Abstract
1. Basic Ideas Regular and singular perturbations Asymptotic approximations Asymptotic and convergent series Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems 2. Singularly perturbed ordinary differential equations Initial value problem The critical case Boundary value problems Spike-type solutions and other contrast (dissipative) structures 3. Singularly perturbed partial differential equations The method of Vishik-Lyusternik Corner boundary functions The smoothing procedure Systems of equations in critical cases Periodic solutions Hyperbolic systems 4. Applied problems Mathematical model of combustion process in the case of autocatalytic reaction Heat conduction in thin Bodies Application of the boundary function method in the theory of semiconductor devices Relaxation waves in the FitzHugh-Nagumo system On some other applied problems Index.
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