June 18, 2006
June 18, 2006
June 21, 2006
11.1377.1 - 11.1377.13
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.
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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