18.305 - Advanced Analytic Methods (Fall, 2020)

Lecturer: Hung Cheng

Email: huncheng @ math . mit .edu

Phone: 3-3663

Website: math.mit.edu/~huncheng

Lectures: MWF 2:00pm - 3:00pm
See Canvas Site for Zoom Link

TA: Chengyang Shao

TA Email: shaoc@ mit . edu

COURSE DESCRIPTION

Covers expansion around singular points: the WKB method on ordinary and partial differential equations; the method of stationary phase and the saddle point method; the two-scale method and the method of renormalized perturbation; singular perturbation and boundary-layer techniques; WKB method on partial differential equations.

Prerequisites: 18.04, 18.075, or 18.112

Text Book: Advanced Analytic Methods in Applied Mathematics, Science, and Engineering, by Hung Cheng, Luben Press

Homeworks: Homeworks will be assigned each week and, unless otherwise specified, will be due in the first class of the following week. Please send your homework to Mr. Gan, your TA. You may discuss the problems with your classmates, but not copy their solutions. No late homework will be accepted without valid excuses. The homeworks will be 50% of the total grade.

Exams: There will be one virtual exam: 2:00--3:00 pm, Oct 16, Fri. It counts as 50% of the total grade.