Level of education
two years of postsecondary education
ECTS
2 credits
Training structure
Faculty of Science
Description
This course covers the theoretical tools used to describe 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 of physics, but also chemistry, economics, etc.).
The following chapters are mainly devoted to the case of one spatial dimension and one time dimension (1+1 D). Chapter 2 discusses convective transport and presents the characteristic method for solving the corresponding first-order quasi-linear 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 Smoluchowski equation, and the derivation of the famous Einstein equation for diffusion.
The course is accompanied by theoretical and numerical tutorials, covering topics such as road traffic and queue modeling.
Mandatory prerequisites
Physics courses in the first year of CPES and the first semester of the second year of CPES