Course meeting times: 1:30-2:20 MWF

Course meeting place: 218 MLH

Discussion section meeting time: 1:30-2:20 T

Discussion section meeting place: 214 MLH

Prerequisites: 22M:055 and 22M:100, or consent of instructor. A course in differential equations. Some knowledge of computer programming with for example Matlab, Maple, Mathematica, or Scilab.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 10:30-noon. 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/m142_08.html. Students are responsible for checking regularly this course web page.

Goals and objectives of the course: This course is at a graduate level and it is assumed that you can work along the course in an independent fashion. This course will cover linear and nonlinear ordinary differential equations (ODEs), numerical methods for ODEs, and some applications. We will prove some but not all theorems and results (some long proofs are discussed in 22M:213/22M:214). At the end of the course the student should master essential issues in the course topics.

Course topics:

• Linear and nonlinear differential equations
• Existence and uniqueness of solutions
• Trajectories, phase space
• Differentiability of solutions
• Derivatives with respect to initial conditions, the resolvent
• Lyapunov stability
• Lyapunov functions
• Gradient systems
• The flow
• Invariant sets
• Fixed points
• Periodic orbits
• Poincare maps, Floquet theory
• Limit sets and limit cycles
• Hamiltonian systems
• Local bifurcations
• The Lorenz equations
• Chaos, strange attractors, Lyapunov exponents
• Taylor series methods
• Runge-Kutta methods
• Butcher trees
• Local and global error estimates
• Numerical linear stability

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

Textbook: 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. Library reference: Engineering QA614.8 .M45 2007. We will not cover the whole book. It is intended to be a reference and a complement giving a different view of the material. Aside from the book, class notes will be distributed based on the lectures.

Additional references:

• Differential Equations and Dynamical Systems by Lawrence Perko, Springer, Series: Texts in Applied Mathematics, Vol. 7, 3rd edition, 2001, 568 pages, Hardcover, 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.
• 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. Table of contents.
• An Introduction to Dynamical Systems: Discrete and Continuous by R. Clark Robinson, Prentice Hall, 2004, 672 pages, ISBN: 0131431404, Library reference: 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, Library reference: ENGINEERING QA614.8 .L97 2004.
• Nonlinear dynamics and chaos by Steven H. Strogatz, Westview Press, 1994, ISBN: 0-7382-0453-6, Library reference: 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, Library reference: 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.

Class procedures: The majority of each class period will be lecture oriented. I will generally hand out in advance the notes related to the material to be covered during the next class(es). It is strongly advised to read the material to be discussed before coming to class. Therefore, if there is a difficult point, you will know beforehand where it arises, so that you can benefit from the lecture more effectively. If the point remains unclear you can always ask questions. Readings will be assigned.

Computer languages: Matlab, Maple, Mathematica, or Scilab. Other programming languages will also be accepted.

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 on one mid-term examination, the final examination, and homework, as follows:

1. The mid-term examination will account for 30% of the course grade. The final examination will account for 40% of the course grade.
2. Homework and project assignments will account for 30% of the course grade. Late homework will be accepted only by special permission of the instructor. The grade for your homework will be based on the best 80% of your homework.

The tests are open books and open notes examinations. Bring a scientific calculator. In assigning grades, plus/minus grading will be used.

Teaching assistant: Da Xu, e-mail: dxu@math.uiowa.edu.

Final examination: To be held on Monday, December 15, 2008, 12:00-2:00 PM in room 218 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. This final examination is an open books and open notes examination. Bring a scientific calculator.

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.

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 Academic Handbook. http://www.clas.uiowa.edu/students/academic_handbook/index.shtml.

Academic Fraud: Plagiarism and any other activities when students present work that is not their own are academic fraud. Academic fraud is reported to the departmental DEO and to the Associate Dean for Academic Programs and Services who enforces the appropriate consequences. http://www.clas.uiowa.edu/students/academic_handbook/ix.shtml.

Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit the instructor, then the course supervisor and the departmental DEO. Complaints must be made within six months of the incident. http://www.clas.uiowa.edu/students/academic_handbook/ix.shtml#5.

Accommodations for Disabilities: A student seeking academic accommodations should register with Student Disability Services and meet privately with the course instructor to make particular arrangements. For more information, visit this site: http://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. For definitions, assistance, and the full University policy visit: http://www.sexualharassment.uiowa.edu.

Reacting Safely to Severe Weather: In severe weather, the class members should seek shelter in the innermost part of the building, if possible at the lowest level, staying clear of windows and free-standing ex- panses. The class will continue if possible when the event is over. (Operations Manual 16.14.i.)

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/mathlab/index.htm
• 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).