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Handbook of Exact Solutions for Ordinary Differential Equations

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Handbook of Exact Solutions for Ordinary Differential Equations

Handbook of Exact Solutions for Ordinary Differential Equations

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

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

L'auteur A.D. Polyanin

Autres livres de A.D. Polyanin

Caractéristiques techniques du livre "Handbook of Exact Solutions for Ordinary Differential Equations"

  PAPIER
Éditeur(s) CRC Press (Taylor and Francis Group)
Auteur(s) A.D. Polyanin, V.F. Zaitsev
Parution 21/01/2003
Édition  2eme 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

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