618-331 Applied Mathematics A

Note:

Credit Points:

Coordinator:

Prerequisite/s:

Timetable:

Contact:

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 on physical problems.

Have developed:

• skills to solve wave equations using the methods of characteristics and shocks;

• skills to solve diffusion equations and their steady state versions;

• skills to solve second order linear partial differential equations using various methods, including eigenfunction methods, integral transforms, and Green's functions.

Appreciate:

• the description of many physical processes (for example traffic flow, sedimentation, head transfer, fluid flow) as partial differential equations;

• the idea of characteristics and propagation of information, the need for shocks;

• the ideas diffusion and flux;

• power of various mathematical techniques to solve real-world problems.

Content:

First order partial differential equations: Continuity equation, wave equation, method of characteristics, shocks; applications from traffic flow, sedimentation. Second order wave equation: d'Alembert's solution, method of characteristics, phase and group velocity, nonlinear wave equations, dispersive waves. Diffusion and conduction: Fick's and Fourier's laws, similarity solutions, Stefan problems, Laplace and Poisson equations for steady-state problems. Second order linear partial differential equations: Classification, eigenfunction methods, integral transforms, Green's functions.

Assessment: