Numerical Methods - APMA 507 - Spring 2007

Course description:

This course covers numerical methods for the solution of nonlinear algebraic equations, interpolation, extrapolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Although the emphasis will be on applications, the course will have a strong theoretical component.

Prerequisite:

MATH 325 and computer proficiency.

Course objectives:

Students are expected lo learn methods for finding approximate solutions to mathematical problems for which exact (analytic) solutions are unavailable and gain an appreciation of the difficulties involved in finding reliable numerical solutions for such problems. Students are expected to develop and strengthen numerical skill and have an insight into efficiency of algorithmic processes.

Textbook:

R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition.

Course web page:

http://www.people.virginia.edu/~im3p/mathpage507_2007.html

Examinations:

Prelim I: Wednesday, February 21, 3:30 - 4:45 pm
Prelim II: Wednesday, March 28th, 3:30 - 4:45 pm
Prelim III: Wednesday, April 25th, 3:30 - 4:45 pm

Notes and textbooks are not allowed during preliminary examination.

Instructor:

Irina Mitrea, 225 Kerchof Hall, Phone: 982-2787, im3p@virginia.edu

Lectures: Monday-Wednesday: 3:30 - 4:45 p.m., THN D223

Office Hours:

Irina Mitrea, 225 Kerchof Hall, Tuesdays 2:00 - 3:30 p.m. (or by appointment).

Tentative Course Outline

Homework:

To be handed in at the Wednesday lecture meeting. Do all problems assigned. These will be graded and returned to you the next week. Please be sure that your work is legible.

No late homework will be accepted. You may work cooperatively on assignments provided

You write up the solution yourself.
You put a note on your homework indicating the names of anyone you worked with.

Of course, when it comes to exams, you are on your own.

You will be required to write a program to solve certain homework problems.The program must be handed in as part of the assignment, together with the output of the program, in the format indicated in the assignment, and an interpretation of the results whenever necessary. All programs should be written in Matlab. The book website contains the code for the problems. You may use this code as a guide, but you must write your own original code for the assignments.

Week by week homework assignments:



Week 1: Jan 17
no homework due
Week 2: Jan 22-24
Homework 1: due Jan 24
Week 3: Jan 29-31
Homework 2: due Jan 31
Week 4: Feb 5-7
Homework 3: due Feb 7
Week 5: Feb 12-14
Homework 4: due Feb 14
Week 6: Feb 19-21
Homework 5: due Feb 21
Prelim I: Feb 21
Week 7: Feb 26-28
no homework due
Week 8: March 5-7
Spring Break
no homework due
Week 9: March 12-14
Homework 6: due Mar 14
Week 10: March 19-21
No homework due
Week 11: Mar 26-28
Homework 7: due Mar 28
Prelim II: Mar 28
Week 12: April 2-4
No homework due
Week 13: April 9-11
Homework 8: due April 11
Week 14: April 16-18
Homework 9: due April 18
Week 15: April 23-25
Homework 10: due April 25
Prelim III: April 25
Week 16: April 30
Review - no homework due

Quizzes:

There will be a short quiz every Monday, unless otherwise announced. It will be returned to you on Wednesday.

Grading:

Prelims count 25% each, and the remaining 25% is apportioned among homework, quizzes and class participation.

Incomplete :

An incomplete will be given only in those rare circumstances where a student has completed all but a small portion of the course with a grade C or better and a severe, unexpected event prevents him/her from completing the course. In particular, if you get behind in the course you cannot ``bail out" by taking an incomplete.

Attendance and absences :

You are responsible for the material covered in class, whether you attend or not. You are also responsible for the announcements made during class; these may include changes in the syllabus.

Academic honesty is fundamental to the activities and principles of a University. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. When in doubt about plagiarism or collaboration, consult the course instructor. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion.

If you need accommodations because of a disability , if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please inform me immediately. Please see me after class, or at my office.

Words of advice: I encourage you to ask questions about the HW. Keep up with the latest materials covered; experience shows that, otherwise, you are likely to get poor grades on the exams. If you miss a class, make sure you get the notes from someone else who attended it. The professor will not assist any absentee to find out what happened in his/her absence. Hard work and regular attendance will get you through this course.