Handbook 1996 : Faculty of Science (Volume 4 page 213)
Mathematics subject : Next:618-340 | Prev:618-331 | Search | Help
618-332 "Mathematical Methods B" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p213) : Next:618-340 | Prev:618-331
Credit points: 15.0
Coordinator: Dr K A Landman
Prerequisite: Mathematics 618- 231 and 232
Contact: 39 lectures (three a week)
Timetable: Second semester
Objectives:
On completion of this subject, students should:Comprehend:
- the various types of partial differential equations and their methods for solution, and how they arise from physical problems.
Have developed:
- skills to solve first order linear and nonlinear partial differential equations using the methods of characteristics and shocks;
- skills to solve second order linear partial differential equations using various methods, including Green's functions and integral representation of solutions and similarity transformations;
- skills to solve dispersive wave equations and some nonlinear second order differential equations.
Appreciate:
- the description of many physical processes (for example traffic flow, sedimentation, heat transfer, fluid flow) as partial differential equations;
- the idea of characteristics and propogation of information; the need for shocks;
- the role of dispersive effects.
Content:
First-order partial differential equations: solution of linear, quasi-linear and general first order partial differential equations in two independent variables by characteristics; non-classical solutions, shocks; applications from traffic flow, sedimentation, gas dynamics and water waves. Second-order partial differential equations: classification of second order linear partial differential equations; existence and uniqueness of solutions with a variety of boundary conditions; Green's function techniques for wave, diffusion and Laplace equations in 2 and 3 dimensions.
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:618-340 | Prev:618-331
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-340 | Prev:618-331
Credit points: 15.0
Coordinator: Dr K A Landman.
Prerequisite: Mathematics 618- 231 and 232
Contact: 39 lectures (three each week)
Timetable: Second semester.
Objectives:
On completion of this subject, students should:Comprehend:
- the various types of partial differential equations and their methods for solution, and how they arise from physical problems.
Have developed:
- skills to solve first order linear and nonlinear partial differential equations using the methods of characteristics and shocks;
- skills to solve second order linear partial differential equations using various methods, including Green's functions and integral representation of solutions and similarity transformations;
- skills to solve dispersive wave equations and some nonlinear second order differential equations.
Appreciate:
- the description of many physical processes (for example traffic flow, sedimentation, heat transfer, fluid flow) as partial differential equations;
- the idea of characteristics and propogation of information; the need for shocks;
- the role of dispersive effects.
Content:
First-order partial differential equations Solution of linear, quasi-linear and general first order partial differential equations in two independent variables by characteristics; non-classical solutions, shocks; applications from traffic flow, sedimentation, gas dynamics and water waves. Second-order partial differential equations Classification of second order linear partial differential equations; existence and uniqueness of solutions with a variety of boundary conditions; Green's function techniques for wave, diffusion and Laplace equations in 2 and 3 dimensions.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
* Note that CONTACT, CONTENT differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p148) : Next:618-340 | Prev:618-331
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.