G63.2701

Courant Institute of Mathematical Sciences

Fall 2002

**Instructor.** Prof. Yu Chen, Warren Weaver Hall (Ciww), Room 1126.
Tel: 998-3285, yuchen@cims.nyu.edu

** Basic Course Information **

** Homework schedule **

Try out A Free Matlab Online Tutorial or look for others by a web search.

**Class Time.**

Lecture: 7:10-9:00 pm, Thursday, Room 813, Warren Weaver Hall (Ciww)

First meeting: Sept 5.

Last day of class: Wednesday, December 11 (runs on Thursday schedule)

Thanksgiving Recess: Thursday, November 28-Saturday, November 30

**Office Hours.** 3:00 pm - 5:00 pm Wednesdays, and by appointment.

**Prerequisite.** Elementary ordinary differential equations, advanced
calculus, linear algebra, and programming with Matlab.

**Required Text.** Principles of applied mathematics : transformation
and approximation, Keener, 2nd Edition, 1995;
available at the university bookstore.

**Syllabus.**
Various methods used for the study of solutions of ODEs, both exact and
approximate. Topics include: integral transforms, Green's functions,
Sturm-Liouville theory and eigenfunction expansions. Asymptotic expansions
of integrals: Watson's lemma and the methods of stationary phase and
steepest descent. Variational formulation of solutions. Hamiltonian
mechanics and canonical transformations. Similarity methods for finding
exact solutions.

**Assignments and Grading. **
Homework assignments will be given weekly, involving analytical work
and computer programming in Matlab, and typically due on Thursday evening
at class. The homework grade contributes about 50% to the final grade.
Grading will reflect not only correctness, but also cleverness and clarity
(i.e. English explanations).

**Reference Texts.**

- Principles and Techniques of Applied Mathematics, by B. Friedman, QA37 .F8565
- Mathematics Applied to Deterministic Problems in the Natural Sciences, by C. C. Lin and L. Segel, QA37.2 .L55
- Calculus of variations, by I. M. Gelfand and S. V. Fomin, QA315 .G417
- Advanced mathematical methods for scientists and engineers, by Carl M. Bender, Steven A. Orszag, QA371 .B43 1999
- Fourier series and boundary value problems, by Churchill, Ruel Vance, QA404 .C6 1987
- Asymptotic expansions, by E.T. Copson, QA312 .C58 1965
- Partial differential equations, an introduction, by Walter A. Strauss, QA374 .S86 1992

yuchen@cims.nyu.edu (Yu Chen)

Last modified: Aug 19, 2002