Asymptotic analysis of differential equations

This thesis is concerned with asymptotic approximation methods used by engineers, particularly physicists and applied mathematicians applied to some special types of differential equations. In this study, various asymptotic methods are introduced for functions that are solutions of differential equations with non-regular singular points. Asymptotic expansions of these functions, which take values in a given region of the complex plane, are obtained by using these methods. Finally, as an introduction to the singular perturbation theory, differential equations depending on a small or large parameter are discussed and the WKB method, which is a more general version of the methods mentioned in the previous section, is introduced for such differential equations. The solutions of the problems related to this method are examined, and uniform asymptotic solutions valid for each value of the independent real variable are found.