Classroom:    Computational Science and Engineering Building (CSEB), B17

Course Web Page:    http://www.ams.jhu.edu/~eyink/Advance-Param

Text:   The notes of the lecturer and cited journal articles will constitute the primary source for the course.

Overview:   This course is a continuation of 560.700, ``Applications of Science-Based Coupling of Models.''
See the link on the main page. Although not strictly a prerequisite, 560.700 shared the main subject and goals
of the present course. The basic topic is the coupling of multi-scale/multi-physics models in the context of
a broad range of science and engineering applications, emphasizing calculable approximation schemes.
The course is fundamentally interdisciplinary. Two of its key objectives are to help students to develop an
appreciation for the many disciplines in which science-based coupling of models is important and also to help
students communicate with researchers in other areas, in order to share and cross-fertilize ideas and methods.

The principal difference of this course from 560.700 is methodological. 560.700 was an introductory survey
that presented a series of sample applications, drawn from diverse fields, discussing the problems, methods,
and prospects in those several areass. The lectures of 560.700 will provide most of the concrete examples
considered in this course. In our discussions, however, the emphasis will be on unity as well as diversity.
An attempt will be made to identify common mathematical structures and methods that cut across the several
fields of research. A deeper understanding of the shared mathematics and tools should permit more effective
communication between researchers and better ability to adapt and exploit new approaches.

Topics Covered:

I.    Dynamics.

II.    Coarse-Grained Dynamics.

III.    Ensembles & Probability.

IV.    Moment Closure.

V.    Statistical Estimation & Uncertainty Quantification.

VI.    Hybrid/Multiscale Algorithms.

Grading:

Your final grade in this class will be determined from homework and from participation in scheduled
classroom conference sessions.