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
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Course Description (Catalog description is obsolete)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.
- Weeks 1-4: Regular and singular perturbation theory for equations
with small and large parameters. Boundary layers and multiple
- 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.
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.
- 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
Note: Some lectures will cover multiple class periods. I'll fill in their dates as we go along.