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| First-Order Differential Equations | |
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| Modeling via Differential Equations | |
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| Analytic Technique: Separation of Variables | |
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| Qualitative Technique: Slope Fields | |
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| Numerical Technique: Euler's Method | |
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| Existence and Uniqueness of Solutions | |
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| Equilibria and the Phase Line | |
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| Bifurcations | |
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| Linear Equations | |
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| Integrating Factors for Linear Equations | |
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| Review Exercises for Chapter 1 | |
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| Labs for Chapter 1 | |
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| First-Order Systems | |
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| Modeling via Systems | |
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| The Geometry of Systems | |
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| Analytic Methods for Special Systems | |
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| Euler's Method for Systems | |
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| The Lorenz Equations | |
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| Review Exercises for Chapter 2 | |
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| Labs for Chapter 2 | |
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| Linear Systems | |
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| Properties of Linear Systems and the Linearity Principle | |
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| Straight-Line Solutions | |
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| Phase Planes for Linear Systems with Real Eigenvalues | |
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| Complex Eigenvalues | |
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| Special Cases: Repeated and Zero Eigenvalues | |
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| Second-Order Linear Equations | |
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| The Trace-Determinant Plane | |
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| Linear Systems in Three Dimensions | |
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| Review Exercises for Chapter 3 | |
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| Labs for Chapter 3 | |
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| Forcing and Resonance | |
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| Forced Harmonic Oscillators | |
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| Sinusoidal Forcing | |
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| Undamped Forcing and Resonance | |
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| Amplitude and Phase of the Steady State | |
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| The Tacoma Narrows Bridge | |
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| Review Exercises for Chapter 4 | |
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| Labs for Chapter 4 | |
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| Nonlinear Systems | |
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| Equilibrium Point Analysis | |
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| Qualitative Analysis | |
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| Hamiltonian Systems | |
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| Dissipative Systems | |
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| Nonlinear Systems in Three Dimensions | |
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| Periodic Forcing of Nonlinear Systems and Chaos | |
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| Review Exercises for Chapter 5 | |
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| Labs for Chapter 5 | |
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| Laplace Transforms | |
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| Laplace Transforms | |
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| Discontinuous Functions | |
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| Second-Order Equations | |
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| Delta Functions and Impulse Forcing | |
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| Convolutions | |
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| The Qualitative Theory of Laplace Transforms | |
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| Table of Laplace Transforms | |
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| Review Exercises for Chapter 6 | |
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| Labs for Chapter 6 | |
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| Numerical Methods | |
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| Numerical Error in Euler's Method | |
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| Improving Euler's Method | |
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| The Runge-Kutta Method | |
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| The Effects of Finite Arithmetic | |
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| Review Exercises for Chapter 7 | |
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| Labs for Chapter 7 | |
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| Discrete Dynamical Systems | |
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| The Discrete Logistic Equation | |
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| Fixed Points and Periodic Points | |
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| Bifurcations | |
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| Chaos | |
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| Chaos in the Lorenz System | |
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| Review Exercises for Chapter 8 | |
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| Labs for Chapter 8 | |
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| Appendices | |
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| Changing Variables | |
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| The Ultimate Guess | |
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| Complex Numbers and Euler's Formula | |
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| Hints and Answers | |
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| Index | |