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, 18.112
Text Book: Advanced Analytic Methods in Applied Mathematics, Science, and Engineering, by Hung Cheng, Luban Press.
Homeworks: Homeworks assigned each week will be collected during the first class of the following week. You may discuss the problems with your classmates, but not copy their solutions. No late homework will be accepted. The homeworks will be 10% of the total grade.
Exams: Three exams: Oct 7, Nov 9, Dec 12. No final. Each exam is 30% of the total grade.