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This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in: - Index to Scientific & Technical Proceedings(R) (ISTP(R) / ISI Proceedings)- Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)- CC Proceedings -- Engineering & Physical Sciences