This is a course on the partial differential equations associated with wave motion. We first study linear scalar second order hyperbolic equations and linear systems of first order hyperbolic equations. We will use energy estimates to address questions of the existence, uniqueness and structure of solutions. We give a brief introduction of continuum mechanics. Next we will study hyperbolic conservation laws: The equations of gas dynamics, the method of characteristics, shock and rarefaction waves, Riemann problems. We will discuss the use of convexity methods to give explicit solutions.
Finally, we will discuss dispersive waves, dispersion relations, and asymptotic calculation of solutions using the method of stationary phase.
Topics in nonlinear scalar hyperbolic equations of second order may be treated if time permits.
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