Asymptotic analysis

Summary

Asymptotic analysis describes the behaviour of functions near a limit point, such as $x \to \infty$ or a small parameter $\varepsilon \to 0$. Its basic tools are big O and little o notation, asymptotic equivalence and asymptotic expansions. An asymptotic expansion need not converge, yet a few of its terms often give an excellent approximation. In differential equations, it gives approximate solutions when exact ones are out of reach, as in perturbation methods.