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Using Macros and Functions To Enhance Teaching Numerical Methods To Engineering Students

Abstract Using mathematical models to predict the behavior of physical systems is an important part of engineering analysis and the techniques of numerical methods are important tools that are used to facilitate the mathematical modeling process. This paper describes techniques developed and used in a numerical methods classroom for engineers titled “Computational Modeling”. The course teaches the foundations of development and usage of numerical methods such as Euler’s method, the Newton-Raphson method, and elimination methods. The techniques used in the classroom are those of developing Microsoft Excel macros and Matlab M-file functions to program the numerical methods and subsequently solve mathematical models of the physical world.

There are two important aspects of using these techniques in the Numerical Methods classroom. First, numerical methods are computationally intensive and structured computer programs provide a most efficient way to solve the mathematical models. Many of the methods are iterative in nature and are facilitated through the use of computer programs. By using the macros and functions it helps to portray to the students the difference between using two or more different numerical techniques and the types and magnitudes of errors that may result. The second main reason for using macros and m-file functions in the numerical methods classroom is that it reinforces the need for engineers to develop well written and structured computer programs that are used as tools in solving engineering-based problems. This paper details the different types of numerical methods that were taught in the class. The paper describes the macros and m-files that were developed as supplemental teaching tools, how they were used in the classroom and how it benefited the instruction of the engineering student.

Introduction Numerical methods are used in approximating derivatives and solving nonlinear equations. Many differential equations cannot be solved analytically, in which case we have to satisfy ourselves with an approximation to the solution. Using mathematical models to predict the behavior of physical system is an important part of engineering analysis. In addition, the techniques of numerical methods are important tools that are used to facilitate the mathematical modeling process. The instructional techniques and algorithms described in this paper were used to compute such an approximation and facilitate teaching numerical techniques to students. Alternative methods are to use techniques from calculus to obtain a series expansion of the solution. The techniques used in the classroom are those of developing Microsoft Excel macros and Matlab M-files functions to program the numerical methods and subsequently solve the mathematical models of the physical world. Using Matlab and Excel facilitate demonstrating the need for repetitive analysis in numerical techniques.

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Lambright, J. (2006, June), Using Macros And Functions To Enhance Teaching Numerical Methods To Engineering Students Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--56