Reaction - Diffusion Analysis

These are rough lecture notes for a course on applied math (Math 350), with an emphasis on chemical kinetics, for advanced undergraduate and beginning graduate students in science and mathematics. There are (Fall 2003) three students enrolled: a second year undergraduate with a major in applied mathematics, a senior with majors in mathematics, chemical engineering, and environmental sciences, and a first year graduate student in chemistry. During the course of the semester the students prepared projects on topics related to the course material and are presently scheduled to present them to each other in a four hour “mini-conference” on exam day, December 17, 2003. Their expositions will be about: pattern formation, implementation of a reaction diffusion system numerically, and use of group theory to study the spectrum of the Laplacian. In parallel to this course (also in the Fall of 2003), Professor Gregory Yablonsky, of the Chemical Engineering Department, taught a course on “Transport in the Environment,” CE 583, for chemical engineering students. Professor Yablonsky and I communicated almost daily during the semester and constantly exchanged ideas about the two courses. Our plan is to combine them into one course that contains both the mathematics at a similar depth as discussed here, but with a much more developed scientific content, emphasizing issues in biochemistry and environmental science. Our lecture notes will be integrated into a single text. Professor Yablosnky’s lecture notes comprise the following main topics: