Many of the problems faced today by physicists, engineers, and applied mathematicians involve difficulties, such as nonlinear governing equations, variable coefficients, and nonlinear boundary conditions at complex known or unknown boundaries, which preclude their solutions exactly. To solve these problems we are forced to resort to a form of approximation, a numerical solution, or a combination of both. Foremost among the approximation techniques is the systematic method of perturbations (asymptotic expansions) in terms of a small or a large parameter or coordinate. This book is concerned only with these perturbation techniques.
According to these perturbation techniques, the solution of the full problem is represented by the first few terms of a perturbation expansion, usually the first two terms. Although these perturbation expansions may be divergent, they can be more useful for a qualitative as well as a quantitative representation of the solution than expansions that are uniformly and absolutely convergent.

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