Math 810 Asymptotic and Perturbation Methods Spring 2013

R. J. Braun

Class Meetings

TR 3:30-4:45, Purnell 238

Tentative Office Hours

MW 2-3, or by appointment

Textbooks (first two are required)

Holmes, Introduction to Perturbation Methods; Springer, 1995, isbn10: 0387942033; isbn13: 978-0387942032.

Hinch, Perturbation Methods; Cambridge U Press, isbn10: 0521378974; isbn13: 978-0521378970.

I will refer to Kevorkian and Cole, Multiple Scale and Singular Perturbation Methods (Springer, 1996) and to Bender and Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw Hill, old and new are exactly the same). I didn't pick them because of high cost however.

Syllabus

Homework Assignments

TBA

Exams

TBA

Tentative Topics

Algebraic problems

Asymptotic expansion of integrals

Initial value ODE problems: linear and nonlinear oscillators, multiple scales, strained coordinates

Boundary value ODE problems: boundary layer theory, matched asymtotic expansions, exponential asymptotics (if time allows)

WKB theory

Partial differential equations: some introductory problems.

Integral equations (a fly-by if time allows)

Applications will include genetic circuits from biology, electronic circuits, fluid dynamics, materials science and others.

Department of Mathematical Sciences