Conservation, dissemination and propagation CPES S4

This course covers the theoretical tools for describing distributed and conserved quantities, such as density, energy or charge density.

The first introductory chapter presents the general conservation equation, and the vector analysis tools needed to understand it, as well as the various fields in which this equation is used (practically all physics, but also chemistry, economics, etc.).

The following chapters are mainly devoted to the case with one dimension of space and one of time (1+1 D). Chapter 2 deals with convective transport, and presents the characteristic method for solving the corresponding quasi-linear first-order partial differential equation. Diffusive transport is then studied in Chapter 3, with the heat equation and the Fourier solution method. Finally, Chapter 4, devoted to reaction-diffusion equations, considers the case of convective and diffusive transport with the Smoluchowsky equation, and the derivation of the famous Einstein equation for diffusion.

The course is accompanied by theoretical and numerical tutorials, covering road traffic and queue modeling, for example.

Physics courses in the first year of CPES and the first semester of the second year of CPES