### SYLLABUS

Meeting times: 9:25-10:40 TTh

Meeting place: 110 MLH

Prerequisites: An introductory course on numerical analysis (like M72/M170/M171) and on differential equations (like M100/M140/M142), and some knowledge of computer programming, or consent of instructor (contact me if you have any question).

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Tuesday 1:30-3:00 and Thursday 1:30-3:00. 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

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/m371_00.html. Students are responsible for checking regularly this course web page.

Textbook: Solving ordinary differential equations~II. Stiff and differential-algebraic problems by E. Hairer and G. Wanner,Springer, Berlin, Second Revised Edition, Comput. Math. series, vol. 14, 1996. I obtained a special price for the textbook from the publisher, \$79.95 instead of \$106! Look at http://www.unige.ch/math/folks/hairer/books/SodeII_preface.ps and http://www.unige.ch/math/folks/hairer/books/SodeII_contents.ps for a preface and table of contents. We will not cover the whole book. It is intended to be a reference and a supplement allowing a deeper understanding of the material. Aside from the book, class notes may be distributed based on the lectures.

Course outline: This course will cover the development, mathematical analysis, implementation issues of practical algorithms, and use of software for the numerical solution of time-dependent differential equations (DEs). We will treat in detail the following classes of DEs:

• Ordinary differential equations (ODEs)
• Differential-algebraic equations (DAEs)
DAEs usually consist of differential equations coupled with nonlinear equations to model for example conservation laws, geometrical/kinematic constraints, Kirchoff's laws, etc. More details about the course content which contain far more topics than we will have time to discuss.

We may consider other classes of DEs depending on the interests raised and on the applications to be treated. The content of this course is intended to be flexible. Any suggestion is welcome, please contact me at the address below. 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.

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. More details about the goals and objectives.

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

Computer languages: The predominant programming languages used in numerical analysis are Fortran and Matlab. For programming assignments, other languages will be accepted; but no programming assistance will be given for such languages (e.g. Mathematica, Maple, Pascal, Java, C, and C++).

Computer resources: Computer accounts will be made available on the Hewlett-Packard Unix workstation network in MLH B5. Check the laboratories reservation schedule and the web page of the Division of Mathematic Sciences Educational Laboratories for more information. Both Fortran and Matlab are also available on the HP/SGI network in MLH 301, and for engineering students, they are also available on the HP workstations in ICAEN.

Grading procedures: Still to be discussed in class. A priori there are two distinct options for the semester grade:

• Recommended: Based on one project with written report (60%) and oral presentation (40%). A minimal constraint on each project is that it must include Runge-Kutta methods as the methods used and/or analyzed. Each student must work on her/his own project. If two persons work together on a bigger project, each report and presentation has to be different.
• Based on one final written examination (50%) (closed books) and also on one final oral examination (50%) (closed books).
Homework is not mandatory, but strongly recommended and encouraged. No take-home examination for this course.

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. Please let your instructor know if you have a disability which requires special arrangements.