Methods of Applied Mathematics is a graduate-level course for students interested in pursuing research in applied mathematics. It provides a concise and self-contained introduction to advanced mathematical methods, especially in the asymptotic analysis of differential equations. Topics include scaling, perturbation methods, stationary phase analysis, multi-scale asymptotics, transform methods, Green's funtions, spectral theory, geometric wave theory, and the calculus of variations.

#### Prerequisites

Multivariable calculus, linear algebra, and differential equations. Some background in complex analysis would be very helpful.#### Textbook

The course textbooks are#### Additional Resources, some on reserve in the library

- Applied Mathematics by David Logan
- Physical Mathematics (Online Lecture Notes) by Michael Brenner
- Scaling, Self-similarity and Intermediate Asymptotics by G. I. Barenblatt
- Perturbation Methods by E. J. Hinch
- Advanced Mathematical Methods for Scientists and Engineers I by Carl M. Bender & Steven A Orszag
- Partial Differential Equations of Mathematical Physics and Integral Equations by Ronald B. Guenther & John W. Lee

#### Assignments and grading

There will be regular (biweekly) assignments and an in-class final You are encouraged to write up your homework and submit in PDF format, generated using LaTeX, Word, etc. If you don't already know LaTeX, it is a typesetting system for producing high-quality scientific and mathematical documents, and it is worthwhile learning. The LyX word processor is an easy to use front-end for LaTeX.Grading will be based 70% on assignments and 30% on the final. Please see NYU's Academic integrity policies.