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.
PrerequisitesMultivariable calculus, linear algebra, and differential equations. Some background in complex analysis would be very helpful.
TextbookThe 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 gradingThere 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.