Since the days of Newton, Leibniz, Euler and Laplace, mathematical physics has been inseparably bound to differential equations. Physical and engineering problems continue to provide very important models for mathematicians studying differential equations, as well as valuable intuition as to the solutions and properties. In recent years, advances in computation and in nonlinear functional analysis have brought rigorous theory closer to realistic applications, and a mathematical physicist must now be quite knowledgeable in these areas.