2009 Spring MATH 281-01
Bulletin Course Description Linear wave motion, dispersion, stationary phase, foundations of continuum mechanics, characteristics, linear hyperbolic systems, and nonlinear conservation laws. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title HYPERBOLIC PDE Department MATH Course Number 2009 Spring 281 Section Number 01 Primary Instructor Venakides,Stephanos Prerequisites Prerequisite: Mathematics 232 or equivalent.
Synopsis of course content
This is a course on the partial differential equations associated with wave motion. We will study the following topics
1) Second order linear hyperbolic equations and systems. In developing this subject, we will review (or derive) results on the wave equation and on basic function space theory and introduce the theory of pseudodifferential operators. We will outline the existence/uniqueness theory and prove the theorem on the propagation of singularities.
2) Continuum mechanics and nonlinear hyperbolic conservation laws:. We will derive the equations of gas dynamics. We will study the method of characteristics, Rankine-Hugoniot and entropy conditions, shock and rarefaction waves, Riemann problems.
3) Dispersive waves, dispersion relations, and the asymptotic calculation of solutions using the method of steepest descent.
Textbooks
G. B. Folland Introduction to Partial Differential Equations, Princeton Acdemic Press
Assignments
Grades will be based on written problem sets.
