Course meeting times: 2:30-3:20 MWF. Standard out-of-class preparation is at least six hours.

Course meeting place: 217 MLH

Prerequisites: 22M:213 or equivalent or consent of instructor.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday 3:30 P.M.-5:00 P.M., Thursday 2:30 P.M.-4:00 P.M. 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_10.html. Students are responsible for checking regularly this course web page.

Textbooks (recommended):

• Nonlinear Differential Equations and Dynamical Systems (second Edition) by Ferdinand Verhulst, Springer, Series: Universitext, 303 pages, Softcover, ISBN-10: 3540609342, ISBN-13: 978-3540609346, list price: $49.95. Library references: Physics Library QA372 .V48513 1996. Table of contents. Erratum. 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-10: 0387001778, ISBN-13: 978-0387001777, list price: $109.00. Table of contents. Library reference: Mathematical Sciences Library QA614.8 .W54 2003. The book on amazon.com. Electronic version.

Additional references:

• Mathematical Methods of Classical Mechanics by V.I. Arnol'd, Springer, Series: Graduate Texts in Mathematics, Vol. 60, 2nd edition 1989, Corr. 4th printing (September 5, 1997), 509 pages, Hardcover, ISBN-10: 0387968903, ISBN-13: 978-0387968902, list price: $69.95. Library references: Engineering Library QA805 .A6813 1989a, Physics Library QA805 .A6813 1989, and Physics Reserve QA805 .A6813 1989b. Table of contents.
• 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. Table of contents. Library reference: Engineering Library QA614.8 .M45 2007 and Mathematical Sciences Library QA614.8 .M45 2007.
• 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. Electronic version.
• 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. Electronic version.
• 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. Electronic version.

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 may 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. There will be 1 test during the semester, it will account for minimum 0%/maximum 15% of the course grade toward your worst grade below in 2,3,4.
2. Homework assignments will account for minimum 20%/maximum 30% of the course grade. For 20% (respectively 30%) you need to pass at least 30% (respectively 50%) of all exercises given (without counting the "Challenge" questions which carry an extra value of two passed exercises).
3. One project assignment will account for minimum 30%/maximum 35% of the course grade. A project of a minimum 5 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 10 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 your project electronically.
4. The final examination will account for minimum 30%/maximum 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.

Grader: Beven Kair, e-mail: bkair@math.uiowa.edu. B20J MLH. Phone: 335-3650.

Final examination: To be held on Friday, May 14, 12:00 P.M. noon in room 217 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination.

Course topics:

• Existence and uniqueness (covered in 22M:213)
• 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)
• Perturbations
• Differential inequalities
• Normal forms
• Unfolding of vector fields
• Invariant (stable, unstable, center) manifolds
• KAM (Kolmogorov-Arnold-Moser) theory
• Poisson systems
• Variational/symplectic integrators
• Structural stability and bifurcations
• Averaging
• 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://provost.uiowa.edu/ucoll/students/registration.htm#cross.

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.

The College of Liberal Arts and Sciences Policies and Procedures

Administrative Home: The College of Liberal Arts and Sciences is the administrative home of this course and governs matters such as the add/drop deadlines, the second-grade-only option, and other related issues. Different colleges may have different policies. Questions may be addressed to 120 Schaeffer Hall, or see the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/.

Electronic Communication: University policy specifies that students are responsible for all official correspondences sent to their University of Iowa e-mail address (@uiowa.edu). Faculty and students should use this account for correspondences. (Operations Manual, III.15.2 at http://www.uiowa.edu/~our/opmanual/iii/15.htm#152/ Scroll down to k.11.)

Accommodations for Disabilities: A student seeking academic accommodations should first register with Student Disability Services and then meet privately with the course instructor to make particular arrangements. See http://www.uiowa.edu/~sds/ for more information.

Academic Fraud: Plagiarism and any other activities when students present work that is not their own are academic fraud. Academic fraud is a serious matter and is reported to the departmental DEO and to the Associate Dean for Undergraduate Programs and Curriculum. Instructors and DEOs decide on appropriate consequences at the departmental level while the Associate Dean enforces additional consequences at the collegiate level. See the CLAS Academic Fraud section of the Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#2.

CLAS Final Examination Policies: Final exams may be offered only during finals week. No exams of any kind are allowed during the last week of classes. Students should not ask their instructor to reschedule a final exam since the College does not permit rescheduling of a final exam once the semester has begun. Questions should be addressed to the Associate Dean for Undergraduate Programs and Curriculum.

Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit the instructor, then the course supervisor, and then the departmental DEO. Complaints must be made within six months of the incident. See the CLAS Student Academic Handbook at http://www.clas.uiowa.edu/students/handbook/x/#5.

Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. All members of the UI community have a responsibility to uphold this mission and to contribute to a safe environment that enhances learning. Incidents of sexual harassment should be reported immediately. See the UI Comprehensive Guide on Sexual Harassment at http://www.uiowa.edu/~eod/policies/sexual-harassment-guide/index.html for assistance, definitions, and the full University policy.

Reacting Safely to Severe Weather: In severe weather, class members should seek appropriate shelter immediately, leaving the classroom if necessary. The class will continue if possible when the event is over. For more information on Hawk Alert and the siren warning system, visit the Public Safety web site at http://www.uiowa.edu/~pubsfty/intlinks.htm.

Resources:

• Writing Center 110 English-Philosophy Building, 335-0188, http://www.uiowa.edu/~writingc
• Speaking Center 12 English-Philosophy Building, 335-0205, http://www.uiowa.edu/~rhetoric/centers/speaking
• Mathematics Tutorial Laboratory 314 MacLean Hall, 335-0810, http://www.math.uiowa.edu/MathTutorialLab/
• Tutor Referral Service Campus Information Center, Iowa Memorial Union, 335-3055, http://www.imu.uiowa.edu/cic/tutor_referral_service

Student Classroom Behavior: The ability to learn is lessened when students engage in inappropriate classroom behav- ior, distracting others; such behaviors are a violation of the Code of Student Life. When disruptive activity occurs, a University instructor has the authority to determine class- room seating patterns and to request that a student exit immediately for the remainder of the period. One-day suspensions are reported to appropriate departmental, collegiate, and Student Services personnel (Office of the Vice President for Student Services and Dean of Students).

University Examination Policies: Missed exam policy. University policy requires that students be permitted to make up examinations missed because of illness, mandatory religious obligations, certain University activities, or unavoidable circumstances. Excused absence forms are available at the Registrar web site: http://www.registrar.uiowa.edu/forms/absence.pdf

Final Examinations: An undergraduate student who has two final examinations scheduled for the same period or more than three examinations scheduled for the same day may file a request for a change of schedule before the published deadline at the Registrar's Service Center, 17 Calvin Hall, 8-4:30 M-F, (384-4300).