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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen
What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen
All HMC Faculty Publications and Research
My first attempt at using computers as an aid to teaching calculus began in 1966 and culminated with the publication in 1971 of Single Variahle Calculus, written jointly with Milton Lees. Everyone used a mainframe and punched cards and few knew how to program. Computer use was limited to supplementary exercises that could be done today with a hand-held programmable calculator. A constructive sequential approach to limits and elementary numerical analysis were emphasized. The absence of programming displeased computer scientists, but it was too avant garde for all but a tiny minority of teachers of calculus. Attempts by others …
A Maple Package For The Variational Calculus, Cinnamon Hillyard
A Maple Package For The Variational Calculus, Cinnamon Hillyard
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
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 …