e Advanced Methods for Ordinary Differential Equations (AMATH 568)

AMATH 568: Advanced Methods for Ordinary Differential Equations

SLN 10228, MWF 1:30-2:20, Mary Gates Hall 271
http://www.atmos.washington.edu/~breth/AM568

Instructor:
Professor Chris Bretherton
breth@washington.edu
ATG 704
Tel: 685-7414
Office hours: Mo Th 2:30-3:20

Course Description

(Catalog description is obsolete) Approximate solution strategies exploiting small or large parameters or variables and their applications to ordinary differential equations. Regular and singular perturbations. Boundary layers and multiple scales. WKB theory. Frobenius expansion about regular singular points. Asymptotic expansions around irregular singular points. Application to Bessel, Airy and error functions. Prerequisites: Undergraduate ODEs and working knowledge of Matlab.

Notes: The Amath 568 catalog description includes topics now covered in Amath 502/402, notably phase plane analysis of linear and autonomous nonlinear systems of ODEs.

Syllabus Supplemental reading Grading Schedule Homework and Exams Lecture Notes Matlab scripts

Syllabus

Weeks 1-4: Regular and singular perturbation theory for equations with small and large parameters. Boundary layers and multiple scales.
Weeks 5-6: Regular and irregular singular points of linear ODEs. Frobenius theory and application to Bessel's equation.
Weeks 7-10: Dominant balance and asymptotic expansion around irregular singular points. Application to Bessel, Airy and error functions. WKB theory.

Supplemental reading

Lecture notes will be posted on this web site. The course material is covered at a much more sophisticated level and with different ordering in Chapters 3-7 of Advanced Mathematical Methods for Scientists and Engineers by Carl M. Bender & Steven A. Orszag, McGraw-Hill Book Company, 1978.

Grading

Homework (60%), posted to class web page and assigned each Friday, due the following Friday. Discussion with your fellow students is encouraged, but please write out your own solutions in your own words. Some assignments may involve computer plotting of solutions. I will set up a dropbox for each assignment in case you want to hand it in electronically. Late homework (after 5pm on due date) must be handed in by 5pm on the Monday after the due date. The first late homework will be accepted without penalty. Thereafter, there will be a 20% deduction on the grade for that assignment.
Midterm (15%), in class We 8 Feb, open book and note. Final Exam (25%), take-home, due We 14 Mar by 5 pm, open book and note.
Please let instructor know well ahead of time if you will have a conflict with midterm exam time so a makeup can be arranged.

Special days

We 13 Jan: No class - Bretherton in Ft. Lauderdale
Mo 16 Jan: No class - MLK Day
We 18 Jan: UW classes cancelled - snow
Mo 16 Jan: UW classes cancelled - snow
Tu 24 Jan: Travel makeup class, 4:00-4:50, ATG 310c (note time change)
We 25 Jan: No class - Bretherton in New Orleans
Tu 31 Jan: Travel makeup class, 3:30-4:20, ATG 310c
We 1 Feb: No class - Bretherton in Boulder, CO
Tu 7 Feb: Snow makeup class, 3:30-4:20, ATG 310c
We 8 Feb: Midterm (in class, open book)
Tu 14 Feb: Snow makeup class, 3:30-4:20, ATG 310c
Mo 20 Feb: No class - Presidents Day

Lecture Notes

Note: Some lectures will cover multiple class periods. I'll fill in their dates as we go along.

1. Introduction (We 4 Jan)

20. Two-scale analysis of dispersive wave packets (We 7 Mar)

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