Zaitsev / Polyanin Handbook of Exact Solutions for Ordinary Differential Equations

2. Auflage 2012
ISBN: 978-1-4200-3533-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 816 Seiten

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.

Zielgruppe

Mathematicians, engineers, physicists, chemists, and students in these fields

Autoren/Hrsg.

Zaitsev, Valentin F.

Polyanin, Andrei D.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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 = Axayß(y'x) ?(y"xx)d
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