Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

First, their algorithm advances a solution forward in time by solving the heat equation (also called the "diffusion equation" ...

Having a closer look on these self-organizing phenomenons it turns out that a lot of them can be well described by a class of reaction-diffusion equations of the following types: Important aspects of ...

The three main types of linear second order partial differential equations will be considered: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation). Techniques ...

Biomedical optics is a rapidly growing area of research. Although many universities have begun to offer courses on the topic, a textbook containing examples and homework problems has not been ...

It represents the solutions to three important equations of mathematical physics – Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen ...