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

Course meeting place: 214 MLH

Prerequisites: 22M:213 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/m214_08.html. Students are responsible for checking regularly this course web page.

Textbooks:

• 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.
• 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 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.

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 semester grade will be based as follows:

1. Homework assignments will account for minimum 15%/maximum 30% of the course grade. For 15% (respectively 30%) you need to pass at least 25% (respectively 50%) of all exercises given (without counting the "Challenge" questions which carry an extra value of two passed exercises).
2. One project assignment will account for maximum 42.5%/minimum 35% of the course grade. A project of a minimum 6 Latex pages (12 pts, single-spaced) per person must be submitted by Monday May 5 (one week before the final exam week). You can work in groups of at most 2 people (in this case a project of a minimum 12 Latex pages must be submitted). Before working on a project topic it needs to be approved by the teacher early in the semester. You must submit electronically a Latex and a pdf file of your project.
3. The final examination will account for maximum 42.5%/minimum 35% of the course grade and it will be comprehensive. The final examination is open books and open notes.

In assigning grades, plus/minus grading will be used.

No grader

Final examination: To be held on Friday, May 16, 12:00 noon-2:00 P.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 (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.

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.