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
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Football Trajectory
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Isoclines
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Solution Targets
2. More first order equations
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Amplitude and Phase: First Order
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Euler’s Method
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Phase Lines
3. Complex Numbers
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Complex Exponential
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Complex Roots
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Trigonometric Identity
4. Second Order Linear Equations
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Amplitude and Phase: Second Order I
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Amplitude and Phase: Second Order II
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Amplitude and Phase: Second Order III
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Amplitude and Phase: Second Order IV
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Damped Vibrations
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Forced Damped Vibration
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Series RLC Circuit
5. Convolution, impulse response
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Convolution: Accumulation
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Convolution: Flip and Drag
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Impulse Response: Natural Frequency
6. Fourier series
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Fourier Coefficients
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Harmonic Frequency Response: Variable Input Frequency
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Harmonic Frequency Response: Variable Natural Frequency
7. Laplace Transform
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Amplitude Response: Pole Diagram
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Poles and Vibrations
8. Linear systems
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Linear Phase Portraits: Cursor Entry
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Linear Phase Portraits: Matrix Entry
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Matrix Vector
9. Partial Differential Equations
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Heat Equation
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Waves
Advanced applications of differential equations
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Amplitude Response: Pole Diagram
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Bode and Nyquist Plots
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Damping Ratio
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Discrete Fourier Transform
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Eigenvalue Stability
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Fourier Coefficients: Complex with Sound
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Impulse Response: Spring System
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Nyquist Plot
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Series RLC Circuit