Handbook of Exact Solutions for Ordinary Differential Equations

A.D. Polyanin, V.F. Zaitsev

814 pages, parution le 21/01/2003 (2^eme édition)

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Résumé

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations.

The authors have made significant enhancements to this edition, including:

An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations
The addition of solutions to more than 1200 nonlinear equations
An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily
Expansion of the supplement on special functions

This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.

Contains solutions to more than 6200 ODEs-more than any other reference available
Offers introductory material describing key concepts, theorems, and methods
Pays special attention to equations dependent on arbitrary functions
Covers Abel, Emden-Fowler, and Painlevé equations
Includes supplemental material on the gamma, beta, Bessel, Legendre, Weierstrass, hypergeometric, and other special functions

Contents

INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND TRANSFORMATIONS

First-Order Differential Equations
Second-Order Differential Equations
Second-Order Nonlinear Differential Equations
Linear Equations of Arbitrary Order
Nonlinear Equations of Arbitrary Order
Lie Group and Discrete-Group Methods

FIRST-ORDER DIFFERENTIAL EQUATIONS

Simplest Equations with Arbitrary Functions Integrable in a Closed Form
Riccati Equation
Abel Equations of the Second Kind
Equations Containing Polynomial Functions of y
Equations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary Parameters
Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Parameters
Equations of the Form F(x,y)y'x = g(x,y) Containing Arbitrary Functions
Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Functions

SECOND-ORDER DIFFERENTIAL EQUATIONS

Linear Equations
Autonomous Equations
Emden-Fowler Equation
Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2
Generalized Emden-Fowler Equation
Equations of the Form y"xx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2
Equations of the Form y"xx = f(x)g(y)h(y'x)
Some Nonlinear Equations with Arbitrary Parameters
Equations Containing Arbitrary Functions

THIRD-ORDER DIFFERENTIAL EQUATIONS

Linear Equations
Equations of the Form y'"xxx = Axayß(y'x)g(y"xx)d
Equations of the Form y'"xxx = f(y)g(y'x)h(y"xx)
Nonlinear Equations with Arbitrary Parameters
Nonlinear Equations Containing Arbitrary Functions

FOURTH-ORDER DIFFERENTIAL EQUATIONS

Linear Equations
Nonlinear Equations

HIGHER ORDER DIFFERENTIAL EQUATIONS

Linear Equations
Nonlinear Equations

SUPPLEMENTS

Elementary Functions and Their Properties
Special Functions and Their Properties
Table of Indefinite Integrals

Caractéristiques techniques

	PAPIER
Éditeur(s)	CRC Press (Taylor and Francis Group)
Auteur(s)	A.D. Polyanin, V.F. Zaitsev
Parution	21/01/2003
Édition	2^eme édition
Nb. de pages	814
Format	18,3 x 26
Couverture	Relié
Poids	1544g
Intérieur	Noir et Blanc
EAN13	9781584882978
ISBN13	978-1-58488-297-8