620-331 Applied Partial Differential Equations

Note

Students may only gain credit for one of 620-331, 618-331 (1997 Handbook), 618-332 (1996 Handbook).

Credit Points

Coordinator

Prerequisites

620-231 (1997 Handbook 618-231) and 620-232 (1997 Handbook 618-232).

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the various types of partial differential equations and their methods for solution, and how they arise on physical problems;

have developed the ability to

• solve wave equations using the methods of characteristics and shocks;
• solve diffusion equations and their steady state versions;
• solve second order linear partial differential equations using various methods, including eigenfunction methods, integral transforms, and Green's functions;

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

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

Up to 24 pages of written assignments and a three-hour end-of-semester written examination.