I plan to cover the following topics: Euler equations; Burger's equation; p-system; symmetric hyperbolic PDE's; shock formation; Lax method of solving Riemann problems; Glimm's method for solving Cauchy problems; Entropy solutions; artificial viscosity.

### Bibliography

- Joel Smoller,
*Shock waves and Reaction Diffusion Equations* - Constantine Dafermos,
*Hyperbolic Conservation Laws in Continuum Physics* - Alexandre Chorin and Jerrold Marsden,
*A Mathematical Introduction to Fluid Mechanics* - Lecture notes of Blake Temple (on his webpage)