Differential Equations, second edition, by Blanchard, Devaney, and
Hall.
Published by Brooks/Cole Publishing Co. (a division of Thomson
Learning),
2002.
ISBN 0-534-38514-1.
Table of Contents
Chapter 1. First-Order Differential Equations
- 1.1 Modeling Via Differential Equations
- 1.2 Analytic Technique: Separation of Variables
- 1.3 Qualitative Technique: Slope Fields
- 1.4 Numerical Technique: Euler's Method
- 1.5 Existence and Uniqueness of Solutions
- 1.6 Equilibria and the Phase Line
- 1.7 Bifurcations
- 1.8 Linear Differential Equations
- 1.9 Changing Variables
- Labs for Chapter 1
Chapter 2. First-Order Systems
- 2.1 Modeling via Systems
- 2.2 The Geometry of Systems
- 2.3 Analytic Methods for Special Systems
- 2.4 Euler's Method for Systems
- 2.5 The Lorenz Equations
- Labs for Chapter 2
Chapter 3. Linear Systems
- 3.1 Properties of Linear Systems and the Linearity Principle
- 3.2 Straight-Line Solutions
- 3.3 Phase Planes for Linear Systems with Real Eigenvalues
- 3.4 Complex Eigenvalues
- 3.5 Special Cases: Repeated and Zero Eigenvalues
- 3.6 Second-Order Linear Equations
- 3.7 The Trace-Determinant Plane
- 3.8 Linear Systems in Three Dimensions
- Labs for Chapter 3
Chapter 4. Forcing and Resonance
- 4.1 Forced Harmonic Oscillators
- 4.2 Sinusoidal Forcing
- 4.3 Undamped Forcing and Resonance
- 4.4 Amplitude and Phase of the Steady State
- 4.5 The Tacoma Narrows Bridge
- Labs for Chapter 4
Chapter 5. Nonlinear Systems
- 5.1 Equilibrium Point Analysis
- 5.2 Qualitative Analysis
- 5.3 Hamiltonian Systems
- 5.4 Dissipative Systems
- 5.5 Nonlinear Systems in Three Dimensions
- 5.6 Periodic Forcing of Nonlinear Systems and CHaos
- Labs for Chapter 5
Chapter 6. Laplace Transforms
- 6.1 Laplace Transforms
- 6.2 Discontinuous Functions
- 6.3 Second-Order Equations
- 6.4 Delta Functions and Impulse Forcing
- 6.5 Convolutions
- 6.6 The Qualitative Theory of Laplace Transforms
- Labs for Chapter 6
Chapter 7. Numerical Methods
- 7.1 Numerical Error in Euler's Method
- 7.2 Improving Euler's Method
- 7.3 The Runge-Kutta Method
- 7.4 The Effects of Finite Arithmetic
- Labs for Chapter 7
Chapter 8. Discrete Dynamical Systems
- 8.1 The Discrete Logistic Equation
- 8.2 Fixed and Periodic Points
- 8.3 Bifurcations
- 8.4 Chaos
- 8.5 Chaos in the Lorenz System
- Labs for Chapter 8
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