18.03 Mathlets

Isoclines Euler's method
Complex roots Complex exponential
Trigonometric identity Phase Lines
Damped vibrations Harmonic frequency response: Variable input frequency
Forced damped vibrations, amplitude and phase: Second order I Amplitude and phase: Second order II
Amplitude and phase: First order Amplitude and phase: Second order III
Amplitude and Phase: Second Order IV Series RLC circuit
Fourier coefficients Fourier coefficients: Complex with sound
Convolution: Accumulation Convolution: Flip and drag
Amplitude response: Pole diagram Poles and vibrations
Linear phase portrait: Matrix entry Linear phase portrait: Cursor entry
Vector fields  

Differential Equations (by topic)

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