Partial Differential Equations, or PDEs, are mathematical equations that involve functions of multiple variables and their partial derivatives. They are used to describe various phenomena in fields like physics, engineering, and finance. For example, PDEs can model how heat spreads through a material or how waves move in water. Solving PDEs can be quite complex, as they often require advanced techniques and numerical methods. However, understanding the basic concepts can help in grasping how these equations apply to real-world situations. By studying PDEs, scientists and engineers can predict behaviors and design systems more effectively.