Partial Differential Equations

Driven by rapid developments in science and engineering, the theory of partial differential equations (PDE) has demonstrated its importance in solving practical problems arising in many fields. Through lectures and hands-on assignments, this course introduces a variety of PDEs with emphasis on the theoretical aspects and related techniques to find solutions and understand their analytic properties.  It familiarizes students with basic concepts and modern techniques for the formulation and solution of various PDE problems.  Main topics include the method of characteristics for first order PDE, formulation and solutions to the wave equation, heat equation and Laplace equation, and classical tools to study properties of these PDEs.