Math 207C

Applied Mathematics

Perturbation and Asympotic Methods

Spring Quarter 2016

Applied Mathematics

Perturbation and Asympotic Methods

Spring Quarter 2016

Instructor: Office: Email: Phone: Office Hours: |
Professor Bob Guy MSB 2136 guy@math.ucdavis.edu 754-9201 Monday 4:15-5:30 Tuesday 1:30-3:00 Wednesday 3:15-4:00 Friday 3:15-4:00 |

Textbook: |
Introduction
to Perturbation Methods, Mark H. Holmes, 2nd Ed.,
Texts in Applied Mathematics 20, Springer, 2013. (An e-book
is available from the UCD Library). |

Webpage: |
http://www.math.ucdavis.edu/~guy/teaching/207c/ Homework and announcements will be posted here. |

Class: |
MWF 12:10-1:00 in
Wellman 207 |

TA: Office: Email: Office Hours: |
Yunshen Zhou MSB 3229 yszhou@math.ucdavis.edu Thursday 2-4 |

Homework and Exams

You are encouraged to talk with your classmates about homework problems. However, you must do your own write-up. All aspects of your write up must be clearly presented. Homework assignments will be posted on the webpage. Homework will be assigned approximately every week or every other week.

We will have a midterm and a final exam.

Homework 1, Due Friday, April 8th

Homework 2, Due Friday, April 15th

Homework 3, Due Friday, April 22nd

Homework 4, Due Friday, April 28th

Midterm exam will be Friday, May 6th!

Homework 5, Due Monday, May 9th.

Homework 6, Due Friday, May 20th.

Homework 7, Due Friday, May 27th.

Homework 8, Due Friday, June 3rd.

Grading

Your grade will be based on your Exam and homework assignments.

Homework | 50% |

Midterm | 20% |

Final Exam | 30% |

What we will cover

- Asymptotic Expansions
- Nondimensionalization
- Regular Perturbations
- Singular perturbations
- Layers and Matched Asymptotic Expansions
- Method of Multiple Scales
- Averaging
- Homogenization
- WKB
- Asymptotics of Integrals

You may find it useful to read other books on this subject in addition to the textbook. There are many. Some suggestions are listed below.

- C.M. Bender and S.A. Orszag,
__Advanced Mathematical Methods for Scientists and Engineers__, Springer, 1999. - J. Kevorkian and J.D. Cole,
__Perturbation Methods in Applied Mathematics__, Springer, 1981. - J.C. Neu,
__Singular Perturbation in the Physical Sciences__, AMS, 2015. - P.A. Lagerstrom,
__Matched Asymptotic Expansions__, Springer, 1988. - M. van Dyke,
__Perturbation Methods in Fluid Mechanics__, Parabolic Press, 1975. - J.P. Keener,
__Principles of Applied Mathematics__, Perseus, 2000.