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Teaching Physics With Computer Algebra Systems

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2009 Annual Conference & Exposition


Austin, Texas

Publication Date

June 14, 2009

Start Date

June 14, 2009

End Date

June 17, 2009



Conference Session

Innovations in Teaching Physics or Engineering Physics

Tagged Division

Engineering Physics & Physics

Page Count


Page Numbers

14.1147.1 - 14.1147.21

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Paper Authors

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Radian Belu Drexel University

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Alexandru Belu Case Western Reserve University

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Teaching Physics with Computer Algebra Systems Abstract

This paper describes some of the merits of using algebra systems in teaching physics courses. Various applications of computer algebra systems to the teaching of physics are given. Physicists started to apply symbolic computation since their appearance and, hence indirectly promoted the development of computer algebra in its contemporary form. It is therefore fitting that physics is once again at the forefront of a new and exciting development: the use of computer algebra in teaching and learning processes. Computer algebra systems provide the ability to manipulate, using a computer, expressions which are symbolic, algebraic and not limited to numerical evaluation. Computer algebra systems can perform many of the mathematical techniques which are part and parcel of a traditional physics course. The successful use of the computer algebra systems does not imply that the mathematical skills are no longer at a premium: such skills are as important as ever. However, computer algebra systems may remove the need for those poorly understood mathematical techniques which are practiced and taught simply because they serve as useful tools. The conceptual and reasoning difficulties that many students have in introductory and advanced physics courses is well-documented by the physics education community about. Those not stemming from students' failure to replace Aristotelean preconceptions with Newtonian ideas often stem from difficulties they have in connecting physical concepts and situations with relevant mathematical formalisms and representations, for example, graphical representations. In this context, a computer algebra system provides a better tool which is both powerful and easy to use. Their appropriate use can therefore be an important aid in the training of better physicists and engineers. In this presentation we will discuss ways in which computer algebra systems like Maple, Mathcad, Macsyma or Mathematica can be used, by instructors and by students, to help students make these connections and to use them once they are made. Benefits that accrue to upper-class students able to make effective use of a computer algebra systems provide a further rationale for introducing student use of these systems into our courses for those who plan to major in physics or other technical fields.

1. Introduction

Physics is guided by simple principles, but for many topics the physics tends to be obscured in the profusion of mathematics. As interactive software for computer algebra, such as Maple, MathCAD, Mathematica or MATLAB can assist educators and students to overcome the obstacle of mathematical difficulties or to improve the lecture presentations via power visualization, animation and graphic facilities of these software packages. The educators and students can take the advantages of the mathematical power of symbolic computation so they can concentrate on applying principles of setting equations, instead of technical details of solving problems. Moreover, most undergraduate physics textbooks were written before advanced computer algebra software became conventionally available. The conventional approach to a topic places emphasis on theory and formalism, devoting many paragraphs to performing algebraic or calculus operations in deriving equations manually, and other than some well known examples, most applications of theory are omitted. One reason that those examples are

Belu, R., & Belu, A. (2009, June), Teaching Physics With Computer Algebra Systems Paper presented at 2009 Annual Conference & Exposition, Austin, Texas.

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