Partial Differential Equations

4-None

Introduces the derivation and solution of the fundamental linear partial differential equations (PDEs): the wave equation, the heat equation and the Laplace equation. These represent, respectively, hyperbolic, parabolic and elliptic PDEs. Focuses on first and second order PDEs. Students will master methods for initial value problems (IVPs) and boundary value problems (BVPs), including the method of characteristics and the foundational techniques of the Fourier transform and potential theory, providing a rigorous basis for understanding dynamic and steady-state physical systems.