CS296.4 Fall 2002

Mathematical Modeling of Continuous Systems

In preparation for courses in artificial intelligence, robotics, and computer vision, this course is a tour through fundamental mathematical techniques used to model continuous objects and events, both deterministic and random, in the physical world. After a fast-paced refresher on the geometric meaning of singular values, the pseudo-inverse, and eigenvalues, the course covers geometric transformations (rotations, similarities, affine and projective transformations), elements of numerical unconstrained optimization, stochastic processes and random fields, deterministic and probabilistic dynamic systems, stochastic filtering and state estimation. Time permitting, the course will also cover elements of tensor fields, variational principles, and flow problems in two dimensions.

Coverage of this rather wide array of topics is made possible by emphasizing the geometric, physical, and intuitive meaning of the various concepts over the details of formal proofs, and by understanding the input/output relationships of classical algorithms viewed as black boxes, rather than by attempting to describe the details of how they work. The class requires some prior exposure to linear algebra, introductory calculus, and elementary probability, but is otherwise self-contained.

Schedule and Venue

Tuesdays and Thursdays 9:10÷10:25 AM in the Levine Science Research Center (LSRC), room D243.

Announcements

10/29/2002
Note the new midterm sample exam under Useful Information below .Solutions to homework and exam samples are handed out in class, not posted on this page.
10/10/2002
The closed-book midterm exam will be in class during regular lecture hours on Thursday, November 7, 2002.
8/16/2002
 Please read the course mechanics carefully.
8/16/2002
 Watch this space for date, time, and venue for the midterm exam.

Mailing List

Feel free to use the mailing list compsci296-04@duke.edu  for discussion. However, please send us mail directly, call us, or visit us if you want to tell us something. Contact information is enclosed below.

Lecture Notes

Notes from an earlier version of the class can be viewed or downloaded in Postscript or PDF format. These earlier notes are provided for your information only. In order to fit Duke's semester structure and mesh with other existing courses, the new version of the course will be compressed in its linear algebra aspects, and expanded with more advanced topics, as summarized above. Relevant notes, both from the old version and original ones, will be handed out in class as necessary, and will be made available through links in this space. Please see the introduction in the old notes for some information about useful books.

Handouts

  1. Algebraic Linear Systems (Postscript, PDF)
  2. The Singular Value Decomposition (Postscript, PDF)
  3. Function Optimization (Postscript, PDF)
  4. Eigenvalues and Eigenvectors (Postscript, PDF)
  5. Ordinary Differential Linear Systems (Postscript, PDF)
  6. Stochastic State Estimation (Postscript, PDF)

Useful Information

  1. Course mechanics. 
  2. A Matlab primer (Postscript, PDF).
  3. Sample Midterm  (Postscript, PDF)

Homework

Teaching Staff

Carlo Tomasi <tomasi@cs.duke.edu>

Last modified: Monday, November 11, 2002 07:09 PM