Equations that describe change.

Unit 1 · First look

Modeling with ODEs

What a differential equation says, order, initial conditions, qualitative behavior.

1 demo lesson · 8 cards Unit 2 · Separable

First-order equations

Separable, linear, exact, integrating factor, Bernoulli.

1 demo lesson · 8 cards Unit 3 · Models

Applications of first order

Growth, decay, cooling, mixing, RC circuits, the logistic equation.

1 demo lesson · 8 cards Unit 4 · Linear

Second-order linear ODEs

Homogeneous, characteristic equation, complex roots, undetermined coefficients.

1 demo lesson · 8 cards Unit 5 · Resonance

Forced oscillations

Harmonic forcing, resonance, beats, damped driven motion.

1 demo lesson · 8 cards Unit 6 · Operator

Laplace transforms

Definition, transforms of common functions, solving initial-value problems.

1 demo lesson · 8 cards Unit 7 · Vectors

Systems of ODEs

Matrix form, phase plane, eigenvalues as the tool for classification.

1 demo lesson · 8 cards Unit 8 · Series

Power-series methods

Solutions near ordinary points, Frobenius, Legendre and Bessel.

1 demo lesson · 8 cards Unit 9 · Continuous

Partial differential equations

Separation of variables, heat, wave, and Laplace equations — and a taste of Fourier.

1 demo lesson · 8 cards