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Using Computational Software Root Solvers: A New Paradigm For Problem Solutions?

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Conference

2006 Annual Conference & Exposition

Location

Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006

ISSN

2153-5965

Conference Session

Improving ME education: Broad Topics

Tagged Division

Mechanical Engineering

Page Count

13

Page Numbers

11.1377.1 - 11.1377.13

DOI

10.18260/1-2--1146

Permanent URL

https://peer.asee.org/1146

Download Count

84

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Paper Authors

biography

B.K. Hodge

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B. K. Hodge is Professor of Mechanical Engineering at Mississippi State University (MSU) where he serves as the TVA Professor of Energy Systems and the Environment and is a Giles Distinguished Professor and a Grisham Master Teacher. He is the author of more than 170 conference papers and archival journal articles and served as President of the American Society for Engineering Education (ASEE) Southeastern Section for the 1999-2000 Academic Year. He was the 2004-2005 Chair of the Mechanical Engineering Division of the ASEE at the national level.

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biography

Rogelio Luck Mississippi State University

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Rogelio Luck received the B.S. degree from Texas Tech University in 1984, and the M.S. and Ph.D. degrees from Penn State Univ., University Park, in 1987 and 1989, respectively, all in Mechanical Engineering. In 1989 he joined the faculty at the Mechanical Engineering Dept. at Mississippi State University where he has been an Associate Professor since 1994. His recent research interest is in the area of inverse heat transfer.

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

Using Computational Software Root Solvers: A New Paradigm for Problem Solutions?

Abstract Many of the “procedures” for solving engineering problems are formulations to solve an algebraic equation or a system of algebraic equations—to extract roots. Computational software systems, such as Mathcad, Mathematica, Matlab, and EES, make possible “direct” solutions of root-finding problems in which the solution procedure is transparent to the user. These computational systems permit a unified approach, a “new” paradigm, to be used for the solution to many engineering problems. The unified approach consists of three steps: (1) formulate a well-posed system of algebraic equations, (2) use a computational system root solver to do the “arithmetic,” and (3) verify the results. This paper explores the use of the unified approach for mechanical engineering problems and investigates the pedagogical inferences of the unified approach using computational software systems for undergraduates in Mechanical Engineering. The unified approach permits the student to focus more on the engineering aspects than the “arithmetic” aspects. With less time spent on arithmetic, more time is available for students to engage is higher-level synthesis and understanding.

Introduction

Many of the “procedures” for solving engineering problems are formulations to solve an algebraic equation or a system of algebraic equations—to extract roots. In general, an algebraic equation can be linear or nonlinear and a system of algebraic equations can contain both linear and nonlinear algebraic equations. Recent computational software systems, such as Mathcad, Mathematica, Matlab, and EES, have made possible “direct” solutions of such problems in which the sometimes-laborious task, the procedure, of obtaining the solution is transparent to the user. Such equation or root solvers allow the students to concentrate on the engineering aspects of the problem, sparing them from being preoccupied by the details of finding the roots; i.e., solving the equations. The students can then focus their efforts on the engineering aspects of the problem by applying their engineering knowledge and skills to obtain a system of equations that represents the problem and that is sufficiently descriptive to provide a solution; i.e., to obtain a well-posed system of equations. An additional pedagogical advantage of using the root solvers is that the students are forced to discern whether the numerical (or symbolic) answers provided by the equation solvers are reasonable. Thus, the advent of such computational systems permits a unified approach, a “new” paradigm, to be used for the solution to many engineering problems. For appropriate problems, the unified approach consists of three steps: (1) formulate a well-posed system of non-linear algebraic equations, (2) use a computational system root solver to do the “arithmetic,” and (3) verify the results.

Computational systems provide robust root solvers for systems of algebraic equations. Reference 1, from Desktop Engineering, presents a convenient summary of capabilities of the most commonly used computational systems. The “solve-block” structure in Mathcad, for example,

Hodge, B., & Luck, R. (2006, June), Using Computational Software Root Solvers: A New Paradigm For Problem Solutions? Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--1146

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