ELEMENTARY NUMERICAL ANALYSIS-22M:072/22C:072, section 101

SPRING SEMESTER 2006


SYLLABUS

Meeting times: 10:30-11:20 MWF. Standard out-of-class preparation is at least six hours.

Meeting place: 105 MLH

Prerequisites: A grade of C- or higher in 22M:022 or 22M:026 or 22M:032 (essentially in single variable calculus). Some computer programming experience, preferably MATLAB, will be helpful. A knowledge of linear algebra and of differential equations is helpful, but a short introduction to these topics will be given in the course.

Instructor: Laurent O. Jay

Office: 225L MLH

Office hours: Monday 2:30-3:30 and Wednesday 2:30-4:30. I may 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_06.html. Students are responsible for checking regularly this course web page.

Textbook (complement): Numerical Computing with MATLAB by Cleve Moler, the founder of Matlab. The book on amazon.com. Book reference: SIAM, Philadelphia, 2004, ISBN: 0-89871-560-1, list price: $42.50. Library reference: Engineering Library QA297 .M625 2004. There is also a FREE electronic version of this book. It is intended to be complement giving a different view of the material. Aside from the book, class notes will be distributed based on the lectures.

Additional useful readings:

Elementary numerical analysis by K. Atkinson and W. Han, third edition, John Wiley & Sons, New York, 2004, (MATH QA297 .A83 2004). This is the textbook used in the other sections.
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).

Course outline: Topics to be covered:

Chapter 1 - Computer representation of numbers
Chapter 2 - Sources and analysis of errors
Chapter 3 - Approximation of functions by Taylor polynomials
Chapter 4 - Interpolation by polynomials and spline functions
Chapter 5 - Numerical integration
Chapter 6 - Matrix operations and systems of linear equations
Chapter 7 - Nonlinear equations
Chapter 8 - Optimization
Chapter 9 - 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. 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.

Homework: Will be assigned 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.

Computer languages: The predominant programming languages used in numerical analysis are Matlab and Fortran. For programming assignments, no other language will be accepted.

Computer resources: Computer accounts will be made available on the Linux network in MLH (lab rooms B5 and 301). Check the laboratories reservation schedule and the web page of the Division of Mathematic Sciences Educational Laboratories for more information.

Grader: Wang, Di, e-mail: dwang3@math.uiowa.edu.

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 15% of the course grade.
  2. Homework 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 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 examination will account for 35% of the course grade, and this test will be comprehensive.

The tests are open books and open notes examinations. Bring a scientific calculator for the tests. In assigning grades, plus/minus grading will be used.

Final examination: To be held on Monday, May 8, 2006, 2:15 P.M.-4:15 P.M. in room 105 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.

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.