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Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto

contact


William Faris
University of Arizona
Reference #
OMN:202209.111340

Attributes

Posted date
2022-10-10 07:16:57
Revised date
2023-07-12 18:25:19
Level
   Undergraduate
   Graduate
Notes type
   Standard Course Offering
   Topics Course
   Research Monographs
Topic
   Geometry
      Differential Geometry

Vector Fields and Differential Forms

Vector fields and differential forms have very different properties. However a given volume element allows vector fields to be converted into twisted differential (n-1)-forms via contraction. Also a metric tensor allows vector fields to be converted into 1-forms. The ultimate theory works with an arbitrary metric tensor in n dimensions. The exposition includes insightful pictures along with extensive computations.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v2 PDF (1.9M) 07/13/23