Handbook of ordinary differential equations : exact solutions, methods, and problems /
Andrei D. Polyanin, Valentin F. Zaitsev.
- Boca Raton : CRC Press, Taylor & Francis Group : 2018.
- xxix, 1456 p. : ill. ; 26 cm.
"A Chapman & Hall book."
Includes bibliographical references (pages 1409-1426) and index.
Methods for first-order differential equations -- Methods for second-order linear differential equations -- Methods for second-order nonlinear differential equations -- Methods for linear ODEs of arbitrary order -- Methods for nonlinear ODEs of arbitrary order -- Methods for linear systems of ODEs -- Methods for nonlinear systems of ODEs -- Elements of bifurcation theory -- Elementary theory of using invariants for solving equations -- Methods for the construction of particular solutions -- Group methods for ODEs -- Discrete-group methods -- First-order ordinary differential equations -- Second-order ordinary differential equations -- Third-order ordinary differential equations -- Fourth-order ordinary differential equations -- Higher-order ordinary differential equations -- Some systems of ordinary differential equations -- Symbolic and numerical solutions of ODEs with Maple -- Symbolic and numerical solutions of ODEs with mathematica -- Symbolic and numberical solutions of ODEs with MATLAB.
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations. The new edition of this popular handbook contains more equations and methods used in the field than any other book currently available. Encompassing more than 7,000 ODEs with solutions, it presents many asymptotic, approximate analytical, symbolic, and quantitative methods used for analyzing and solving linear and nonlinear equations. This edition covers first-, second-, third-, fourth- and higher-order differential equations and systems along with new nonlinear equations, formulas for effectively constructing solutions, and various equations arising in applications, such as heat and mass transfer, hydrodynamics, and other areas. --