18.305 - Advanced Analytic Methods (Fall, 2021)

Lecturer: Hung Cheng

Email: huncheng @ math . mit .edu

Phone: 3-3663

Website: math.mit.edu/~huncheng

Office: Room 2-379

Office Hours: F 3:00–5:00 pm.

Lectures: MWF 2:00pm - 3:00pm, 2-151


TA Email:


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 will be due in the first class of the following week--unless otherwise specified. You are encouraged to discuss the problems with your classmates but not copy their solutions. No late homework will be accepted without valid excuses. The homeworks will be 25% of the total grade.

Exams: There will be three exams: 2:00--3:00 pm, Oct 8, Fri, Nov 12, Fri; Dec 8, Wed. They count as 75% of the total grade.