In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. This course introduces the topic of partial differential equations for students in mathematics, engineering, and the sciences. Four main topics will be included in the course: the physical origins of partial differential equations, partial differential equations on unbounded domains, orthogonal expansions, partial differential equations on bounded domains. Focus will be on three generic types of partial differential equations: the wave equation, the heat equation, the Laplace equation. Also, students will be introduced with different behavior of the solutions.