18.325 Topics in Applied Mathematics

Problem Sets for Spring 2001

1. Problem Set 1a (ps). Due Tu Feb 27. Kramers-Moyal expansion, galvanostatic electrodeposition, arcsine law (for fraction of time spent on one side of the origin), geometrically decaying Pearson walk. (Complete solutions by K. Dorfman: ps,pdf, Solutions to 1+2 by S. Yang: ps)

2. Problem Set 1b (ps). Due Th Mar 1. Similarity solution for electrodeposition, Gram-Charlier expansion with non-zero skewness. (Solutions by S. Yang: ps, Solutions by E. Silva: ps)

3. Problem Set 2a (ps). Due Tu Mar 20. Inelastic diffusion, normal diffusion with fat tails (student-t), anomalous diffusion with very fat tails (Cauchy). (Solutions by E. Silva: ps, solutions by B. White: ps)

4. Problem Set 2b (stated in "2a" above). Non-reversing random walk, self-trapping random walk, self-avoiding random walk. (Solutions by D. Harmon: ps, Solutions by E. Silva: ps)

5. Problem Set 3. (ps) Percentile order statistics, saddle-point asymptotics, diffusing-void model for sand draining out of a container, sorption/desorption from a lattice with excluded volume interactions. (Solutions to #3,4 by G.-S. Kim: ps, Solutions by D. Harmon:ps)

Note: solutions are no longer accessible as of August 2002.