Math 4800: Selected Numerical Algorithms and Their Analysis

Instructor: Yekaterina Epshteyn

Meeting times: M W 4:35 pm - 5:55 pm, GC 3015

Office Hours

TBA
Office: LCB 337
E-mail: [email protected]

The course

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!

Projects

Some Projects will be suggested during 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 Adobe PDF format.

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 selected numerical methods for partial differential equations (PDEs) (e.g., numerical methods for conservation and balance laws, numerical methods for convection-diffusion problems, introduction to meshfree approximations methods). Applications will include (but are not limited) to chemotaxis models in Biology, shallow water models in Fluid dynamics and grain growth models in Materials Science.

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 strongly encouraged.

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)

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

ADA Statement

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.