Course meeting times: 1:30-2:20 MWF. Standard out-of-class preparation is at least six hours.

Course meeting place: 214 MLH

Discussion section meeting time: 2:00-2:50 T

Discussion section meeting place: 110 MLH

Prerequisites: 22M:055 (MATH:3770) and 22M:100 (MATH:3600), 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 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: laurent-jay@uiowa.edu

Mailbox: in Mailroom 15 MLH

Course web page: Assignments and other information about the course will be given at the course web page http://www.math.uiowa.edu/~ljay/m142_12.html. Students are responsible for checking regularly this course web page.

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
• Variational calculus
• 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.

Objectives and goals 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 of the proofs are discussed in 22M:213/22M:214). At the end of the course the student should master essential issues in the course topics.

Textbook (recommended): Ordinary Differential Equations and Dynamical Systems by Gerald Teschl, American Mathematical Society, Providence, Series: Graduate Studies in Mathematics, vol. 140, to appear in Sep. 2012, 356 pages, Softcover, ISBN-10: 0-8218-8328-3, ISBN-13: 978-0-8218-8328-0, list price: $64.00. Electronic version and erratum. We will not cover the whole book. It is intended to be a reference and a complement giving a different view of the material.

Additional references:

• 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.
• Nonlinear Differential Equations and Dynamical Systems (second Edition) by Ferdinand Verhulst, Springer, Series: Universitext, 303 pages, Softcover, Corr. 2nd printing, 1996, ISBN-10: 3540609342, ISBN-13: 978-3540609346, list price: $49.95. Library reference: Physics Library QA372 .V48513 1996. Table of contents. Erratum. The book on amazon.com.
• Ordinary Differential Equations by Vladimir I. Arnol'd (Author), R. Cooke (Translator), Springer, 272 pages, Softcover, 3rd edition, 1992, ISBN-13: 978-3540345633, list price: $64.95. The book on amazon.com.
• The Theory of Differential Equations: Classical and Qualitative by Walter G. Kelley and Allan C. Peterson, Springer, Series: Universitext, Vol. 278, 424 pages, Softcover, 2nd edition, 2010, ISBN-10: 1441957820, ISBN-13: 978-1441957825, list price: $69.95. The book on amazon.com. Electronic version.
• Differential Equations: Theory and Applications by Davis Betounes, Springer, 2nd edition, 2010, 620 pages, Hardcover, ISBN-10: 1441911626, ISBN-13: 978-1441911629, list price: $79.95. Library reference: Engineering Library QA371.5.D37 B47 2010. The book on amazon.com. Electronic version.
• Principles of Differential Equations by Nelson G. Markley, Wiley-Interscience, Hoboken, N.J., Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts, 2004, 352 pages, Hardcover, ISBN: 0-471-64956-2. Table of contents. Library reference: MATH QA371 .M264 2004.
• 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-10: 0387001778, ISBN-13: 978-0387001777, list price: $109.00. Table of contents. Library reference: Mathematical Sciences Library QA614.8 .W54 2003. Electronic version.
• 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. 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.

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

Homework: Will be assigned approximately weekly. Presentation of your results is very important. Scratch paper will not be accepted. Do not expect good grades if your solution to a problem is poorly communicated. Like for everything, if you cannot explain something in great details, you certainly have not fully understood it. The importance of doing homework cannot be overemphasized, most of human people learn by doing, not only by watching and/or listening. Late homework may not be accepted, you need to request permission first or to provide a reasonable justification. Late homework is not accepted once a correction is given.

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 also 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 course grade will be calculated as follows:

1. There will be 2 tests during the semester, with each test to account for 20% of the course grade.
2. The final examination will account for 40% of the course grade.
3. Homework and project assignments will account for 20% 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 all the homeworks minus your worst 2 scores. Each homework has the same weight.

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

Teaching assistant: Ekaterina (Katya) Nathanson, e-mail: ekaterina-nathanson@uiowa.edu. B12 MLH. Phone: 353-2509. Office hours: 9:30-10:30 MW and 3:00-4:00 T.

Final examination: To be held on Wednesday, December 12, 2012, 12:30-2:30 PM in room 214 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. The final examination date and time will be announced during the first half of the semester by the Registrar. I will announce here and in class the final examination date and time for this course once it is known. Do not plan your end of the semester travel plans until the final exam schedule is made public.

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.

DEO: 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. DEO: Dan Anderson, 14A 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 Academic Policies 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, Operations Manual III.15.2. 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 www.uiowa.edu/~sds/ for more information.

Academic Honesty: All CLAS students have, in essence, agreed to the College's Code of Academic Honesty: "I pledge to do my own academic work and to excel to the best of my abilities, upholding the IOWA Challenge. I promise not to lie about my academic work, to cheat, or to steal the words or ideas of others; nor will I help fellow students to violate the Code of Academic Honesty." Any student committing academic misconduct is reported to the College and placed on disciplinary probation or may be suspended or expelled (CLAS Academic Policies Handbook).

CLAS Final Examination Policies: The date and time of every final examination is announced during the fifth week of the semester by the Registrar. No exams of any kind are allowed during the last week of classes. All students should plan on being at the UI through the final examination period.

Making a Suggestion or a Complaint: Students with a suggestion or complaint should first visit with the instructor (and the course supervisor), and then with the departmental DEO. Complaints must be made within six months of the incident (CLAS Academic Policies Handbook).

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 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 website.