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.
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.