linear partial differential equation

A linear partial differential equation (PDE) is a mathematical formula that relates a function with its rates of change across multiple variables, like time and space. "Linear" means the function and its derivatives appear in the equation without being multiplied together or raised to powers. These equations are used to model many real-world phenomena, such as heat transfer, sound, and electromagnetic waves, where the current state depends linearly on other variables. Solving a linear PDE helps us understand how these systems evolve over time and space in a predictable way.