This work is devoted to the impulsive differential equations with a small parameter. It consists of three chapters. Chapter 1 serves as an introduction. In chapter 2, regularly perturbed impulsive differential equations are considered. Modifications of the method of the small parameter, the averaging method, and the method of the integral manifolds are proposed. In chapter 3 singularly perturbed differential equations are considered. A modification of the method of the boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method. The book is written clearly, strictly and understandably. It is intended for mathematicians, physicists, chemists, biologists, and economists, as well as for senior students of these specialities.
