# Courses

## Precalculus

- Affine Coordinate Changes
- Beats
- Beats with Sound
- Graphing Rational Functions
- Linear Programming
- Trigonometric Identity

## Calculus

### 1. Differentiaton

- Amplitude and Phase: First Order
- Creating the Derivative
- Hypocycloids
- Secant Approximation
- Tangent Approximation

### 2. Higher derivatives

### 3. Integration

### 4. Vectors and matrices

## Differential Equations

### 1. First order equations

### 2. More first order equations

### 3. Complex Numbers

### 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

### 6. Fourier series

- Fourier Coefficients
- Harmonic Frequency Response: Variable Input Frequency
- Harmonic Frequency Response: Variable Natural Frequency

### 7. Laplace Transform

### 8. Linear systems

- Coupled Oscillators
- Linear Phase Portraits: Cursor Entry
- Linear Phase Portraits: Matrix Entry
- Matrix Vector

### 9. Partial Differential Equations

## Advanced applications of differential equations

- Amplitude Response: Pole Diagram
- Bode and Nyquist Plots
- Damping Ratio
- Discrete Fourier Transform
- Fourier Coefficients: Complex with Sound
- Impulse Response: Spring System
- Series RLC Circuit

## Probability and Statistics

- Beta Distribution
- Confidence Intervals
- Conjugate Priors
- Linear Regression
- Probability Distributions
- T Distribution