15 interactive notebooks ready to launch.
Discretize differential operators to approximate solutions numerically.
Simulate wave transport using the 1D advection equation.
Explore the Courant-Friedrichs-Lewy stability condition for PDE solvers.
Solve the heat equation numerically and visualize diffusion.
Extend diffusion simulation to two spatial dimensions.
Use implicit schemes and linear algebra to solve PDEs stably.
Simulate wave propagation with the 1D wave equation.
Study wave interactions and boundary conditions in PDEs.
Model 2D wave propagation and interference patterns.
Solve Laplace’s equation and explore harmonic functions.
Solve Poisson’s equation with source terms and boundary conditions.
Use linear algebra to solve elliptic PDE discretizations.
Solve Burgers’ equation and study shock formation in nonlinear flow.
Simulate pattern formation with reaction-diffusion systems.
Model shallow water waves and fluid flow with PDEs.