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Full-Text Articles in Physical Sciences and Mathematics
Validation Study: A Case Study Of Calculus 1 (Math 1210), Abibat Adebisi Lasisi
Validation Study: A Case Study Of Calculus 1 (Math 1210), Abibat Adebisi Lasisi
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
This report discusses the process of assessing the validity of a test. We provide an analysis of the validation study of a test administered to the first semester calculus students at Utah State University in the Fall 2011 semester. The results of our analysis suggest that the test has some measurement relevance. This implies that the subject contents of the test correlate with the syllabus of the course. Thus, the measurement has some learning level relevance. Our analysis also revealed that the measurement has a high reliability coefficient which signifies some internal consistency of the mea- surement. The relevancy and …
The Inverse Problem Of The Calculus Of Variations For Scala Fourth Order Ordinary Differential Equations, Mark E. Fels
The Inverse Problem Of The Calculus Of Variations For Scala Fourth Order Ordinary Differential Equations, Mark E. Fels
Mark Eric Fels
A simple invariant characterization of the scalar fourth-order ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier are expressed in terms of the vanishing of two relative invariants which can be associated with any fourth-order equation through the application of Cartan's equivalence method. The solution to the inverse problem for fourth-order scalar equations provides the solution to an equivalence problem for second-order Lagrangians, as well as the precise relationship between the symmetry algebra of a variational equation and the divergence symmetry algebra of the associated Lagrangian.
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 …
Decision Problems, Lowell Anderson
Decision Problems, Lowell Anderson
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
From an intuitive point of view the notion of effective procedure consists of a set of rules or instructions that enables one, in a finite number of steps and in a purely mechanical way, to answer yes or no to any one of a given class of questions. This procedure requires no intelligence to carry out the instructions and, in fact, it is conceivable that some mechanical contrivance may be constructed to carry out these instructions. Should such an effective procedure exist, that answers either yes or no, then the group of problems in question is said to be effectively …