Differential-difference equations / [by] Richard Bellman [and] Kenneth L. Cooke.

Format:

Book

Author/Creator:

Bellman, Richard, 1920-1984.

Contributor:

Cooke, Kenneth L.

Series:

Mathematics in science and engineering ; v. 6.

Mathematics in science and engineering ; v. 6

Language:

English

Subjects (All):

Differential-difference equations.

Differential equations.

Physical Description:

1 online resource (xvi, 462 pages) : illustrations

Place of Publication:

New York : Academic Press, 1963.

Language Note:

English

Contents:

Front Cover; Differential-Difference Equations; Copyright Page; Contents; Dedication; Introduction; Chapter 1. The Laplace Transform; 1.1. Introduction; 1.2. Existence and Convergence Exercises; 1.3. The Inversion Problem; 1.4. Behavior of the Dirichlet Kernel; 1.5. Analytic Details Exercises; 1.6. Statement of Result; 1.7. Jump Discontinuity; 1.8. Functions of Bounded Variation; 1.9. Contour Integration.; 1.10. Examples; 1.11. The Fejér Transform; 1.12. The Inverse Inversion Problem; 1.13. The Convolution Theorem Exercises; 1.14. The Fourier Transform; 1.15. Plancherel-Parseval Theorem

1.16. Application to Laplace Transform; 1.17. The Post-Widder Formula; 1.18. Real Inversion Formulas Exercise; Miscellaneous Exercises and Research Problems; Bibliography and Comments; Chapter 2. Linear Differential Equations; 2.1. Introduction; 2.2. Linear Differential Equations; 2.3. Fundamental Existence and Uniqueness Theorem; 2.4. Successive Approximations; 2.5. A Fundamental Lemma; 2.6. Uniqueness Theorem; 2.7. Fixed-point Techniques; 2.8. Difference Schemes; 2.9. The Matrix Equation; 2.10. Alternative Derivation; 2.11. The Inhomogeneous Equation; 2.12. The Adjoint Equation

2.13. Constant Coefficients-I; 2.14. Constant Coefficients-II; 2.15. Laplace Transform Solution; 2.16. Characteristic Values and Characteristic Funotions; Miscellaneous Exercises and Research Problems; Bibliography and Comments; Chapter 3. First-order Linear Differential-Difference Equations of Retarded Type with Constant Coefficients; 3.1. Introduction; 3.2. Examples Exercises; 3.3. Equations of Retarded, Neutral, and Advanced Type; 3.4. The Existence-Uniqueness Theorem Exercises; 3.5. Exponential Solutions Exercises; 3.6. Order of Growth of Solutions Exercises

3.7. Laplace Transform Solution Exercises; 3.8. Solution of a Differential Equation in the Form of a Definite Integral; 3.9. Solution of a Differential-Difference Equation in the Form of a Definite Integral Exercises; Miscellaneous Exercises and Research Problems; Bibliography and Comments; Chapter 4. Series Expansions of Solutions of First-order Equations of Retarded Type; 4.1. The Characteristic Roots; 4.2. Series Expansions; 4.3. Other Forms of the Expansion Theorem Exercises; 4.4. Asymptotic Behavior of the Solution Exercises; 4.5. Stability of Equilibrium Exercises

4.6. Fourier-type Expansions Exercises; 4.7. The Shift Theorem Exercises; Miscellaneous Exercises and Research Problems; Bibliography and Comments; Chapter 5. First-order Linear Equations of Neutral and Advanced Type with Constant Coefficients; 5.1. Existence-Uniqueness Theorems Exercises; 5.2. Solution by Exponentials and by Definite Integrals: Equations of Neutral Type Exercises; 5.3. Series Expansions: Equations of Neutral Type Exercise; 5.4. Asymptotic Behavior and Stability: Equations of Neutral Type; 5.5. Other Expansions for Solutions of Equations of Neutral Type Exercises; 5.6. Equations of Advanced Type

Notes:

Description based upon print version of record.

Includes bibliography.

ISBN:

1-282-28918-7

9786612289187

0-08-095514-2

OCLC:

316566888