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

Course meeting place: 213 MLH

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

Discussion section meeting place: 118 MLH

Prerequisites: 22M:100 or consent of instructor. A course in differential equations. Some knowledge of computer programming. The language Matlab will be used. Programming in Maple or Mathematica is acceptable.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday and Wednesday 2:30-4:00. 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/m142_06.html. Students are responsible for checking regularly this course web page.

Textbook (complement, recommended): 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, list price: $84.95. Table of contents. The book on amazon.com. Library reference: MATH QA372 .P47 1991.

Additional references:

• 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).

Goals and objectives of the course: This course is a graduate course and it is assumed that you can work along the course in an independent fashion. This course will cover continuous dynamical systems (linear/nonlinear differential equations), one- and two-dimensional flows, stability, phase plane, limit cycles, bifurcations, chaos, numerical methods for differential equations, and some applications. At the end of the course the student should master essential issues in those topics.

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

Computer languages: Matlab. Programming in Maple or Mathematica will also be accepted.

Computer resources: Computer accounts will be made available on the network in MLH B5. Check the laboratories reservation schedule and the web page of the Division of Mathematics Sciences Educational Laboratories for more information.

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.
2. The final examination will account for 35% of the course grade.
3. Homework and project assignments will account for 35% 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: Hun Kwon, e-mail: hkwon@math.uiowa.edu.

Final examination: To be held on Monday, December 11, 2006, 12:00-2:00 P.M. in room 213 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.

Course outline: Examples of topics:

• Linear and nonlinear differential equations;
• Trajectories, phase space, flows, limit sets;
• Derivatives with respect to initial conditions, the resolvent;
• Critical points, invariant manifolds;
• Stable, unstable, and center manifolds;
• Periodic orbits, limit cycles, Poincare maps, Floquet theory;
• Hamiltonian systems, Liapunov functions and stability;
• Modelling interacting species;
• Bifurcation theory;
• Local and global bifurcations;
• Three dimensional autonomous systems and chaos, Lyapunov exponents;
• Homoclinic orbits, heteroclinic orbits;
• Strange attractors;
• The second part of David Hilbert's 16'th problem;
• Limit cycles of Lienard 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.

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.

I would like to hear from anyone who has a disability which may require seating modifications or testing accommodations or accomodations of other class requirements, so that appropriate arrangements may be made. Please contact me during my office hours.

This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Procedures for student complaints and the collegiate policy on plagiarism and cheating can be found at "Student Rights and Responsibilities" and "Student Academic Handbook". All students in the College have specific rights and responsibilities. You have the right to adjudication of any complaints you have about classroom activities or instructor actions. Information is available in the College's Student Academic Handbook (http://www.clas.uiowa.edu/students/academic_handbook/). You also have the right to expect a classroom environment that enables you to learn, including modifications if you have a disability. Your responsibilities to this class and to your education as a whole-include attendance and participation. You are also expected to be honest and honorable in your fulfillment of assignments and in test-taking situations (the College's policy on plagiarism and cheating is on-line in the College's Student Academic Handbook, at http://www.clas.uiowa.edu/students/academic_handbook/). You have a responsibility to the rest of the class-and to the instructor-to help create a classroom environment where all may learn. At the most basic level, this means that you will respect the other members of the class and the instructor, and treat them with the courtesy you hope to receive in turn. Cell phones and pagers must be on silent mode during lecture and they are not allowed in class during exams. If you do bring a cell phone or pager to an exam, you may leave it in the front of the class during the exam. If a student is found to have a cell phone or pager during an exam, the cell phone or pager will be taken from the student and procedures for cheating may be followed.

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