This course is a continuation of 22M:213 (Ordinary Differential Equations I). 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.

ASSIGNMENTS/HOMEWORK

1. hmwk1.ps, hmwk1.pdf due 02/04/08.
2. hmwk2.ps, hmwk2.pdf due 02/13/08.
3. hmwk3.ps, hmwk3.pdf due 02/25/08.
4. hmwk4.ps, hmwk4.pdf due 03/05/08.
5. hmwk5.ps, hmwk5.pdf due 03/12/08.
6. hmwk6.ps, hmwk6.pdf due 03/26/08.
7. hmwk7.ps, hmwk7.pdf due 04/11/08.
8. hmwk8.ps, hmwk8.pdf due 04/18/08.
9. hmwk9.ps, hmwk9.pdf due 05/05/08.

READINGS FROM THE 2 TEXTBOOKS (AND FROM OTHER REFERENCES)

• Meiss: 9.3, 9.4
• Meiss: 9.5; Wiggins: 13.7AB
• Meiss: 9.6
• Wiggins: 13.7C, 14.4
• Wiggins: 13.8
• Meiss: 9.12; Wiggins: 14.5, 14.6
• Meiss: 9.13; Wiggins: 14.7
• Meiss: 8.5; Wiggins: 19.1; Perko: 2.13
• Meiss: 8.3, 8.4, 8.6; Wiggins: 20.3, 20.4AD; Perko: 4.3; Strogatz: 3.6
• Strogatz: 7.6
• Meiss: Lemma 3.13, p.95

GENERAL INFORMATION

• Syllabus
• ICON
• Textbook 1: Differential Dynamical Systems by James D. Meiss, Society for Industrial and Applied Mathematics (SIAM), Series: Monographs on Mathematical Modeling and Computation, 2007, 412 pages, Softcover, ISBN-10: 0898716357, ISBN-13: 978-0-898716-35-1, list price: $79.00. Table of contents; Preface; Index.
• The book on amazon.com. This book is $55.30 for SIAM members if you order through SIAM.
• Textbook 2: 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 (covered in 22M:213)
• Variational calculus (covered in 22M:213)
• Lagrange's and Hamilton's mechanics (covered in 22M:213)
• Noether's theorem (covered in 22M:213)
• Divergence free ODEs (Poincare recurrence theorem) (covered in 22M:213)
• Reversible systems (covered in 22M:213)
• Invariant (stable, unstable, center) manifolds (covered in 22M:213)
• 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/m214. Group you belong to: m214.
• 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.