22M:140
Continuous Mathematical Models
Spring 2006

This course will cover continuous mathematical models of materials that flow or deform, as well as with spatial models of chemical and biological processes. The emphasis will be on continuum models, and how to represent properties like conservation of mass and energy. The course will aim to show how to model the behavior of solids and fluids. We will be deriving the equations describing these kinds of systems, and their characteristics, rather than giving analytical or numerical solutions to them.

The philosophy of the course is to show applications of mathematics to realistic problems.

Contact/class information

Instructor:	Dr. David Stewart
Phone:	335-3832
Email:	dstewart(at)math(dot)uiowa(dot)edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office hours:	TBD
Class times:	10:30-11:20am MWF
Class location:	219 JH

You can see me outside the office hours provided it is mutually convenient.

This course will use ICON; go to http://icon.uiowa.edu/ and log in with your HawkID and password.

Textbook

The main textbook will be Mathematical Modeling in Continuum Mechanics by R. Temam and A. Miranville (Cambridge University Press, paperback 2005).

Suitable additional references include:

• Continuum Mechanics and Applied Continuum Mechanics by T.J. Chung (oriented more towards engineers),
• Continuum Mechanics by A. J. M. Spencer (Dover reprint, very inexpensive),
• An Introduction to Continuum Mechanics by M.E. Gurtin (more for mathematicians), and
• A First Course in Rational Continuum Mechanics by C. Truesdell (very advanced).

The last two are advanced in terms of mathematical rigor.

Syllabus

• Rigid motions
• Vectors, matrices and tensors
• Deformations and flows
• Conservation of mass and ``going with the flow''
• Convection and diffusion processes
• Reaction and population models with spatial variation
• Stress and strain
• Hydrostatic pressure and ideal fluids
• Linear elasticity and Newtonian (viscous) fluids
• Electromagnetism (Maxwell's equations) (optional)

Preparation

You will need to review multivariate calculus and linear algebra. However, you will not need any background in mechanics; that will be taught as needed.

Assessment

There will be one exam (30%), homework (40%), and a project (30%).

Additional Notes

1. The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes. You should also make a habit of reviewing the class web page, which is accessible via: 
   http://www.math.uiowa.edu/~dstewart/classes/ 
   This page will have homework details and other information posted to it as the class progresses.
2. The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.
3. Please let you instructor know if you have a disability that requires special arrangements. I need to hear from anyone who has a disability which may require some modification of seating, testing or other class requirements so that appropriate arrangements can be made. Please see me after class or during my office hours.
4. Be sure to read the section titled Student Complaints Concerning Faculty Actions in the Schedule of Classes.
5. This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences. Details of the University policy of cross enrollments may be found at:

   http://www.uiowa.edu/~provost/deos/crossenroll.doc .

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