Math 512 Contemporary Applications of Mathematics

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Contents:

• Course contact information.
• Course description.
• Good things to have.
  
• Tentative project list.
• Current milestones.
  
• Related links.

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Contact information.

Instructor:	Prof. J. A. Pelesko	Prof. L. F. Rossi
Email:	pelesko@math.udel.edu	rossi@math.udel.edu
Phone:	(302) 831-1467 (UDel x1467)	(302) 831-1880 (UDel x1880)

Meetings: MWF 2:30-3:20

Snail mail:

Department of Mathematical Sciences
University of Delaware
Newark, DE 19711
USA

Course description.

This course focuses on modeling and the application of mathematical methods to open problems.  The course will be problem- and data-driven, and students will be expected to attack open problems from a variety of areas including engineering, physics, biology and economics.   

It will also focus on critical analysis of the quality of a model, and effective verbal and written exposition of solutions.  Most of the course content will be a single project that you will explore with two or three of your fellow classmates.

Students will have a variety of resources available to them.  Essentially, you can use anything you need to get the job done.  One unique aspect of this course is the MEC lab, a laboratory for doing small, careful mathematical experiments.  Thus, mathematical analysis, computations and experimentation are all in play with this course.

Good things to have.

• Download a free Acrobat reader so that you can read PDF files.
• Download a free syllabus if you lost the one we gave you in class.
  

Tentative project list.

Successful students in Math512 will build connections between problems, mathematics, computations and experiments.  For instance, consider these two images.

The image at left is an optimized air bearing used in robotics, hard drives and other microcontrolled machinery.  (Think of a air hockey puck.)  The white parts are grooves cut into the smooth surface.  A computer program optimized the grooves to yield the greatest possible lift.  Why are grooves so important?  At right is an image of a starfish leg skeleton.  Does it look the same to you?  It ought to!  It too was optimized by thousands of generations of evolutionary pressure to supply nutrients and remove waste from the starfish's limbs.  Question: Why is the branching structure optimal?  What are its properties?  How does the quality being optimized affect the branched structure?

Your project may be one of the following:

• How do vortices shed from flexible structures such as leaves or bridges?
• How is flow around a building with a rectangular footprint different from flow around a building with a circular footprint?
• What are the features of an effective optimization routine for a communications network?  What if there are barriers or other constraints?
• How can we model complex chemical reactions involving dozens or hundreds of steps?
• Is it easier to walk with a square mug or a round mug of coffee with spilling it?
• How do certain optimization processes lead to branched structures in blood vessels, lungs, roots, shrubs and airbearings?
  

Prerequisite: A 300 level course in differential equations.

Extras:  Though this course only has one prerequisite, we will draw on material from many diverse areas.  If you have had a course on linear algebra or finite math, you may enjoy the class all the more.  If you know a programming language, even Matlab, you may find it useful for solving certain problems.  Like many things in life, you bring to bear whatever you have to make the most of a given situation

If you are interested in solving open problems that are accessible to undergraduates, take a peek at last year's Mathematical  Contest in Modeling problems.

You can download a course syllabus in PDF (requires a free reader from Adobe) or HTML.

Back to the top.

Current milestones.

• Altea project milestone #5 [download].
• Altea project milestone #4 [download].
• Airbearing project milestone #5 [download].
  
• Airbearing project milestone #4 [download].
• Airbearing project milestone #3 [download].
• Brigg-Raucher project milestone #4 [download]

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Links.

• The MEClab home page.
  
• The Consortium on Mathematics and its Applications (COMAP) home page.
• Prof. Pelesko's home page.
  
• Prof. Rossi's home page.
• The Department of Mathematical Sciences home page.
• A virtual encyclopedia of mathematics: Eric Weisstein's World of Mathematics.

Last modified: 7 Dec 2003.