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Professor: Dr. Nathan Louis Gibson
Office: Kidd 352
Office Hours: TBDCourse Website:
http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH656-001S14 |
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Course Description
Background:
Accurate estimates for the propagation of uncertainty through complex systems is necessary for predictive simulation, robust design, and failure analysis. This course is concerned with the numerical solution of differential equations which include uncertainty, either in system parameters, source terms, or in initial/boundary conditions.Content:
In this course we will develop basic mathematical foundations and algorithmic aspects of stochastic computations and uncertainty quantification theory.
The necessary background in polynomial approximation, numerical integration, and probability theory will be developed.
While the emphasis will be on random differential equations, stochastic differential equations will be discussed.
Methods covered will include Karhunen-Loeve expansion, generalized Polynomial Chaos, Stochastic Collocation, Spectral Stochastic Finite Element Method, Euler-Maruyama method for SDEs, among others.
Topics will include convergence, stability, error estimates and implementation issues.
As time allows, we will discuss challenges arising from high-dimensional problems, inverse problems/robust optimization and data assimilation.Students:
The course will provide a working understanding of several numerical solution
methods and MATLAB sample solutions to examples of applications.
The course is intended for graduate students of mathematics, computer science, biology, science, and engineering. The content of the course is largely self-contained. For general
pre-requisites, students should have some familiarity with probability, linear algebra, ordinary and partial differential equations, and introductory numerical analysis. Please contact the instructor with questions about background. Course requirements will be two
or three homework assignments, which will consist of a mixture of
analytical work and numerical computations with MATLAB, and a term project
on a topic chosen by the student.Text:
There is no required text for the course, but the following are recommended:
| Homework | 50% |
| Final Project | 50% |
| Total | 100% |
Oregon State University has subscribed to a Total Academic Headcount (TAH) Site License for MATLAB. This new licensing includes many, but not all MATLAB toolboxes. OSU faculty, staff and students can install on up to 4 personally-owned devices or computers.
For more information visit Information Services -- MATLAB or matlab.mathworks.com.
The following are online resources for learning Matlab:
A computational project is required for this course. Students must work
individually on a topic/problem of their choice involving random or stochastic problems
(can be from research/thesis work). Students must submit a typed (less
than or equal to two pages) research proposal, including questions to be
answered
midway through the course.
Final papers will be submitted as a typed report including tables or
graphs as figures with captions, and references to them inside the
body of the text, and a bibliography. Students will give brief (10
minute) presentations on results during the last day of classes or the
day reserved for a final exam.
Kalman Filter via Linear Algebra
Sample Beamer Presentation
Matlab
Matlab is required for this course. Matlab is
preferred due to the integration of computation and visualization.
Homework
Homework is required for this course. There will be a few short
assignments, and they will be posted on the website. Problems will
reinforce theoretical and computational concepts from lecture.
Students are encouraged to
work together, but must turn in individual papers.
Final Project
Supplements
Intro to Data Assimilation