Sturm-Liouville theory

Sturm-Liouville theory deals with a special type of differential equation used in many scientific fields, like physics and engineering. It focuses on finding solutions called eigenfunctions and their associated eigenvalues, which describe natural modes or patterns of a system, such as vibrations or heat distribution. These solutions form a complete set, meaning they can be combined to represent more complex behaviors. The theory provides a structured way to analyze and solve these equations, especially when boundary conditions are involved, helping us understand how systems behave under various constraints.