18.311 Principles of Applied Math
Spring 2009
Turing pattern in a 1D reaction-diffusion system.
Instructor: Aslan R Kasimov
TA: Peter M Buchak
Lecture:
TR9.30-11
(4-145)
Office hours (Aslan): T12:30-2:30
(2-339)
Office hours (Peter): T11:30-12:30, W4:30-5
(2-331)
Information:
This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems, etc. To name a few specifics, these could be: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation.
Although I will be reasonably rigorous (meaning, will not skip explanations of why things are true), the style is not that of endless "Theorem-Proof"'s. There will be physical explanations of what a specific formula/statement/solution means and numerical illustrations of solutions, most likely, using Matlab. I do not anticipate any discussion of numerical methods in this class, but it may be helpful if you know how to use Matlab (or something similar) in order to do some basic programming and visualization of your solutions.
The main (required) book is D. Logan, "An Introduction to
Nonlinear Partial Differential Equations," and my plan is to
cover:
1. Dimensional analysis, scaling
2. Basic perturbation methods
3. Review of linear PDE and methods of their solution (series
expansions, transforms)
4. Conservation laws, quasi-linear equations, method of
characteristics, wave breaking
5. Weak solutions, shocks, jump conditions
6. Hyperbolic systems
7. Diffusion and reaction-diffusion processes, similarity
solutions
8. Pattern formation
9. Stability and bifurcation
In addition to the main text, the following recommended books
will also be used (all on reserve in Science Library):
D. Logan, Applied Mathematics
S. Howison, Practical Applied Mathematics
G. Whitham, Linear and Nonlinear Waves
R. Haberman, Mathematical Models
The coursework will be graded based on six problem sets (30%), an in-class midterm exam (%30) and the final exam (%40).
Announcements
IMPORTANT: 2nd edition of the required book is available now in Coop
Dear all,If you purchased the first edition of Logan's book, you can return it an exchange for the second edition, which should be now available in MIT Coop.
Aslan
Announced on 05 February 2009 8:59 a.m. by Aslan Kasimov
MIT LIBRARY QUICK START