UID:
edoccha_9958087977002883
Format:
1 online resource (239 p.)
ISBN:
1-283-52567-4
,
9786613838124
,
0-08-095556-8
Series Statement:
Mathematics in science and engineering
Content:
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Note:
Description based upon print version of record.
,
Front Cover; Comparison and Oscillation Theory of Linear Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Sturm-Type Theorems for Second Order Ordinary Equations; 1. Comparison Theorems for Self-Adjoint Equations; 2. Additional Results of Leighton; 3. Extension to General Second Order Equations; 4. Comparison Theorems for Singular Equations; 5. Comparison Theorems for Eigenfunctions; 6. Reid's Comparison Theorems on Focal Points; 7. Levin's Comparison Theorems; 8. The Order of Zeros; Chapter 2. Oscillation and Nonoscillation Theorems for Second Order Ordinary Equations
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1. The Oscillation Criteria of Hille and Nehari2. Conditionally Oscillatory Equations; 3. Nehari's Comparison Theorems; 4. The Hille-Wintner Comparison Theorem; 5. Hille's Necessary and Sufficient Conditions for Nonoscillatory Equations; 6. Leighton's Oscillation Criteria; 7. Potter's Oscillation Criteria; 8. Hille's Kneser-Type Oscillation Criteria; 9. Nonoscillation Theorems of Hartman and Wintner; 10. Asymptotic Estimates for the Number of Zeros of a Solution of (1.1) or (2.1); 11. Nonoscillation Criteria for Hill's Equation; 12. Nonoscillation Criteria for Complex Equations
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Chapter 3. Fourth Order Ordinary Equations1. Introduction; 2. Separation Theorems; 3. Comparison Theorems for (3.2) and (3.3); 4. Comparison Theorems for Other Fourth Order Equations; 5. Comparison Theorems for Eigenfunctions; 6. Nonoscillation Theorems; 7. Leighton and Nehari's Sufficient Conditions for Nonoscillatory Equations; 8. Comparison Theorems for Nonoscillation; 9. Howard's Comparison Theorems for Eigenvalue Problems; Chapter 4. Third Order Ordinary Equations, nth Order Ordinary Equations and Systems; 1. Introduction; 2. Separation Theorems for Third Order Equations
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3. Comparison Theorems for Third Order Equations4. Oscillation Criteria for Third Order Equations; 5. Separation and Comparison Theorems for nth Order Equations; 6. General Oscillation Theorems; 7. Nonoscillation Theorems for Systems of Differential Equations; 8. Whyburn's Second Order System; Chapter 5. Partial Differential Equations; 1. Introduction; 2. Comparison Theorems for Self-Adjoint Equations in Bounded Domains; 3. Comparison Theorems for General Second Order Elliptic Equations; 4. Comparison Theorems on Unbounded Domains; 5. Extension to Complex-Valued Solutions and Subsolutions
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6. Lower Bounds for Eigenvalues7. Oscillation Theorems; 8. Comparison Theorems for Eigenfunctions; Bibliography; Author Index; Subject Index; Mathematics in Science and Engineering
,
English
Additional Edition:
ISBN 0-12-678950-9
Language:
English
