Course meeting times: 2:30-3:20 MWF

Course meeting place: 214 MLH

Prerequisites: 22M:142 or equivalent or consent of instructor.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 11:30-1:00. I will also be available at other times. Just drop by my office or send me an e-mail to make an appointment.

Telephone: (319)-335-0898

Fax: (319)-335-0627

E-mail address: ljay@math.uiowa.edu

Mailbox: in Mailroom 15 MLH

Course web page: Assignments and other information about the course will be given in http://www.math.uiowa.edu/~ljay/m213_07.html. Students are responsible for checking regularly this course web page.

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.

Additional references:

• Differential Equations and Dynamical Systems (Hardcover) by Lawrence Perko, Springer, Series: Texts in Applied Mathematics, Vol. 7, 3rd edition, 2001, 568 pages, ISBN: 0-387-95116-4. Table of contents. Library reference: MATH QA372 .P47 1991.
• Stability, instability and chaos by Paul Glendinning, Cambridge University Press, Cambridge texts in applied mathematics 11, 1994, 388 pages, ISBN: 0-521-42566-2, reprinted 1999.
• An Introduction to Dynamical Systems: Discrete and Continuous by R. Clark Robinson, Prentice Hall, 2004, 672 pages, ISBN: 0131431404, (ENGINEERING QA614.8 .R65 2004). Table of contents, information and errata on the book by the author.
• Dynamical Systems with Applications using Matlab by Stephen Lynch, Birkhauser, Boston, 2004, 450 pages, ISBN 0-8176-4321-4, (ENGINEERING QA614.8 .L97 2004).
• Nonlinear dynamics and chaos by Steven H. Strogatz, Westview Press, 1994, ISBN: 0-7382-0453-6, (MATH Q172.5.C45 S767 1994).
• Chaos: an introduction to dynamical systems by Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, Springer, New York, Textbooks in mathematical sciences, 1997, 603 pages, ISBN: 0387946772, (MATH QA614.8 .A44 1997).
• Solving ordinary differential equations I. Nonstiff problems by E. Hairer, S. P. Norsett, and Gerhard Wanner, Springer, Berlin, Springer Series in Computational Mathematics, vol. 8, Second Revised Edition, 1993, 528 pages, ISBN: 978-3-540-56670-0. Table of contents. Library reference: MATH QA372 .H16 1993 v.1.
• Solving ordinary differential equations II. Stiff and differential-algebraic problems by E. Hairer and G. Wanner, Springer, Berlin, Springer Series in Computational Mathematics, vol. 14, Second Revised Edition, 1996, 614 pages, ISBN: 978-3-540-60452-5. Table of contents. Library reference: MATH QA372 .H16 1993 v.2.
• Geometric numerical integration: structure-preserving algorithms for ordinary differential equations by E. Hairer, Ch. Lubich, and G. Wanner, Springer, Berlin, Springer Series in Computational Mathematics, vol. 31, Second Revised Edition, 2006, 644 pages, ISBN: 978-3-540-30663-4. Library reference: MATH QA299.3 .H35 2006.

Goals and objectives of the course: This course is an advanced graduate course and it is assumed that you can work along the course in an independent fashion. 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.

Class procedures: The majority of each class period will be lecture oriented. Readings will be assigned.

Linux computer accounts: Linux computer accounts will be made available on the Linux network in MLH (computer lab rooms B5 and 301). You can use the NoMachine NX Client Windows software to access your Linux computer account remotely. 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.

Grading procedures: The final grade will be based as follows:

1. One midterm test will account for 20% of the course grade.
2. One Latex assignment will account for 25% of the course grade: each student will once type in Latex the material discussed during 3 consecutive classes. One student will be assigned (randomly and preferably from a list of volunteers) to type the notes after each 3 consecutive classes. 2 weeks of time will be given to submit your Latex file by e-mail. After correction by the teacher the notes will be printed and distributed to all students taking the class.
3. Homework assignments will account for 25% of the course grade. You need to pass at least 25% of all exercises given (without counting the "Challenge" questions which carry an extra value of two passed exercises).
4. The final examination will account for 30% of the course grade and it will be comprehensive.
5. You have the possibility to work on a project during the semester. If you choose this option it can account for up to 30% of the course grade and it will replace any portion of the semester grade with a lower score. A project can only improve your grade, not lower it. Before working on a project it needs to be approved by the teacher early in the semester.

The midterm test and final examination are open books and open notes examinations. In assigning grades, plus/minus grading will be used.

No grader

Final examination: To be held on Tuesday, December 18, 2007, 7:30-9:30 A.M. in room 214 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination.

Course topics:

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

This course plan may be modified during the semester. Such modifications will be announced in advance during class periods and on the course web page; the student is responsible for keeping abreast of such changes.

Add or drop: Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences.

Cross enrollments : Details of the University policy of cross enrollments may be found at: http://www.uiowa.edu/~provost/deos/crossenroll.doc.

Notes to student: The Department of Mathematics has offices in 14 MLH. To make an appointment to speak with the Chair of the Department, call 335-0714 or contact the Departmental Secretary in 14 MLH.

Academic Fraud: Plagiarism and any other activities that result in a student presenting work that is not his or her own are academic fraud. Academic fraud is reported to the departmental DEO and then to the Associate Dean for Academic Programs and Services in the College of Liberal Arts and Sciences. www.clas.uiowa.edu/students/academic_handbook/ix.shtml.

Making a Suggestion or a Complaint: Students have the right to make suggestions or complaints and should first visit with the instructor, then with the course supervisor if appropriate and next with the departmental DEO. All complaints must be made within six months of the incident. www.clas.uiowa.edu/students/academic_handbook/ix.shtml#5.

Accommodations for Disabilities: A student seeking academic accommodations first must register with Student Disability Services and then meet with a SDS counselor who determines eligibility for services. A student approved for accommodations should meet privately with the course instructor to arrange particular accommodations. See www.uiowa.edu/~sds/.

Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. Visit www.sexualharassment.uiowa.edu/ for definitions, assistance, and the full policy.

Administrative Home of the Course: The administrative home of this course is the College of Liberal Arts and Sciences, which governs academic matters relating to the course such as the add / drop deadlines, the second-grade-only option, issues concerning academic fraud or academic probation, and how credits are applied for various CLAS requirements. Please keep in mind that different colleges might have different policies. If you have questions about these or other CLAS policies, visit your academic advisor or 120 Schaeffer Hall and speak with the staff. The CLAS Academic Handbook is another useful source of information on CLAS academic policy: www.clas.uiowa.edu/students/academic_handbook/index.shtml.