Elementary Numerical Analysis II
Math 352, CRN 23734
Lecture: MWF, 14:00-14:50, 208 Deady
Instructor: Yuan Xu, Office:
Deady 101, Telephone: 346-5619,
MF 11:00-11:50, W 1:00-1:50 or by appointmen.
Cheney/Kincaid: Numerical Mathematics and Computing, 6ed or 7ed.
This is the second half of a two term sequece. Here is the link to the course webpage of the first part,
M351. I will basically follow the text book. I plan
to cover most of the Chapters 2, 8 (sections 8.1 and 8.2), 6, 9, 7 in 7ed of the textbook
(or the Chapters 2, 8 (sections 8.1 and 8.2), 9, 12, 11 in 6ed of the textbook). Topics include:
solving systems of linear equations, spline functions (Compute Aided Design), smoothing of data
and least square method, solving ordinary differential equations.
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.
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.
For in-class computer demonstrations we will use Mathematica , a
powerful computer program for symbolic and numerical mathematical
computations. You may also want to use it for your homework and project.
Mathematica is installed in most of the computer labs on campus.
This year students are able to download Mathematica software on their personal computers
due to an addition of the student option to UO site license. Here is what you
need to do: go to the IT Website
select Mathematica from the software list; Login with their uoregon username and
password to view available downloads; and select "Student Mathematica Activation File".
This will direct students to the Wolfram Student Portal for the University of Oregon
(To get immediate access to Mathematica activation file, you need to login to this
portal from your uoregon.edu email address).
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.
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.
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.
There will be one midterm exam in class on Wednesday, Feburary 12. 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 Thursday, March 19 at 14:45 in 208 Deary.
Option 1: If you choose NOT to do a project, your grade will be based on your homework, midterm and final, distributed as
|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 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!
The University of Oregon is working to create inclusive learning environments.
Please notify me if there are aspects of the instruction or design of this
course that result in disability-related barriers to your participation. You
are also encouraged to contact the Accessible Education Center in 360 Oregon
Hall at 541-346-1155 or firstname.lastname@example.org.
The University Student Conduct Code (available at
http://dos.uoregon.edu/conduct) defines academic misconduct. Students are
prohibited from committing or attempting to commit any act that constitutes
academic misconduct. By way of example, students should not give or receive
(or attempt to give or receive) unauthorized help on assignments or
without express permission from the instructor. Students should properly
acknowledge and document all sources of information (e.g. quotations,
paraphrases, ideas) and use only the sources and resources authorized by
the instructor. If there is any question about whether an act constitutes
academic misconduct, it is the students' obligation to clarify the question
with the instructor before committing or attempting to commit the act.
Department of Mathematics
University of Oregon, Eugene OR 97403-1222.
Email: < email@example.com