Contents Preface xiii Historical Prologue xvii Part 1. Systems of Nonlinear Differential Equations Chapter 1. Geometric Approach to Differential Equations 3 Chapter 2. Linear Systems 11 2.1. Fundamental Set of Solutions 13 Exercises 2.1 19 2.2. Constant Coefficients: Solutions and Phase Portraits 21 Exercises 2.2 48 2.3. Nonhomogeneous Systems: Time-dependent Forcing 49 Exercises 2.3 52 2.4. Applications 52 Exercises 2.4 56 2.5. Theory and Proofs 59 Chapter 3. The Flow: Solutions of Nonlinear Equations 75 3.1. Solutions of Nonlinear Equations 75 Exercises 3.1 83 3.2. Numerical Solutions of Differential Equations 84 Exercises 3.2 96 3.3. Theory and Proofs 97 Chapter 4. Phase Portraits with Emphasis on Fixed Points 109 4.1. Limit Sets 109 vii
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