Sturm-Liouville Theory is a framework in the field of differential equations that deals with the properties of linear differential operators and their eigenfunctions, particularly focusing on boundary value problems. It provides a systematic method for solving a wide range of physical problems by expanding functions in terms of orthogonal eigenfunctions, which are solutions to Sturm-Liouville problems.

Sturm-Liouville Theory

Differential equations are mathematical equations that involve functions and their derivatives, representing physical phenomena and changes in various fields such as physics, engineering, and economics. They are essential for modeling and solving problems where quantities change continuously, providing insights into the behavior and dynamics of complex systems.

differential equations

linear differential operators

Eigenfunctions are solutions to differential equations that remain unchanged except for a scaling factor when acted upon by a linear operator. They play a crucial role in quantum mechanics, vibrations analysis, and other fields where systems are described by linear operators, as they simplify complex problems into more manageable forms.

eigenfunctions

Boundary value problems are a type of differential equation where the solution is required to satisfy certain conditions at the boundaries of the domain. These problems are crucial in mathematical physics and engineering, as they model a wide range of phenomena including heat conduction, wave propagation, and quantum mechanics.

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