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
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