Course announcement. This course is a natural continuation of 22M:142 (nonlinear dynamics with numerical methods). Though the course is mostly about the theory of ordinary differential equations (ODEs), we will consider this theory in conjunction with some theoretical and practical aspects of numerical methods for ODEs. If you have a high interest in a specific topic related to ODEs, please let me know. If a majority of students taking the class is interested in the topic then I may cover it during Spring semester 2008.

ASSIGNMENTS/HOMEWORK

1. hmwk1.ps, hmwk1.pdf due 09/10/07.
2. hmwk2.ps, hmwk2.pdf due 09/17/07.
3. hmwk3.ps, hmwk3.pdf due 09/24/07.
4. hmwk4.ps, hmwk4.pdf due 10/08/07.
5. hmwk5.ps, hmwk5.pdf due 10/17/07.
6. hmwk6.ps, hmwk6.pdf due 10/26/07.
7. hmwk7.ps, hmwk7.pdf due 11/09/07.
8. hmwk8.ps, hmwk8.pdf due 11/16/07.
9. hmwk9.ps, hmwk9.pdf due 11/26/07.
10. hmwk10.ps, hmwk10.pdf due 12/03/07.

READINGS FROM THE TEXTBOOK (AND FROM OTHER REFERENCES)

• Introduction
• 1.1, 1.2
• Chapter 2
• Introduction of Chapter 7, 7.1, 7.2, 7.3, 7.4
• From [HNW,1993] you can read section II.2 if you wish
• Introduction of Chapter 3, 3.1, 3.2, 3.4 (and 3.5 if you are adventurous!)
• Introduction of Chapter 18, 18.1, 18.3, and 18.5
• Section 2.7 and 2.12 from Perko's book
• Introduction of Chapter 5, 5.1
• 7.6
• Introduction of Chapter 13, 13.1, 13.2, 13.3, 13.5, 13.7AB
• Introduction of Chapter 14, 14.1, 14.2, 14.3
• Introduction of Chapter 16, 16.1, 16.2

GENERAL INFORMATION

• Syllabus
• ICON
• Textbook: Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins, Springer, Series: Texts in Applied Mathematics, Vol. 2, 2nd edition, 2003, 808 pages, Hardcover, ISBN: 978-0387001777, list price: $99.00. Table of contents. The book on amazon.com.
• Some notes and references on dynamical systems

COURSE TOPICS

• Lyapunov-stability
• Variational calculus
• Lagrange's and Hamilton's mechanics
• Noether's theorem
• Divergence free ODEs (Poincare recurrence theorem)
• Reversible systems
• Invariant (stable, unstable, center) manifolds
• Poisson systems
• Variational/symplectic integrators
• Differential inequalities
• KAM (Kolmogorov-Arnold-Moser) theory
• Normal forms
• Structural stability
• Perturbations
• Averaging
• Bifurcations
• Homoclinic orbits
• Melnikov's method
• Boundary value problems (Sturm-Liouville systems)
• etc.

MATLAB

• Free electronic textbook Numerical Computing with MATLAB by Cleve Moler himself!, the founder of Matlab.
• Matlab Help is available directly from the Help menu of the Matlab window.
• A Very Elementary MATLAB Tutorial, MATLAB Tutorials from Other Universities, MATLAB & Simulink Tutorials, MATLAB Homework Helper, all presented by Mathworks, Inc., producers of Matlab.
• Crash Course in MATLAB by Tobin Driscoll, University of Delaware.
• Some Matlab tutorials from Edward Neuman
• Matlab tutorial - University of New Hampshire
• Matlab tutorial - University of British Columbia
• Matlab tutorial - University of Florida
• MATLAB Online Reference Documentation provides direct hypertext links to specific MATLAB function descriptions (from the Math Dept, University of Florida).
• Matlab Primer (ps) (for an earlier version of Matlab)
• Matlab 5 introduction (ps, see also html)
• MATLAB Guide by D. J. Higham and N. J. Higham, SIAM, Philadelphia, 2005 (ENGINEERING QA297 .H5217 2005)
• Introduction to Engineering Programming: in C, MATLAB and JAVA by Mark A. Austin.
• Matlab for first order ODEs
• Matlab for higher order ODEs and systems of ODEs
• Matlab for PDEs

FORTRAN

• Type "man f90" on Linux terminals for information on how to compile.
• A list of Fortran tutorials, Fortran 90 for the Fortran 77 programmer, Fortran 90 for Fortran 77 programmers.

LINUX COMPUTER ACCOUNTS

• Linux computer accounts will be made available on the Linux network in MLH (computer lab rooms B5 and 301). You can also use the NoMachine NX Client Windows software to access your Linux computer account remotely.
• Selected Unix commands.
• Class directory: /group/class/m213. Group you belong to: m213.
• If you do not know your password go to 303A MLH.
• Accounts for students who are not majoring in Computer Science, Mathematics, or Statistics and Actuarial Science will be deleted after the term has ended! Note the expiration date at the top of your Unix Account Information form.
• The directory for this class will be removed before the beginning of the next term! If there is anything in this directory that you would like to save, you must archive it to your own home directory.

NO GRADER