**1. First order equations**
• Football Trajectory
• Isoclines
• Solution Targets |
**2. More first order equations**
• Amplitude and Phase: First Order
• Euler’s Method
• Phase Lines |

**3. Complex Numbers**
• Complex Exponential
• Complex Roots
• Trigonometric Identity |
4. Second Order Linear Equations
• Amplitude and Phase: Second Order I
• Amplitude and Phase: Second Order II
• Amplitude and Phase: Second Order III
• Amplitude and Phase: Second Order IV
• Damped Vibrations
• Forced Damped Vibration
• Series RLC Circuit |

**5. Convolution, impulse response**
• Convolution: Accumulation
• Convolution: Flip and Drag
• Impulse Response: Natural Frequency |
**6. Fourier series**
• Fourier Coefficients
• Harmonic Frequency Response: Variable Input Frequency
• Harmonic Frequency Response: Variable Natural Frequency |

**7. Laplace Transform**
• Amplitude Response: Pole Diagram
• Poles and Vibrations |
**8. Linear systems**
• Linear Phase Portraits: Cursor Entry
• Linear Phase Portraits: Matrix Entry
• Matrix Vector |

**9. Partial Differential Equations**
• Heat Equation
•Waves |
**Advanced applications of differential equations**
• Amplitude Response: Pole Diagram
• Bode and Nyquist Plots
• Damping Ratio
• Discrete Fourier Transform
• Eigenvalue Stability
• Fourier Coefficients: Complex with Sound
• Impulse Response: Spring System
• Nyquist Plot
• Series RLC Circuit |