18.300 - Principles of Continuum Applied Mathematics (Spring 2019)

Instructor: Stuart Thomson

Email: thomsons [at] mit .edu

Office: Room 2-239B

Office Hours: TBA

Lectures: TR 1-2:30 pm 2-139

COURSE DESCRIPTION

Physical systems arising in Nature are often comprised of a large number of constituent particles, motivating the construction of mathematical models at the macroscopic level relating continuous quantities such as density, velocity, and temperature. Models of this type often take the form of partial differential equations (p.d.e.) and are derivable from conservation laws. Part I of this course provides the mathematical framework in which to construct and analyse such models, and we will show how they can be used to describe a diverse range of phenomena such as traffic flow, gas dynamics, shallow water flow and elasticity. Part II of the course is dedicated to the numerical solution of two prototypical p.d.e., namely the wave equation and the diffusion equation. Some familiarity with Matlab will be required.

Prerequisites: Calculus II (GIR) and (18.03 or 18.032)

Text Book: None required