### SYLLABUS

Meeting times: 11:30-12:20 MWF

Meeting place: 210 MLH

Prerequisites: 22M:027 and 22M:028, or 22M:040 and 22M:042, or 22M:056, or consent of instructor. A knowledge of computer programming.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday 2:30-4:30 and Friday 2:30-3:30. 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/m170_99.html. Students are responsible for checking regularly this course web page.

Textbook: Introduction to numerical analysis by J. Stoer & R. Bulirsch, second edition, Springer-Verlag, Texts in Applied mathematics, New York, 1993, ISBN 0-387-97878-X, US\$54.95. 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 will be distributed based on the lectures. The book will be the same for 22M:171/22C:171-Numerical analysis: differential equations and linear algebra.

Course outline: Topics to be covered:

Chapter 1 - Computer representation of numbers
Chapter 2 - Sources and analysis of errors
Chapter 3 - Interpolation
Chapter 4 - Approximation of functions
Chapter 5 - Numerical integration
Chapter 6 - Finding zeros of nonlinear equations by iterative methods

An introduction to numerical analysis by K. Atkinson, second edition, John Wiley & Sons, New York, 1989, US\$88.95 (MATH Course Reserve QA297 .A84 1989).
Numerical computation 1 & 2. Methods, Software, and Analysis by C. W. Ueberhuber, Springer-Verlag, Berlin, 1997.
Accuracy and stability of numerical algorithms by N.J. Higham, SIAM, Philadelphia, 1996, US\$32.00 (MATH Course Reserve QA297 .H53 1996).

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. The courses sequence 22M:170-171/22C:170-171 will cover some modern basic topics of numerical analysis. The main objective will be to have a clear understanding of the ideas and techniques underlying the numerical methods, results, and algorithms that will be presented, where error analysis plays an important role. You will then be able to use this knowledge to analyze the numerical methods and algorithms that you will encounter, and also to program them effectively on a computer. This knowledge will be useful in your future not only to solve problems with a numerical component, but also to develop numerical procedures of your own.

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.

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. This room will be reserved on Tuesdays from 3:30 until 4:30. 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: The final grade will be based on one mid-term examination, the final examination, and homework, as follows:

1. The mid-term examination and the final examination will each account for 30% of the course grade.
2. Homework and project assignments will account for 40% 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 75% 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: Natalie Kleinfelter, e-mail: nkleinfe@math.uiowa.edu.

Final examination: To be held on Thursday, December 16, 9:45-11:45 AM in room 210 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. This final examination will be done with open books and open notes. Bring a scientific calculator.

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.