Introduction to Asymptotic Analysis and Singular Perturbations

Math 490/710 - Special Topics in Applied Mathematics

Fall 1999 - Schedule Numbers 7511/3197

Matthias K. Gobbert, Weijia Kuang, and Thomas I. Seidman

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Grading Information

Scores and grades will be posted here beginning after the midterm.


Asymptotic Analysis includes a wide range of techniques in applied mathematics used to analyze or simplify problems involving multiple scales (in length or time) whose ratio appears as a `small' parameter.

The first half of this course will be devoted to a short but thorough introduction with a particular emphasis on boundary value problems in ordinary differential equations. These serve as prototype examples of applications with boundary layers, which will be studied in more detail in the second half of the semester in problems arising in fluid mechanics.

Hopefully, there will be time to highlight some other areas of asymptotic analysis, for instance, multi-scale analyses and homogenization techniques.

This course will require familiarity with differential equations (Math 225) and some formal background (Math 301) and is therefore accessible to incoming graduate students, senior undergraduates, as well as students from application areas in the physical sciences and engineering.

In practice, asymptotic analysis has to be used in concert with other techniques to extract as much information from a given model as possible; accordingly, this course will also use other aspects of mathematical modeling and analysis, and familiarity with some mathematical software package is recommended, but not required.

Basic Information

Recommended Literature for Asymptotic Analysis

Recommended Literature for Fluid Mechanics

Other Information

Copyright © 1999 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.6, December 1999.