Date of Award:
5-1992
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Department name when degree awarded
Mathematics
Committee Chair(s)
Ian M. Anderson
Committee
Ian M. Anderson
Committee
Renate Schaaf
Committee
Charles Torre
Abstract
The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete listing of the Maple code for HELMHOLTZ is found in an appendix.
Checksum
d40b081f932a113c4497ee7376b0aa3c
Recommended Citation
Hillyard, Cinnamon, "A Maple Package for the Variational Calculus" (1992). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7124.
https://digitalcommons.usu.edu/etd/7124
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