In this module, two main topics will be covered. The first part will cover Partial Differential Equations, including the origin of partial differential equations, linear partial differential equations of first order, quasi-linear partial differential equations of second order, Homogeneous and non-homogeneous PDEs. In the second part, Applications of PDEs to physics: the (hyperbolic) wave equation, the (parabolic) heat equation, and the (elliptic) Laplace equation.