Math 207C

Applied Mathematics

Perturbation and Asympotic Methods

Spring Quarter 2018

Applied Mathematics

Perturbation and Asympotic Methods

Spring Quarter 2018

Instructor: Office: Email: Phone: Office Hours: |
Professor Bob Guy MSB 2136 guy@math.ucdavis.edu 754-9201 M,W: 11-12 Th: 1-3 |

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 10:00-10:50 in
Wellman 229 |

TA: Office: Email: Office Hours: |
Carter Johnson MSB 2141 caljohnson@ucdavis.edu W: 2:30-4:30 |

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.

We will have a midterm and a final exam.

Homework 1, Due Friday, April 13th

Homework 2, Due Friday, April 20th

Homework 3, Due Friday, April 27th

Homework 4, Due Friday, May 4th

Midterm exam will be Wednesday, May 9th!

Homework 5, Due Friday, May 18th

Homework 6, Due Friday, May 25th

Homework 7, Due Friday, June 1st

Homework 8, Due Friday, June 8th, 5:00 PM

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.