Mathematics 281: Partial Differential Equations II: Hyperbolic PDE
(Fall 2003)
Instructor
Stephanos Venakides
Description
Topics to be covered:
- Linear wave motion: hyperbolic and dispersive waves, dispersion
relations, asymptotic calculation of solutions using the methods of Laplace,
stationary phase, and steepest descent.
- Green's functions and scattering off an obstacle in the context of the
Helmholtz equation
- Hyperbolic conservation laws: The equations of gas dynamics, the
method of characteristics, shock and rarefaction waves, Riemann problems.
- Integrable nonlinear equations and inverse scattering, the Korteweg-de
Vries equation, Lax pairs, the focusing and defocusing Nonlinear
Schroedinger equations.
This course is not a prerequisite for Math 282
(PDE III: Elliptic Partial Differential Equations).
Prerequisites
Math 232 (Introduction to Partial Differential Equations) or equivalent.
Course Website
For more information see Professor Venakides.
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