Partial differential equations (PDEs) are mathematical equations that involve multiple independent variables and their partial derivatives. They are used to describe various phenomena in fields such as physics, engineering, and finance, where systems depend on more than one variable. For example, PDEs can model heat distribution, fluid flow, and wave propagation. Solving PDEs can be complex, as they often require specialized techniques and numerical methods. Common types of PDEs include the heat equation, wave equation, and Laplace's equation. Understanding these equations is essential for analyzing dynamic systems and predicting their behavior over time.