Integro-Differential Equations

Integro-differential equations are mathematical formulas that combine derivatives (which measure how a quantity changes) and integrals (which accumulate total amounts). They describe systems where the current state depends both on its rate of change and on the overall history or accumulated effect. These equations are used in fields like physics, biology, and engineering to model complex phenomena such as heat transfer, population dynamics, or material behavior, capturing both local behavior and the influence of past states within a unified framework.