Handbook of Exact Solutions for Ordinary Differential Equations

ISBN-13: 9781584882978 / Angielski / Twarda / 2002 / 816 str.

A. D. Polianin; Andrei D. Polyanin; Valentin F. Zaitsev

Opis

The new edition of this bestselling handbook contains the solutions for an additional 700 ordinary differential equations (ODEs) and now provides more than 6200 solutions. It also includes a new introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ODEs, along with basic definitions and discussion of using modern computer algebra systems to solve ODEs. Subsections are now organized into paragraphs, and the rearrangement of equations into these paragraphs allows for an expanded table of contents that helps readers find equations more quickly. More than ever, the handbook is indispensable to a wide range of mathematicians, scientists, engineers, and students.

Recenzje

"…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

Spis treści

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

O autorze

Valentin F. Zaitsev, Andrei D. Polyanin