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.
Textbook
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.
Grade
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
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