CAM 397 Introduction to Mathematical Modeling
Fall 2008
Faculty Coordinators:
Prof. Graham Carey, Aerospace Engineering and Engineering Mechanics
Office: ACE 6.430, Phone 471-4207
Office: WRW 301D, Phone 471-4069
E-Mail: carey@ices.utexas.edu
Prof. Todd Arbogast, Mathematics
Office: ACE 5.334, Phone: 475-8628
Office: RLM 11.162, Phone: 471-0166
E-Mail: arbogast@ices.utexas.edu
Meeting:
MWF 2:00-3:00 p.m., ETC 2.102. (Some seminar lectures may be held in
the ACES building.)
Course Description:
This course will introduce the student to various fields of science
and engineering at an elementary, ad-vanced undergraduate to first
semester graduate level. Emphasis will be on the concepts and
techniques of modeling natural, engineered, scientific, or social
systems and problems.
Each week, generally on Monday and Wednesday, one or two faculty
experts will lecture on mathemati-cal modeling concepts in the area of
their research. Generally, Friday will be a recitation session.
The course objectives are to:
- Teach the concepts and techniques of mathematical modeling;
- Introduce the students to the broad spectrum of research conducted at ICES;
- Introduce the students to many of the ICES Core faculty and aid them in
finding a Ph.D. advisor and research project;
- Introduce the student to academic research and its technical oral and
written presentation.
Regular Assignments:
A reading assignment will be given approximately each week, due
generally on Friday. The student is required to write and hand in a
summary of the material (approximately one page), be prepared to
discuss it, and possibly to take a quiz on the material.
Semester Project:
The student is required to select and receive approval of a research
topic in modeling. The student will research the literature on the
topic and write a report on the subject. The report will be judged
both on its content and on the quality, clarity, and terseness of its
written presentation. The report should be about ten pages. During
finals week, the findings will be presented orally to the class, and
the presentation will be judged for its content and clarity.
Grades:
Final grades will be assigned based on the weekly written summaries,
quizzes (if any), and the final re-search project and presentation.
Semester Project Reporrts and Presentations:
The semester project reports are due on Saturday, December 13 at
2:00-5:00. Presentations will be made at the same time. Each presenter
will have 12 minutes for their presentation.
Lecture Notes:
Schedule
December 1: Chelikowski. Material science.
November 24: Gamba. Modeling large numbers of particles.
November 17: Demkowicz. Electromagnetics.
Maxwell's Equations
November 10: Hughes. Isogeometric Analysis.
Isogeometric Analysis
November 3: Press. Biostastics.
Statistical Modeling
October 27: Gonzalez. Aspects of DNA modeling.
Part I
Part II
October 20, 22: Rodin. Multiscale mechanics.
Micromechanics
Hashin
October 20, 22: Ghattas. Inverse Modeling.
PDE Optimization
October 6: Oden. Continuum mechanics.
Nonlinear Continuum Mechanics
September 29: Dawson. Hurricane surge modeling.
Shallow Water Equations
September 22: Elber. Biological sequence-structure asymmetry.
Part I
Part II
September 3: Arbogast. Introduction to Aspects of Multiscale Modeling
as Applied to Porous Media
Part I
Part II
Part III
Part IV
Reading Assignments:
November 10: Hughes.
- Reading assignment handed out in class.
October 27: Gonzalez.
September 29: Dawson. (No summary due--homework assignment instead)
- Reading assignment from the book by Vreugdenhil.
September 15: Carey.
- Reading assignment handed out in class.
September 8: Arbogast. Summary page write-up due M 9/15.
- Homogenization and Porous Media, by U. Hornung, Chapter 1, pp. 1-25.
September 3: Arbogast. Summary page write-up due M 9/8.
- Dynamics of Fluids in Porous Media, by J. Bear, pp. 15-26.
- Groundwater, by R. A. Freeze and J. A. Cherry, pp. 15-38 and 69-76.
Exercises:
References: