MTH 420: Tensors and Differential Forms
Winter 1999

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Tevian Dray
Office hours: by appt in Kidder 306
Phone: 737-5159
Email: tevian@math.orst.edu

Web Site: http://math.oregonstate.edu/~tevian/onid/Courses/MTH420

Lectures:
MWF at 3 in Kidder 280

Course Description:
This course is a self-contained introduction to the many uses of differential forms, which are roughly speaking the things one integrates, i.e. the integrands. This approach emphasizes geometric content in a coordinate independent way; a good analogy is the use of vectors, rather than their components, to describe a given situation. We will spend some time developing the necessary mathematical tools, as well as applying these tools to concrete examples drawn from the physical sciences. Sample applications include:

  • conserved currents
  • Hamiltonian systems
  • Jacobians
  • Lagrangians
  • Laplacians
  • Maxwell's equations
  • PDE's
  • phase space

    Prerequisites:
    The main prerequisite is a certain amount of scientific maturity, rather than background in a particular area. The only specific requirements are a working knowledge of multivariable calculus and linear algebra.

    Grades:
    There will be (roughly) weekly homework, an in-class midterm, and a take-home final.

    Texts: These are both inexpensive paperbacks.

  • Harley Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1963 & 1989.
  • Richard L. Bishop & Samuel I. Goldberg Tensor Analysis on Manifolds, Dover, New York, 1968 & 1980.
    Optional Text: Robert H. Wasserman, Tensors & Manifolds, Oxford University Press, Oxford, 1992.

    WARNING: We will only follow the texts rather loosely.


    tevian@math.orst.edu