Level of Education
2 years of post-secondary education
ECTS
2 credits
Training Structure
College of Sciences
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 (virtually all of physics, but also chemistry, economics, and more...).
The following chapters are primarily devoted to the case with one spatial dimension and one temporal dimension (1+1 D). Chapter 2 addresses 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, along with the heat equation and the Fourier method. Finally, Chapter 4, devoted to reaction-diffusion equations, considers the case of convective and diffusive transport using the Smoluchowsky equation, and derives the famous Einstein equation for diffusion.
The course includes theoretical and computational tutorials covering topics such as road traffic and queueing models.
Mandatory Prerequisites
Physics Courses for the First Year of the CPES Program and the First Semester of the Second Year of the CPES Program