Heat Transfer
2D Steady-State Conduction
Set the temperature on four walls — or insulate them — add internal heat, and watch a plate relax to steady state by the same relaxation the computer uses. Find out when the problem has no answer at all.
Transient Conduction
Quench a hot slab and watch the temperature ride inward over time. Lumped capacitance, the Biot number, and the exact moment the simple model starts to lie.
Convection & Boundary Layers
Blow fluid over a hot surface and grow the thermal boundary layer. Reynolds, Prandtl, Nusselt — and the moment laminar trips into turbulence.
Thermal Radiation
Heat a surface and watch its spectrum slide from infrared toward visible. Planck, Wien, Stefan–Boltzmann — then trade photons between two gray surfaces.
Math Methods
Fourier Series Builder
Stack sines until a square wave appears. Drag the number of terms, watch the Gibbs overshoot refuse to die — then flip to the spinning-circle phasor view.
Phase Portraits & Direction Fields
Click anywhere to drop a trajectory onto a vector field and watch it flow. Eigenvalue classification, saddles & spirals, plus nonlinear classics with limit cycles.
The Heat & Wave Equations
Separation of variables, made visible. Pluck a string or heat a rod and watch the modes evolve — one equation forgets, the other remembers.
Custom Fourier & PDE Solver
Bring your own function. Type any f(x), pick a sine/cosine/full series, read off the coefficients, then send it into the heat or wave equation. Built for checking real PDE homework.
The Auto-Tuner
Drive a damped oscillator with a square or sawtooth wave decomposed into Fourier harmonics. Each one passes through the transfer function — and one landing near resonance can dominate the rest.
Vibrations & Dynamics
The Spring–Mass–Damper
The one system to rule them all. Pluck it and watch it ring down, or drive it with a shaker, tune mass, stiffness and damping, and cross into resonance.
Frequency Response & Bode Plots
Sweep the forcing frequency and trace the Bode magnitude and phase. Watch input and output sinusoids scale and slip out of step — where machines shake themselves apart.
Numerical Methods
Root Finding & Fixed-Point Iteration
Newton, secant, and fixed-point iteration hunting a root. Watch the cobweb staircase converge — or fly off, when the same equation is rearranged the wrong way.
ODE Solver — Slope Fields & RK4
Type y′ = f(x, y), see the direction field, click to drop an initial condition, and race Euler against Runge–Kutta — with a mini ODE textbook alongside.
Gauss–Seidel & Jacobi
Solve a linear system by iteration — watch it converge sweep by sweep, or diverge when the matrix isn't diagonally dominant. Includes a heated-fin and a circuit system to play with.
Games
Match the Mystery Wave
A secret wave hides on screen, built from pure harmonics. Dial in the sliders to land on top of it, climb the match meter, and earn your stars. Fourier decomposition, by feel.
Classify the Fixed Point · Make It Converge
A phase-portrait quiz against the clock, and a linear-algebra puzzle where you swap rows to make the system converge. On the way.