First semester of a one-year survey of topics and methods of applied mathematics, emphasis on applications from physics and engineering. The full sequence includes introductions to mathematical aspects of mechanics (e.g., conservation laws), asymptotic expansions, systems of ODE and stability, integral equations and calculus of variations, PDE with boundary value problems and generalized solutions (including wave, heat, and potential equations), numerical methods and stability. Prerequisite: MATH 2250, 4200 or 4400, and 2310 or 4430. 9/4/2019 - 12/13/2019, Lecture