Contents
IAS/Park City Mathematics Institute ix
Preface xi
Acknowledgments xiii
Introduction 1
Chapter 1. Differential Equations and Their Solutions 5
1.1. First-Order ODE: Existence and Uniqueness 5
1.2. Euler’s Method 16
1.3. Stationary Points and Closed Orbits 19
1.4. Continuity with Respect to Initial Conditions 22
1.5. Chaos—Or a Butterfly Spoils Laplace’s Dream 25
1.6. Analytic ODE and Their Solutions 31
1.7. Invariance Properties of Flows 33
Chapter 2. Linear Differential Equations 37
2.1. First-Order Linear ODE 37
2.2. Nonautonomous First-Order Linear ODE 48
2.3. Coupled and Uncoupled Harmonic Operators 50
2.4. Inhomogeneous Linear Differential Equations 52
2.5. Asymptotic Stability of Nonlinear ODE 53
2.6. Forced Harmonic Oscillators 55
2.7. Exponential Growth and Ecological Models 56
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