Elementary Numerical Analysis I
Math 351, CRN 13783
Fall, 2019
Lecture: MWF, 14:00-14:50, 307 Deady
Instructor: Yuan Xu, Office:
Deady 101, Telephone: 346-5619,
e-mail:
yuan@uoregon.edu .
Office Hours: MF 11:00-11:50, W 1:00-1:50 or by appointment.
Textbook
Cheney/Kincaid: Numerical Mathematics and Computing, 6ed or 7ed.
Course description
Numerical analysis studies methods and algorithms for mathematical
computation. This course is the first half of a two term sequence.
We will cover most of the Chapters 1-6 of the textbook. Topics include:
approximations by Taylor series, representation of numbers in different
bases, loss of significance, methods for locating roots of equations,
polynomial interpolation, and numerical integration.
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.
Leaning outcomes
Students should be able to make computations in a finite precision arithmetic,
identify machine numbers corresponding to exact calculations, find relative errors
of machine computations, and identify situations when large machine errors can occur.
They should be able to compute loss of significant digits for machine arithmetic
operations, foresee situations when computations can not be done accurately, and
propose methods of avoiding loss of significance. Students should be able to perform
methods for locating roots of equations such as: bisection method, Newton's method,
and secant's method, analyze convergence of these methods, estimate errors of
approximations, and show limitations of each method. They should be able to compute
interpolating polynomials by Lagrange interpolation and divided differences,
demonstrate fundamental properties of interpolating polynomials, and estimate errors
in polynomial interpolation. They need to derive formulas for approximating first and
higher order derivatives of functions, estimate corresponding errors, and compute
derivatives using Richardson extrapolation method. Students should be able to compute
approximations of integrals using methods such as: Riemann sums, midpoint rule,
trapezoid rule, Simpsons' rule, Romberg's method, estimate corresponding errors, and
analyze the number of steps needed to get results with desired accuracy.
Mathematica
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
https://it.uoregon.edu/software/list;
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.
Here are a few Mathematica notebooks related to the course that you can use.
More will be posted later in the term.
Homework
There will be a homework assignment for each week. You can check
ASSIGNMENTS here. Homework will be collected each Wedensday 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
Part of your grade will be based on a programming or research project due
on the last day of 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 Monday, November 4. If you must
miss this exam due to extraordinary circumstances, you must ask for my
permission and schedule a make-up exam in advance. The final exam is scheduled
on 14:45 Wednesday, December 11 in 307 Deady.
Grade
Your course grade will be based on your homework, project, midterm and final.
| 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.
Academic Misconduct
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 examinations
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.