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

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 in undergraduate mechanical engineering education. The unified approach permits the student to focus more on the engineering aspects of a problem than the “arithmetic” aspects. With less time spent on arithmetic, more time is available for students to engage is higher-level synthesis and understanding.