Math 4800: Selected Numerical Algorithms and Their Analysis
Instructor: Yekaterina Epshteyn
Meeting times: M W 1:25 pm - 2:45 pm, JTB 110
Office Hours (tentative (not finalized yet), it may be some changes to the office
hours at the beginning of the semester)
M 3:00pm - 3:30pm, W 3:00pm - 4:00pm, or by appointment
Office: LCB 337
Math 4800 will provide an introduction to the research in the
area of the Numerical Analysis and Scientific Computing through
lectures, students' presentations and projects.
The main goal of the
course that we all learn something new!
Some Projects will be suggested at the beginning of the semester, and will include some theoretical analysis
and/or computational part.
For the computational part, students are encouraged to use MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good
place to begin and is available in
4800 Some Preliminary/Tentative Topics (based on the course progress):
Selected topics in numerical linear algebra: least squares
problems, iterative methods for linear systems (some examples: Krylov subspace
methods, multigrid methods, domain decomposition methods,
etc). Introduction to the numerical methods for partial differential
equations (PDEs) involving interfaces and irregular domains: Difference
Potentials Method (DPM), Immersed Interface Method (IIM) and Ghost
Fluid Method (GFM). Introduction to meshfree approximations methods.
4800 Tentative Plan (can be adjusted based on the course progress):
The course will start by series of lectures. Lectures will
introduce necessary background/basics on the selected numerical
algorithms. Several exercises/questions (theoretical, computational or both) during series of the lectures will be given
and students will write and submit their solutions for some selected
exercises. Students will have one or two weeks to work on these
selected questions before submitting their solutions. It will help to
understand the covered material better and it will help with a work on
a bigger project later on in the course.
I will give back my
comments, suggestions on the submitted solutions to these selected
questions but I will not assign/give a grade for these exercises.
Further into the course, students will be asked to present
some selected topics (give a few lectures on the favorite topics related
to the course's theme) or to discuss their progress on the project.
Prior to meetings, students are encouraged to read the suggested material, and to be prepared to discuss it during meetings.
Students will be offered a list of the original projects and a list of some selected
topics. Students will choose either to work
on one project during semester or to present few lectures on the
selected/favorite numerical algorithms.
Work on the project in a team of two or three students is also
Students would need to write the final report and give short presentation at the end of semester on their progress in the course.
Course Materials (including initial ideas about possible projects
- will be discussed in greater details later on in the course)
Course Materials: Materials
Some References on Numerical Methods (but the course will be mainly based on lecture notes, research papers and projects)
Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM, 2007
Trefethen and Bau, Numerical Linear Algebra, SIAM, 1997
The Americans with Disabilities Act requires that reasonable accommodations be
provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities.
Please contact me at the beginning of the semester to discuss any such accommodations for the course.
Evaluation and Course Work: Course participation 65%, topics
presentations and/or project 35%