Meeting times: 10:30-11:20 MWF

Meeting place: 213 MLH

Prerequisites: A grade of C- or higher in 22M:022 or 22M:026 or 22M:036 or 22M:046 or 22M:048 (essentially in single variable calculus) and computer programming experience are required. A knowledge of linear algebra and of differential equations is helpful, but an introduction to these topics will be given in the course.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: 9:30-10:30 MWF. 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/m72_01f.html. Students are responsible for checking regularly this course web page.

Book: MATLAB Guide by Desmond J. Higham and Nicholas J. Higham, 283 pp., SIAM, Philadelphia, 2000, ISBN 0-89871-469-9. This book is intended to be a reference book to program in Matlab. Aside from this book, class notes will be distributed based on the lectures.

Course outline: Topics to be covered:

Chapter 1 - Computer representation of numbers and errors

Chapter 2 - Approximation of functions by Taylor polynomials

Chapter 3 - Interpolation by polynomials and spline functions

Chapter 4 - Numerical integration

Chapter 5 - Matrix computations and systems of linear equations

Chapter 6 - Nonlinear equations

Chapter 7 - Optimization

Chapter 8 - Ordinary differential equations

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 will cover some basic topics of numerical analysis at an introductory level (see the course outline above for the list of topics to be covered). 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. 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. A topic will generally be illustrated by examples during the class. I will hand out in advance some notes related to the material to be covered during the next class(es).

Computer languages: The predominant programming languages used in numerical analysis are Fortran and Matlab. For programming assignments NO other language will be accepted. Matlab is especially powerful and convenient when preparing graphs and solving problems in linear algebra.

Other course resources: The student will need a scientific calculator, both for homework assignments and for tests.

Grader: Koung Hee Leem, e-mail: khleem@math.uiowa.edu.

Additional useful readings:

Elementary numerical analysis by K. Atkinson, second edition, John Wiley & Sons, New York, 1993, (MATH QA297 .A83 1993).

Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB: second edition by Charles F. Van Loan, Prentice Hall, NJ, 2000, (MATH QA76.95 .V35 2000).

(MATH QA297 .A83 1993).

An introduction to numerical analysis by K. Atkinson, second edition, John Wiley & Sons, New York, 1989, (MATH QA297 .A84 1989).

Introduction to numerical analysis by J. Stoer and R. Bulirsch, second edition, Springer-Verlag, Texts in Applied mathematics, New York, 1993, (MATH QA297 .S8213 1993).

Numerical computation 1 & 2. Methods, Software, and Analysis by C. W. Ueberhuber, Springer-Verlag, Berlin, 1997.

Numerical mathematics by A. Quarteroni, R. Sacco, and F. Saleri, Springer-Verlag, Texts in Applied mathematics, New York, 2000, (MATH QA297 .Q836 2000).

Grading procedures: The final grade will be based on tests and homework, as follows:

1. There will be two tests during the semester, with each test to account for 20% of the course grade.
2. Homework 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 75% of your homework. Only a portion of each homework assignment may be graded, based on the availability of assistance from a grader for the course.
3. The final test will account for 30% of the course grade, and this test will be comprehensive.

Bring a scientific calculator for the tests. In assigning grades, plus/minus grading will be used.

Final examination: To be held at 4:30PM on Friday December 21 in room 213 MLH. Only under exceptional circumstances will a student be permitted to shift the time of this examination. 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.