Master the mathematics of change through 30 interactive demonstrations. Watch direction fields guide solution curves, explore phase portraits, and discover chaos in the Lorenz attractor.
See also: Real Analysis for existence and uniqueness via fixed-point arguments, Linear Algebra for matrix exponentials and eigenvalue methods, and Fourier Analysis for the spectral approach to linear PDEs.
Direction fields, solution curves, and separable equations
Spring-mass systems, damping, and resonance
2D systems, trajectories, and nullclines
Fixed points, linearization, and classification
Predator-prey, van der Pol, and limit cycles
Saddle-node, pitchfork, and Hopf bifurcations
Sensitive dependence, strange attractors, and butterfly effects
Euler, Runge-Kutta, and adaptive step methods
Circuits, population dynamics, epidemics, and mechanics
Enter any ODE system and explore its behavior