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More About This Textbook
Overview
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:
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.
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.
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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