In mathematics and physics, a Green’s function is a mathematical function that describes the response of a linear, time-invariant system to an impulse or “delta function” input. It is a fundamental concept used in solving differential equations, particularly partial differential equations (PDEs) and integral equations. Key properties of Green’s functions include:

Linearity: The response to a sum of inputs is the sum of the responses to each individual input.

Homogeneity: Scaling the input scales the output.

Shift Invariance: Shifting the input in time or space shifts the output.

Green’s functions have applications in various fields, including electromagnetics, quantum mechanics, fluid dynamics, and heat transfer, providing a powerful and versatile tool for solving differential and integral equations.