Asymptotic Analysis in Differential Equations
This is not the current course catalog
Asymptotic Analysis is a fascinating subfield of differential equations in which interesting and unexpected phenomena can occur. Roughly speaking, the problem is this: Given a differential equation depending on a parameter epsilon, what happens to the solutions to the equation as we let epsilon go to 0? After an extensive survey of examples, we will cover asymptotic evaluation of integrals, such as stationary phase and Laplace’s method, multiple scales, WKB approximations, averaging methods, matched asymptotic expansions, and boundary layers. If time permits, we will also discuss bifurcation theory and the Nash-Moser Inverse Function Theorem.
The Class: Type: lecture
Requirements/Evaluation: evaluation will be based primarily on homework and exams
Extra Info: may not be taken on a pass/fail basis; not available for the fifth course option
Prerequisites: MATH 350 or MATH 351
Distributions: Division III;