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| Preface | |
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| Introduction | |
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| Historical Notes | |
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| Exact Equations | |
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| Elementary First-Order Equations | |
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| First-Order Linear Equations | |
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| Second-Order Linear Equations | |
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| Preliminaries to Existence and Uniqueness of Solutions | |
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| Picard's Method of Successive Approximations | |
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| Existence Theorems | |
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| Uniqueness Theorems | |
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| Differential Inequalities | |
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| Continuous Dependence on Initial Conditions | |
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| Preliminary Results from Algebra and Analysis | |
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| Preliminary Results from Algebra and Analysis (Contd.) | |
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| Existence and Uniqueness of Solutions of Systems | |
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| Existence and Uniqueness of Solutions of Systems (Contd.) | |
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| General Properties of Linear Systems | |
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| Fundamental Matrix Solution | |
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| Systems with Constant Coefficients | |
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| Periodic Linear Systems | |
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| Asymptotic Behavior of Solutions of Linear Systems | |
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| Asymptotic Behavior of Solutions of Linear Systems (Contd.) | |
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| Preliminaries to Stability of Solutions | |
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| Stability of Quasi-Linear Systems | |
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| Two-Dimensional Autonomous Systems | |
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| Two-Dimensional Autonomous Systems (Contd.) | |
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| Limit Cycles and Periodic Solutions | |
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| Lyapunov's Direct Method for Autonomous Systems | |
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| Lyapunov's Direct Method for Nonautonomous Systems | |
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| Higher-Order Exact and Adjoint Equations | |
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| Oscillatory Equations | |
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| Linear Boundary Value Problems | |
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| Green's Functions | |
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| Degenerate Linear Boundary Value Problems | |
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| Maximum Principles | |
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| Sturm-Liouville Problems | |
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| Sturm-Liouville Problems (Contd.) | |
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| Eigenfunction Expansions | |
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| Eigenfunction Expansions (Contd.) | |
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| Nonlinear Boundary Value Problems | |
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| Nonlinear Boundary Value Problems (Contd.) | |
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| Topics for Further Studies | |
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| References | |
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| Index | |