Partial Differential Equations

Partial Differential Equations (PDEs) are mathematical equations that involve functions of multiple variables and their partial derivatives. Unlike ordinary differential equations, which deal with functions of a single variable, PDEs describe how a system changes in relation to more than one dimension, such as time and space. They are essential for modeling complex phenomena in physics, engineering, and finance, capturing how changes in one variable affect another. Examples include heat conduction, fluid dynamics, and wave propagation. Solving PDEs helps us understand and predict behaviors in these real-world systems.