Differential equations

Planned

In learning order. These are not pages yet.

1. Slope fields: reading an ODE before solving itIntro
2. Exponential growth and decay: dy/dt = kyIntro
3. The heat equation: why heat spreads the way it doesAdvanced undergrad
4. Mean reversion as an ODE: dy/dt = θ(μ − y)Intro
5. Second-order linear ODEs: springs and dampingIntro
6. Separation of variables and Fourier modesAdvanced undergrad
7. Boundary conditions: what happens at the edgesAdvanced undergrad
8. Heat, wave, and Laplace: the three kinds of PDEAdvanced undergrad
9. Linear systems x′ = Ax and phase portraitsIntro
10. Resonance and frequency response: driving an oscillatorIntro
11. The Laplace transform: turning an ODE into algebraIntro
12. The wave equation and characteristics: d'Alembert's solutionAdvanced undergrad
13. When an ODE has more than one solution: existence and uniquenessAdvanced undergrad
14. Stability of equilibria and linearizationIntro
15. The heat kernel: a Gaussian that widens like √tAdvanced undergrad
16. Laplace's equation and harmonic functions: solving the Dirichlet problem with random walksAdvanced undergrad
17. Removing drift and decay terms to reach the heat equationAdvanced undergrad
18. The Fokker-Planck equation: how a probability density movesAdvanced undergrad