Textbook: Differential Equations, Fourth Edition, Paul Blanchard, Robert L. Devaney, Glen R. Hall
Chapter 1 First-Order Differential Equations
- Sect. 1.1 Modeling via DE
- Sect. 1.2 Analytic Technique, Separation of Variables
- Sect. 1.3 Qualitative Technique, Slope Fields
- Sect. 1.4 Numerical Technique, Euler’s Method
- Sect. 1.5 Existence and Uniqueness of Solutions
- Sect. 1.6 Equilibria and The Phase Line
- Sect. 1.7 Bifurcations
- Sect. 1.8 Linear Equations
- Sect. 1.9 Integrating Factors for Linear Equations
Chapter 2 First-Order Systems
- Sect. 2.1 First-Order Systems
- Sect. 2.2 The Geometry of Systems
- Sect. 2.3 The Damped Harmonic Oscillator
- Sect. 2.4 Additional Analytic Methods for Special Systems
- Sect. 2.6 Existence and Uniqueness for Systems
Chapter 3 Linear Systems
- Sect. 3.1 Properties of Linear Systems and the Linearity Principle
- Sect. 3.2 Straight-Line Solutions
- Sect. 3.3 Phase Portraits for Linear Systems with Real Eigenvalues
- Sect. 3.4 Complex Eigenvalues
- Sect. 3.5 Special Cases, Repeated and Zero Eigenvalues
- Sect. 3.6 Second Order Linear Equations
- Sect. 3.7 The Trace-Determinant Plane
- Sect. 3.8 Linear Systems in Three Dimensions
Chapter 4 Forcing and Resonance
- Sect. 4.1 Forced Harmonic Oscillator
- Sect. 4.2 Sinusoidal Forcing
- Sect. 4.3 Undamped Forcing and Resonance
- Sect. 4.4 Amplitude and Phase of the Steady State
- Sect. 4.5 The Tacoma Narrows Bridge
Chapter 5 Nonlinear Systems
Jeaheang Bang 