All readings will be listed here, organized by topic. Dates indicate the
class by which you should have read the indicated material. Some readings
may be announced here before they are announced in class, in case you want to
read ahead. Sometimes, particularly if I am traveling, you may find some
references posted at the library class reserves before they are linked here.

If a reading does not have a date, you don't have to worry about it yet.

Assigned Readings

- Holmes, Introduction to Perturbation Methods, Secs. 1.1-1.6 (02/01/10)
- Hinch, Perturbation Methods, Sec. 1.1 (02/04/10)
- Lin & Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences, Sec. 6.3 (02/08/10)
- Hinch, Perturbation Methods, Sec. 4.2 (02/11/10)

Assigned Readings

- Holmes, Introduction to Perturbation Methods, Secs. 2.1 & 2.2 (03/18/10)
- Holmes, Introduction to Perturbation Methods, Secs. 2.3 (03/18/10)
- Holmes, Introduction to Perturbation Methods, Secs. 2.4 (03/22/10)
- Holmes, Introduction to Perturbation Methods, Secs. 2.5 (03/25/10)
- Holmes, Introduction to Perturbation Methods, Appendix A.1.2 (03/25/10)
- O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, Sec. 2C (04/01/10)
- O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, Sec. 2G (04/01/10)
- O'Malley, Singular Perturbation Methods for Ordinary Differential Equations, Sec. 3O (04/05/10)

Optional Readings

- Lagerstrom, Matched Asymptotic Expansions, Secs. 1.3- 2.1

- extensive discussion about the theory behind matched asymptotic expansions
- Lagerstrom, Matched Asymptotic Expansions, Secs. 2.2

- systematic approach to computing matched asymptotic expansion

- construction of corner layers for discontinuous derivatives

Method of Multiple Scales

Assigned Readings

- Holmes, Introduction to Perturbation Methods, Secs. 3.1 & 3.2 (05/10/10)
- Holmes, Introduction to Perturbation Methods, Sec. 3.3 (05/10/10)
- Holmes, Introduction to Perturbation Methods, Sec. 3.4 (05/10/10)
- Holmes, Introduction to Perturbation Methods, Sec. 3.6 (05/10/10)
- Holmes, Introduction to Perturbation Methods, Sec. 3.7 (05/10/10)

Method of Averaging

Assigned Readings

- Novozhilov, Fractional Analysis, Methods of Motion Decomposition Introduction to Perturbation Methods, Secs. 6 & 7 (05/10/10)
- Novozhilov, Fractional Analysis, Methods of Motion Decomposition Introduction to Perturbation Methods, Sec. 10. 1 (05/10/10)

WKB Method

Assigned Readings

- Holmes, Introduction to Perturbation Methods, Secs. 4.1 & 4.2 (05/10/10)
- Holmes, Introduction to Perturbation Methods, Sec. 4.3 (05/10/10)

Homogenization

Assigned Readings

- Holmes, Introduction to Perturbation Methods, Secs. 5.1 & 5.2 (05/17/10)
- Holmes, Introduction to Perturbation Methods, Sec. 5.3 (05/17/10)
- Kramer and Majda, Introduction to Turbulent Diffusion, Secs. 8.1 & 8.2 (05/17/10)

Optional Readings

- Kramer and Majda, Introduction to Turbulent Diffusion, Sec. 8C (05/17/10)