Handbook of Exact Solutions for Ordinary Differential Equations: 2nd Edition (Hardback) book cover

Handbook of Exact Solutions for Ordinary Differential Equations

2nd Edition

By Valentin F. Zaitsev, Andrei D. Polyanin

Chapman and Hall/CRC

816 pages | 4 B/W Illus.

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Hardback: 9781584882978
pub: 2002-10-28
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Description

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.

  • Reviews

    "…I have been reading the Polyanin books "Handbook of Linear Partial Differential Equations for Engineers and Scientists" and "Handbook of Exact Solutions for Ordinary Differential Equations". I think these books are extraordinary, and are destined to become classics … CRC Press has provided an invaluable service to science and engineering by publishing these books."

    - William Schiesser, Lehigh University

    "In summary, this is a very useful and easy-to-read handbook for anyone involved in ordinary differential equations…"

    - SIAM Review, 1997, on the first edition

    "This best-selling handbook … is now in its second edition and has been substantially updated and improved … book is highly recommended for mathematicians, scientists, and

    engineers. It would be a useful edition to academic sci-tech libraries, including those that already have the first edition."

    - Holly Flynn in E-STREAM

    Table of Contents

    INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND TRANSFORMATIONS

    First-Order Differential Equations

    Second-Order Differential Equations

    Second-Order Nonlinear Differential Equations

    Linear Equations o Arbitrary Order

    Nonlinear Equations of an Arbitrary Order

    Group Methods and Discrete Group Analysis

    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 = Axαyß(y'x) γ(y"xx)δ

    Equations of the Form y'"xxx = f(y)g(y'x)h(y"xx)

    Some 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

    REFERENCES

    INDEX

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT003000
    MATHEMATICS / Applied
    MAT007000
    MATHEMATICS / Differential Equations