Perturbation theory is a fascinating and fundamental topic in mathematics and its applications to the natural and engineering sciences. In this workbook, each explicit example is studied and methods introduced, beginning without proof, a learning method very suitable for singular perturbation problems. The text includes an extensive discussion of timescales and apriori knowledge of the presence of certain timescales. This comprehensive introduction to singular perturbation covers a broad range of topics, includes odes' and pde's, boundary value problems, and problems with initial values.

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Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.

Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

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