ODE Lessons | MathCodes

Direction Fields

Visualize solution families for first-order ODEs with direction fields.

Euler vs The World

Compare Euler’s method to more accurate numeric solvers.

Runge Kutta RK4

Use the RK4 method to solve ODEs with higher accuracy.

// Unit 2: Systems of ODEs

SIR Epidemic Model

Simulate SIR disease spread dynamics with coupled ODEs.

Predator Prey Lotka-Volterra

Model predator-prey interactions with the Lotka-Volterra system.

Phase Portraits

Plot phase portraits to analyze ODE system behavior.

// Unit 3: Second-Order Systems

State Space Representation

Translate higher-order ODEs into first-order state-space systems.

Damped Harmonic Oscillator

Analyze damping and resonance in second-order oscillators.

Nonlinear Pendulum

Study nonlinear pendulum dynamics beyond small-angle approximations.

// Unit 4: Non-Linearity and Chaos

Bifurcation and Population Collapse

Track how nonlinear systems bifurcate and collapse in population models.

Double Pendulum

Simulate the chaotic double pendulum with its sensitive dependence on initial conditions.

Lorenz Attractor

Visualize the Lorenz attractor from its differential equations.

// Unit 5: Boundary Value Problems

Shooting Method

Solve boundary value problems numerically using a shooting approach.

Eigenvalue Problems & Resonance

Explore boundary value eigenproblems and resonance phenomena.

Gateway to PDEs

Use ODE boundary problem methods as a foundation for PDE study.