Perturbation Theory: Analyzing the Impact of Small Changes on Functions

In mathematical analysis, particularly in the realm of perturbation theory, we often study the effects of small disturbances on systems or functions. Consider a function 'f' and a small perturbation 'εη' added to it. The resulting perturbed function can be represented as 'f + εη'. Analyzing this perturbed function allows us to understand how sensitive 'f' is to small changes and how its behavior might be affected by these disturbances. This approach finds applications in various fields, including physics, engineering, and numerical analysis, where understanding the impact of uncertainties and small errors is crucial.