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Introduction to Asymptotic Methods introduces mathematical methods of perturbation theory and reviews methods of singular perturbations within the scope of the applications of differential equations. Emphasizing fundamental elements of the mathematical modeling process, this book provides comprehensive coverage of asymptotic approaches, regular and singular perturbations, one-dimensional non-stationary non-linear waves, Padé approximations, oscillators with negative Duffing type stiffness, and differential equations with discontinuous nonlinearities. It also offers a method of construction for canonical variables transformation in parametric form along with a number of examples and applications.