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Zusatztext "The author has invested a great amount of effort into determining all the power series and computing the functions depicted in the figures."-Mathematical Reviews! Issue 2005h "? an excellent reference to researchers! engineers! and interested individuals in helping them tackle nonlinear problems in an analytical fashion?a good subject index and an outstanding list of bibliography with 136 references cited?very well written and is relatively easy to follow to the mathematically literate person. I highly recommend that it be acquired by interested individuals and libraries throughout."-Applied Mathematics Review! Vol. 57! No. 5! September 2004 "This monograph offers the opportunity to explore the details of the valuable new approach both in the theory and on many interesting examples. It will be useful to specialists working in applied nonlinear analysis."-Zentralblatt MATH 1051 Informationen zum Autor Shijun Liao (Shanghai Jiao Tong University, Shanghai, China) Klappentext Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. The author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is the first book to explore the details of this valuable new approach. Zusammenfassung Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. This book introduces an analytic method for nonlinear problems - homotopy analysis - that remains valid even with strong nonlinearity. It explores the details of this valuable approach. Inhaltsverzeichnis PART I BASIC IDEAS: Introduction. Illustrative Description. Systematic Description. Relations to Some Previous Analytic Methods. Advantages, Limitations, and Open Questions. PART II APPLICATIONS: Simple Bifurcation of a Nonlinear Problem. Multiple Solutions of a Nonlinear Problem. Nonlinear Eigenvalue Problem. Thomas-Fermi Atom Model. Volterra's Population Model. Free Oscillation Systems with Odd Nonlinearity. Free Oscillation Systems with Quadratic Nonlinearity. Limit Cycle in a Multidimensional System. Blasius' Viscous Flow. Boundary-layer Flow with Exponential Property. Boundary-layer Flow with Algebraic Property. Von Kármán Swirling Flow. Nonlinear Progressive Waves in Deep Water. BIBLIOGRAPHY. INDEX...
