Modern Nonlinear Equations (Dover Books on Mathematics)

Saaty, Thomas L.; Mathematics

ISBN 10: 0486642321 / ISBN 13: 9780486642321

Editore: Dover Publications, 2011

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Dati bibliografici

• Titolo: Modern Nonlinear Equations (Dover Books on Mathematics)
• Editore: Dover Publications
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 0486642321
• ISBN 13: 9780486642321
• Rilegatura: Paperback
• Condizione: Very Good
• Peso: 18 once

Descrizione articolo

Riassunto

This volume covers many major types of classical equations, including operator equations, functional equations, difference equations, delay-differential equations, integral equations, integro-differential equations, and stochastical differential equations. Its clear organization and copious references make it suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." — Math Reviews. 1964 edition.

Contenuti

1. Basic Concepts in the Solution of Equations 1.1 Operator Equations 1.2 Review of Basic Ideas 1.3 Inverse Operators and the Solvability of Equations 1.4 Existence Theorems 2. Some Iterative and Direct Techniques for Nonlinear Operator Equations 2.1 Introduction--Remarks on the Theory of Convergence 2.2 Iterative Methods (useful for Bounded Operators) 2.3 Direct Methods 3. Functional Equations 3.1 Introduction 3.2 Examples of Functional Equations 3.3 Continuous, Discontinuous, and Measurable Solutions--Cauchy's Additive Equation 3.4 Some Generalizations 3.5 Measurable and Bounded Solutions--A Generalization of an Equation due to Banach 3.6 Analytic Solutions of a Generalization of a Trigonometric Identity 3.7 A Continuous Strictly Increasing Solution 3.8 Various Types of Solutions--Even, Positive, Entire Exponential, Bounded, and Periodic 3.9 Convex Solution of g(x+1) - g(x)= log x 3.10 Three Examples--Series Expansion, Reduction to Simpler Forms, and Successive Approximations 3.11 A General Method of Solution 3.12 Functional Inequalities 3.13 Optimization and Functional Equations 4. Nonlinear Difference Equations 4.1 Introduction 4.2 Linear Difference Equations 4.3 A General Difference Equation of the First Order 4.4 Solutions of Some Nonlinear Equations 4.5 Stability of Some Difference Approximations 4.6 Stability 4.7 Differential-difference Equations--An Example 4.8 Optimization and Difference Equations 5. Delay-Differential Equations 5.1 Introduction 5.2 A Linear Equation of Neutral Type 5.3 What is a Solution? 5.4 Linear Delay-Differential Equations 5.5 Existence and Some Methods of Solution 5.6 Perturbation Methods 5.7 Solution and Stability of a Nonlinear Delay Equation 5.8 A Brief Discussion of Stability, with Examples 5.9 Optimization Problems with Delay 6. Integral Equalities 6.1 Introduction 6.2 Some Examples of Physical Problems Leading to Integral Equations 6.3 Linear Integral Equations of Fredholm Type 6.4 Linear Equations with Symmetric Kernels 6.5 Nonlinear Volterra Equations 6.6 Hammerstein's Theory 6.7 Nonlinear Integral Equations Containing a Parameter--Branching of Solutions 6.8 Some Results on Nonlinear Operator Equations 7. Integrodifferential Equations 7.1 Introduction 7.2 Examples 7.3 An Example of an Integrodifference Equation 7.4 Brief Illustration of Existence 7.5 A Nonlinear Equation--Boltzmann's Equation 7.6 Some Methods of Solution 7.7 Stability 8. Stochastic Differential Equations 8.1 Introduction 8.2 Random Initial Conditions 8.3 Random Forcing Function 8.4 Random Coefficients 8.5 General Properties 8.6 Appendix: Probability Theory Index