Applied Mathematics I
Courant Institute of Mathematical Sciences
Fall 2002

Instructor. Prof. Yu Chen, Warren Weaver Hall (Ciww), Room 1126. Tel: 998-3285,

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.

  1. Principles and Techniques of Applied Mathematics, by B. Friedman, QA37 .F8565
  2. Mathematics Applied to Deterministic Problems in the Natural Sciences, by C. C. Lin and L. Segel, QA37.2 .L55
  3. Calculus of variations, by I. M. Gelfand and S. V. Fomin, QA315 .G417
  4. Advanced mathematical methods for scientists and engineers, by Carl M. Bender, Steven A. Orszag, QA371 .B43 1999
  5. Fourier series and boundary value problems, by Churchill, Ruel Vance, QA404 .C6 1987
  6. Asymptotic expansions, by E.T. Copson, QA312 .C58 1965
  7. Partial differential equations, an introduction, by Walter A. Strauss, QA374 .S86 1992 (Yu Chen)
Last modified: Aug 19, 2002