# Elementary Numerical Analysis II

## Math 352, CRN 24139

### Winter, 2013

Lecture: MWF, 14:00-14:50, 191 ANS
Office Hours: MWF 11:00-12:00 or by appointment.

### Course description

I will basically follow the text book. I plan to cover most of the Chapters 7, 10, 8, 9. It will certainly be a plus if you have some skill of writting computer program. However, the emphasis is on the mathematical aspects of the algorithms rather than on the computer language used to implement them. We will use Mathematica to handle examples.

### Learning outcomes

Students should be able to solve systems of linear equations using gaussian elimination with scaled pivoting, compute error and residual vectors, solve tridiagonal and banded systems, identify strictly diagonal matrices, compute matrix LU factorization and Cholesky factorization, compute the condition number, identify ill-conditioned systems of linear equations, solve systems of linear equations using iterative methods such as Jacobi and Gauss-Siedel iterations and identify when these methods converge. They should be able to identify and compute first and second degree splines, estimate accuracy of spline approximation, identify and compute natural cubic splines, and perform interpolation and approximation using B splines. Students should be able to derive solutions of ordinary differential equations using Taylor series and Runge-Kutta methods and estimate their errors. They should be able to approximate given data using the method of least squares both for polynomial and non-polynomial basis functions.

### Mathematica

If you want to learn mathematica, you can start from the following notebook. Some notebooks (Mathematica files) related to the course material will be posted here as we go along.

### Homework

There will be a homework assignment for each week. You can check the assignments here. Homework will be collected each Wednesday in class on the material of the previous week. Late homework will not be accepted. Your lowest homework score will be dropped. It is very important to keep up with your homework. Start it early, do not wait until the night before you have to turn it in.

### Project

If you so choose, part of your grade will be based on a programming or research project due on the last day of the class. Possible projects include implementing the algorithms discussed in class in your favorite programming language, or researching a numerical analysis topic. A list of suggested projects will be posted after the midterm.

### Exams

There will be one midterm exam in class on Wednesday, Feburary 13. If you must miss this exam due to extraordinary circumstances, you must get my permission and schedule a make-up exam in advance. The final exam is sheduled for Tuseday, March 19 at 15:15 in ANS 191.

Option 1: If you choose NOT to do a project, your grade will be based on your homework, midterm and final, distributed as
 Homework: 20% Midterm Exam: 40% Final Exam: 40%
Option 2: If you choose to do a project, your grade will be based on your homework, project, midterm and final, distributed as
 Homework: 20% Project: 20% Midterm Exam: 30% Final Exam: 30%

### Incomplete

Incomplete are only awarded in the Mathematics Department when two criteria have been satisfied: first, a student must have a passing grade at the time the ``I'' is assigned; secondly, some work could not be completed due to extenuating circumstances (illness, auto accident, etc.). Under no circumstances will an ``I'' be awarded as a substitute for a ``W'', ``D'' or ``F/N''. If you find yourself in trouble, drop the course!

### Disability Service

If you are a student with a documented disability please meet with me soon to discuss your needs. If you have not already requested a notification letter from Disability Services outlining recommended accommodations, please do so soon.

Yuan Xu
Department of Mathematics
University of Oregon, Eugene OR 97403-1222.
Phone 346-4729
Email: < yuan@math.uoregon.edu . >