, applications; Laplace transform, inversion, examples; application to ordinary differential equations; convolution, examples; application to partial differential equations; Mellin transform examples. Asymptotics: asymptotic expansions, application of Mellin transform; Laplace's method for integrals, method of steepest descent, applications; method of stationary phase, examples; WKB method for ordinary differential equations.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
1. Mathematics, Faculty of Science (v4, p213) : Next:618-332 | Prev:618-322
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-332 | Prev:618-312
Note: To enter 618-331 using 618-252 or 618-202 (1995 Handbook) a grade of H3 or better will normally be required.
Credit points: 15.0
Coordinator: Dr R Brak.
Prerequisite: Mathematics 618-202 or 618-252 (See Note above), 231 and 232.
Contact: 39 lectures (three each week)
Timetable: First semester.
Objectives:
On completion of this subject, students should:Comprehend:
- how to evaluate real integrals using complex analysis;
- how to evaluate and invert Fourier, Laplace and Mellin transforms, and how these can be applied to solve differential and integral equations, to sum series and to compute asymptotic series;
- 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;
- how to find asymptotic solutions to ordinary differential equations.
Have developed:
- the necessary mathematical skills and knowledge to apply a range of mathematical techniques to correctly solve applied mathematics problems.
Appreciate:
- the power of these techniques to solve mathematical problems.
Content:
Complex analysis Contour integration, branch cuts, evaluation of integrals. Integral transforms Wave equation, Fourier series; Fourier transform, Fourier integral theorem, convolution, applications; Laplace transform, inversion, examples; application to ordinary differential equations; convolution, examples; application to partial differential equations; Mellin transform examples. Asymptotics Asymptotic expansions, application of Mellin transform; Laplace's method for integrals, method of steepest descent, applications; method of stationary phase, examples; WKB method for ordinary differential equations.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
* Note that CONTACT, CONTENT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-332 | Prev:618-312
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.