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| Preface | |
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| Systems of Differential Equations | |
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| A Simple Mass-Spring System | |
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| Coupled Mass-Spring Systems | |
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| Systems of First-Order Equations | |
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| Vector-Matrix Notation for Systems | |
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| The Need for a Theory | |
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| Existence, Uniqueness, and Continuity | |
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| The Gronwall Inequality | |
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| Linear Systems, with an Introduction to Phase Space Analysis | |
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| Introduction | |
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| Existence and Uniqueness for Linear Systems | |
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| Linear Homogeneous Systems | |
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| Linear Nonhomogeneous Systems | |
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| Linear Systems with Constant Coefficients | |
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| Similarity of Matrices and the Jordan Canonical Form | |
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| Asymptotic Behavior of Solutions of Linear Systems with Constant Coefficients | |
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| Autonomous Systems--Phase Space--Two-Dimensional Systems | |
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| Linear Systems with Periodic Coefficients | |
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| Miscellaneous Exercises | |
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| Existence Theory | |
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| Existence in the Scalar Case | |
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| Existence Theory for Systems of First-Order Equations | |
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| Uniqueness of Solutions | |
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| Continuation of Solutions | |
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| Dependence on Initial Conditions and Parameters | |
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| Miscellaneous Exercises | |
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| Stability of Linear and Almost Linear Systems | |
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| Introduction | |
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| Definitions of Stability | |
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| Linear Systems | |
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| Almost Linear Systems | |
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| Conditional Stability | |
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| Asymptotic Equivalence | |
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| Stability of Periodic Solutions | |
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| Lyapunov's Second Method | |
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| Introductory Remarks | |
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| Lyapunov's Theorems | |
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| Proofs of Lyapunov's Theorems | |
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| Invariant Sets and Stability | |
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| The Extent of Asymptotic Stability--Global Asymptotic Stability | |
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| Nonautonomous Systems | |
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| Some Applications | |
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| Introduction | |
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| The Undamped Oscillator | |
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| The Pendulum | |
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| Self-Excited Oscillations--Periodic Solutions of the Lienard Equation | |
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| The Regulator Problem | |
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| Absolute Stability of the Regulator System | |
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| Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of Matrices | |
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| Canonical Forms of 2 x 2 Matrices | |
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| The Logarithm of a Matrix | |
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| Some Results from Matrix Theory | |
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| Bibliography | |
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| Index | |