# Courses

## Precalculus

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

## Calculus

• Sinusoids

### 1. Differentiaton

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

### 2. Higher derivatives

• Graph Features
• Linearized Trigonometry
• Taylor Polynomials

• Riemann Sums

### 4. Vectors and matrices

• Hypocycloids
• Matrix Vector
• Wheel

## Differential Equations

### 1. First order equations

• Ballistic Trajectory
• Isoclines
• Periodic Box
• Solution Targets

### 2. More first order equations

• Amplitude and Phase: First Order
• Euler's Method
• Phase Lines

### 3. Complex Numbers

• Complex Arithmetic
• 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
• Sinusoids

### 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

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

### 9. Partial Differential Equations

• Damped Wave Equation
• Heat Equation
• Wave Equation

## 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