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Handbook of ordinary differential equations. (Spravochnik po obyknovennym differentsial’nym uravneniyam.) (Russian) Zbl 0999.34001

Moskva: Fizmatlit. 576 p. (2001).
This nice handbook provides the reader with the description of about 5.200 ordinary differential equations with their solutions. Choosing material for the book, the authors pay special attention to the following two types of equations: (a) equations of simple form which are difficult to integrate (for instance, Abel’s and Emden-Fowler equations), and (b) equations which are frequently encountered in applications (heat transfer, nonlinear mechanics, hydrodynamics, combustion, etc.).
The book briefly introduces the reader to exact, asymptotic, and numerical methods for solving ordinary differential equations, gives exact solutions and useful transformations for many classes of equations, discusses exact and asymptotic solutions to many problems in nonlinear mechanics and theoretical physics. In addition, fundamental properties of some elementary and special functions are collected in the Appendices. This handbook is a valuable tool for researchers, engineers and students dealing with ordinary differential equations. Exact solutions and various asymptotic and numerical methods have their independent interest as well.

MSC:

34-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34E05 Asymptotic expansions of solutions to ordinary differential equations
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