Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems

ISBN-13: 9781466569379 / Angielski / Twarda / 2016 / 1496 str.

Andrei D. Polyanin; Valentin F. Zaitsev

Opis

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.

Spis treści

EXACT SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS: First-Order Differential Equations. Second-Order Differential Equations. Third-Order Differential Equations. Fourth-Order Differential Equations. Higher-Order Differential Equations. Systems of Ordinary Differential Equations. SOLVING METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: First-Order Differential Equations. Second-Order Linear Differential Equations. Second-Order Nonlinear Differential Equations. Linear Equations of Arbitrary Order. Nonlinear Equations of Arbitrary Order. Analytic Ordinary Differential Equations and Their Local Classification. Lie Group and Discrete Group Methods. Linear Systems of Ordinary Differential Equations. Nonlinear Systems of Ordinary Differential Equations. Integrability of Polynomial Differential Systems. Hamiltonian Systems, Periodic, and Homoclinic Solutions by Variational Methods. Bifurcation Theory of Limit Cycle of Planar Systems. Successive Approximation Method for Nonlinear Boundary Value Problems. Application of Integral Equations for the Investigation of Differential Equations. Exact Methods for Construction of Particular Solutions for Nonlinear Equations. SYMBOLIC AND NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH MAPLE, MATHEMATICA, AND MATLAB: Ordinary Differential Equations with Maple. Ordinary Differential Equations with Mathematica. Ordinary Differential Equations with MATLAB. Supplements. References. Index.