Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial value problems - ...

Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace/Poisson equation. Initial value problems - ...

The classic quantum mechanics problem is a particle in a 1-D box. ... Why not just adopt some type of wave equation for ... Recall that I arbitrarily set this equal to a value of 1 for the initial ...

Initial value problem: PDE in question describes time evolution, i.e., ... the goal is to find how the dependent variable propagates in time. Example: The diffusion equation. -Boundary value problem: ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...