Lecture notes

  • Lecture 1: Differential forms (.dvi) (.ps ) (.pdf)
  • Lecture 2: Euclidean spaces, affine spaces, and homogenous spaces in general (.dvi) (.ps ) (.pdf)
  • Lecture 3: Curves in Euclidean and affine spaces (.dvi) (.ps ) (.pdf)
  • Lecture 4: Surfaces in Euclidean and affine spaces (.dvi) (.ps ) (.pdf)
  • Lecture 5: Surfaces in projective space (.dvi) (.ps ) (.pdf)
  • Lecture 6: Pseudospherical surfaces and Backlund's Theorem (.dvi) (.ps ) (.pdf)
  • Lecture 7: Minimality and variational calculations (.dvi) (.ps ) (.pdf)
  • Lecture 8: Weierstrass formulae (.dvi) (.ps ) (.pdf)
  • Lecture 9: Moving frames in the nonhomogenous case: frame bundles (.dvi) (.ps ) (.pdf)

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    Videotapes of the lectures are at http://www.msri.org; click on "Video," then on "Spring 1999," then on "Lie groups and the method of the moving frame / Exterior Differential Systems, July 12-23, 1999. "  You will need RealPlayer to watch the videos.

    Forms package for Maple

    This is a Maple package for doing computations involving differential forms.  It was written by Yunliang Yu of Duke University and maintained by him through Maple V, Release 4.  I made some minor modifications to make it compatible with Maple V, Release 5.  Both versions are posted here with his permission.
     
  • Forms package for Maple V, release 4
  • Forms package for Maple V, release 5

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    In order to install the package, start up Maple and type

    "read(`forms5`);"

    (This assumes that you downloaded the version for release 5.)  Maple will create some files in your home directory and exit.  Then you need to make sure that Maple knows to look in your home directory for packages; on most systems this is accomplished by creating a file called "MapleInit" (".mapleinit" on Unix systems) which contains the single line

    libname:= libname, "directoryname"

    where "directoryname" is the name of the directory where the Forms package lives.  The MapleInit file should live in the same directory as the Maple program (or your home directory on Unix systems).  Once this is all set up, you can use the package by starting Maple and typing

    "with(Forms);"

    The files above include descriptions of each of the commands; in theory these should work as online help, but in practice they don't seem to.