Numerical Methods / Elementary Numerical Analysis - APMA 507 / MATH 430 - Spring 2005

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 in 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.html

Examinations:

Prelim I: Tuesday, February 22nd, 2:00 - 3:15 pm
Prelim II: Thursday, March 31st, 2:00 - 3:15 pm
Prelim III: Tuesday April 26th, 2:00 - 3:15 pm

Notes and textbooks are not allowed during preliminary examination.

Instructor:

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

Graduate Teaching Assistant:

Radivoje Zarubica, 241C Thornton Hall, Phone: 924-7532, rz4a@virginia.edu

Lectures: Tuesday-Thursday: 2:00 - 3:15 p.m., THN E303

Office Hours:

Irina Mitrea, 225 Kerchof Hall, Wednesdays 1:00 - 2:30 p.m. (or by appointment).
Radivoje Zarubica, Applied Mathematics Workshop 104 Small Hall, Mondays 5:00 - 7:00 p.m. (subject to change)

Tentative Course Outline

Homework:

To be handed in at Thursday 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. You can write the programs either Matlab or Maple. 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 20
no homework due
Week 2: Jan 25-27
Homework 1: due Jan 27
Week 3: Feb 1-3
Homework 2: due Feb 3
Week 4: Feb 8-10
Homework 3: due Feb 10
Week 5: Feb 15-17
Homework 4: due Feb 17
Week 6: Feb 22-24
Prelim I: Feb 22
Week 7: March 1-3
Homework 5: due March 3
Week 8: March 8-10
Spring Break
no homework due
Week 9: March 15-17
Homework 6: due Mar 17
Week 10: March 22-24
Homework 7: due Mar 24
Week 11: Mar 29-31
Homework 8: due Mar 31
Prelim II: Mar 31
Week 12: April 5-7
No homework due
Week 13: April 12-14
Homework 9: due April 14
Week 14: April 19-21
Homework 10: due April 21
Week 15: April 26-28
Prelim III: April 26
Homework 11: due April 28
Week 16: May 3
Review - no homework due

Quizzes:

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

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.