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1 – 10 of 870Mathematica is computer software from Wolfram Research, Inc. Mathematica provides an environment for manipulating mathematical ideas symbolically. For example, you can ask …
Abstract
Mathematica is computer software from Wolfram Research, Inc. Mathematica provides an environment for manipulating mathematical ideas symbolically. For example, you can ask Mathematica to factor[X2−Y2]and Mathematica will return: (X−Y)(X+Y). You can as easily deal with the equation for a line in algebra as take the derivative of a function in calculus, or solve an elaborate mathematical model in engineering or economics. Mathematica, then, allows you to use the language of mathematics with about the same terms as in a textbook and about the same ease as doing arithmetic on a calculator.
Cheddi Kiravu, Kamen M. Yanev, Moses O. Tunde, Anna M. Jeffrey, Dirk Schoenian and Ansel Renner
Integrating laboratory work into interactive engineering eLearning contents augments theory with practice while simultaneously ameliorating the apparent theory-practice gap in…
Abstract
Purpose
Integrating laboratory work into interactive engineering eLearning contents augments theory with practice while simultaneously ameliorating the apparent theory-practice gap in traditional eLearning. The purpose of this paper is to assess and recommend media that currently fulfil this desirable dual pedagogical goal.
Design/methodology/approach
The qualitative approach compares the eLearner-content interactivity deriving from Mathematica’s Computable Document File (CDF) application, Pearson’s myLab and Lucas-Nuelle’s UniTrain-I. Illustrative interactive examples written in JavaScript and Java are thereby drawn from an engineering eLearning course developed at the University of Botswana (UB).
Findings
Based on its scientific rigour, wide application scope, engineering analytical depth, minimal programming requirements and cross-subject-cum-faculty application and deployment potential, the authors found the CDF to be a versatile environment for generating dynamically interactive eLearning contents. The UniTrain-I, blending a multimedia information and communication technology (ICT)-based interactive eLearner-content philosophy with practical laboratory experimentation, is recommended for meeting the paper’s dual eLearning goal as the most adept framework to-date, blending dynamic interactive eLearning content with laboratory hands-on engineering experimentation.
Research limitations/implications
The lack of other competing frameworks limited the considerations to only the three mentioned above. Consequently, the results are subject to review as the ongoing research advances new insights.
Originality/value
The conclusions help eLearning designers plan ICT-based resources for integration into practical electrical engineering eLearning pedagogy and both CDF and UniTrain-I help dispel the prevailing apparent disquiet regarding the effectiveness of the eLearning-mediated electrical engineering pedagogy. In addition, the cited examples document an original electrical engineering eLearning course developed at the UB.
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M. Walker, T. Reiss, S. Adali and P.M. Weaver
The optimal design of a laminated cylindrical shell is obtained with the objectives defined as the maximisation of the axial and torsional buckling loads. The ply angle is taken…
Abstract
The optimal design of a laminated cylindrical shell is obtained with the objectives defined as the maximisation of the axial and torsional buckling loads. The ply angle is taken as the design variable. The symbolic computational software package MATHEMATICA is used in the implementation and solution of the problem. This approach simplifies the computational procedure as well as the implementation of the analysis/optimisation routine. Results are given illustrating the dependence of the optimal fiber angle on the cylinder length and radius. It is shown that a general purpose computer algebra system like MATHEMATICA is well suited to solve small boundary value problems such as structural design optimisation involving composite materials.
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M. Bektas, M. Inc and Y. Cherruault
The purpose is to study an analytical solution of non‐linear Korteweg‐de Vries (KdV) equation by using the Adomian decomposition method (ADM).
Abstract
Purpose
The purpose is to study an analytical solution of non‐linear Korteweg‐de Vries (KdV) equation by using the Adomian decomposition method (ADM).
Design/methodology/approach
The solution is calculated in the form of a series with easily computable components. The non‐linear KdV equation has been considered and the analytic solution is compared with its numerical solution by using the ADM and Mathematica software program.
Findings
This approach to the non‐linear evolution equation was found to be valuable as a tool for scientists and applied mathematicians, because it provides immediate and visible symbolic terms of analytical solution as well as its numerical approximate solution to both linear and non‐linear problems without linearization or discretization.
Research limitations/implications
This geometrical interpretation and the produced approximate solution of the non‐linear KdV equation illustrates the use of the ADM. Research using ADM is ongoing but already the numerical results obtained in this paper justify the advantages of this methodology, even in a few terms of approximation.
Practical implications
Using the Mathematica software package the ADM was implemented for homogenous KdV equation as an illustrative example which has distinct applications for scientists and applied mathematicians.
Originality/value
This is an original study of the use of ADM for the solution of the non‐linear KdV equation. It also shows how the Mathematica software package can be used in such studies.
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This paper presents a set of Mathematica modules that organizes numerical integration rules considered useful for finite element work. Seven regions are considered: line segments…
Abstract
This paper presents a set of Mathematica modules that organizes numerical integration rules considered useful for finite element work. Seven regions are considered: line segments, triangles, quadrilaterals, tetrahedral, wedges, pyramids and hexahedra. Information can be returned in floating‐point (numerical) form, or in exact symbolic form. The latter is useful for computer‐algebra aided FEM work that carries along symbolic variables. A few quadrature rules were extracted from sources in the FEM and computational mathematics literature, and placed in symbolic form using Mathematica to generate own code. A larger class of formulas, previously known only numerically, were directly obtained through symbolic computations. Some unpublished non‐product rules for pyramid regions were found and included in the collection. For certain regions: quadrilaterals, wedges and hexahedra, only product rules were included to economize programming. The collection embodies most FEM‐useful formulas of low and moderate order for the seven regions noted above. Some gaps as regard region geometries and omission of non‐product rules are noted in the conclusions. The collection may be used “as is” in support of symbolic FEM work thus avoiding contamination with floating arithmetic that precludes simplification. It can also be used as generator for low‐level floating‐point code modules in Fortran or C. Floating point accuracy can be selected arbitrarily. No similar modular collection applicable to a range of FEM work, whether symbolic or numeric, has been published before.
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Mark Dynarski and Patricia Grosso
This brief article seeks to answer, with examples, some of the more common questions that policy‐makers and practitioners in children's services often ask about randomised…
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This brief article seeks to answer, with examples, some of the more common questions that policy‐makers and practitioners in children's services often ask about randomised controlled trials (RCTs). It is essentially a primer, and those wishing to read further on these issues might find it helpful to start with the books discussed in the review article by Hobbs and colleagues in this special edition (p40).
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The first Principia Mathematica (1686) by Sir Isaac Newton with reference to natural philosophy and his system of the world has largely contributed to the first revolution in…
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The first Principia Mathematica (1686) by Sir Isaac Newton with reference to natural philosophy and his system of the world has largely contributed to the first revolution in scientific thinking in modern times. It has created the conceptual basis of modern science in the classical tradition by providing the tools of analysis and the technique of reasoning in terms of stability—from—within or, as we would say today, the model of stable equilibrium conditions.