Applied Mathematics I G63.2701

Monday 7:10-9:00

Instructor: Dr. John Greer
Office hours: M 2-3 and Th 12-1 in 621 Warren Weaver Hall
Office Phone: (212) 998-3148
Email Address: greer@cims.nyu.edu

Course Information

Prerequisites: undergraduate ordinary differential equations or the equivalent; undergraduate complex variables: must be able to do contour integrals (There will be a very short review of contour integration in class).
Material Covered: Various methods used for the study of solutions of ODEs. Topics include: local analysis of linear ODEs. Dimensional analysis, scaling and self-similarity. Asymptotic expansions of integrals: Watson's lemma and the methods of stationary phase and steepest descent. Regular and singular perturbation theory, including boundary layer problems, WKB theory, and the solution of nonlinear algebraic equations.
Grading: Grades will be determined by weekly homework assignments (70%) and a final exam (30%).
Required text: Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, C. M. Bender and S. A. Orszag. Springer-Verlag, 1999, ISBN 0-387-98931-5. Available at the NYU bookstore.
Suggested texts: Introduction to Perturbation Techniques, Ali Hasan Nayfeh. Wiley-Interscience, 1993, ISBN 0-471-31013-1.
Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics, G. I. Barenblatt. Cambridge University Press, 1996. ISBN 0-521-43522-6.

Course Material

Course description and lecture plan.

Homework Assignments

All assignments are due by noon on the given day (each due date is a Tuesday).

  1. Due 9/19. --------- Solutions.

  2. Due 9/26. --------- Solutions.

  3. Due 10/3: 6.17(b), 6.18(all), 6.19(a), 6.28(all), 6.29. All problems are in B+O.--------- Solutions.

  4. Due 10/13: 6.31, 6.32, 6.35, 6.49, 6.56(all). All problems are in B+O. Solutions.

  5. Due 10/24: 6.53,6.72, 6.83(a,b). Solutions.

  6. Due 10/31: 3.3, 3.13, 3.33(a). Solutions. -- change 3.3c to regular singular point at infinity

  7. Due 11/7: 3.39(a,b,e,f,g,i), 3.44, 3.46(a,b).

  8. Due 11/14.

  9. Due 11/28. ----- C++ code giving numerical approximation of solution for the last question. ----- Instructions for the code.

  10. Due 12/5:3.39(f),3.44,3.46(a).

  11. Due 12/12: 10.36.