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Session 2520

Using Spreadsheets to Teach Engineering Problem Solving: Differential and Integral Equations

James P. Blanchard University of Wisconsin - Madison

ABSTRACT

Spreadsheets offer significant advantages for teaching numerical problem solving because of their intuitive interface. Students have little difficulty implementing algorithms in spreadsheets, allowing them to study the behavior of algorithms without having to spend significant amounts of time writing routines that implement them. This has been found to be particularly true for the solution of differential and integral equations, where Runge-Kutta and finite difference algorithms are often used. This paper describes the use of a particular spreadsheet application (Microsoft Excel 5.0) to solve a variety of equations in an undergraduate problem solving course. The advantages and disadvantages of this approach are discussed.

Introduction

Numerical solutions to engineering problems have historically been carried out using procedural programming languages. This is not efficient from a pedagogical perspective because students typically must put more effort into learning the language itself than they put into solving problems. For example, the numerical solution of a boundary value problem in one dimension using finite difference techniques generally involves the creation of a system of linear equations and the conversion of that system into an equivalent matrix equation that then can be solved. Many students find this process confusing, so, for instance, a simple change such as modifying the boundary conditions often takes substantial effort to incorporate into a working solution. The difficulty here is that students become bogged down in forcing the algorithm to fit a structure required by the procedural language, rather than implementing the change in a more natural way. Modern computational tools can alleviate this difficulty, easing the programming effort required and allowing students to spend more time focusing on the performance of the algorithms and on the behavior of the resulting solutions. Students are able to implement algorithms in a more convenient format, removing some of the steps typically required in reaching a solution and thus allowing more effort to be spent comparing various algorithms and studying the behaviors of the equations themselves.

One example of a tool with which equations are easily solved is the spreadsheet, which is particularly well-suited to the numerical solution of both differential and integral equations. In this paper, Microsoft Excel 5.0 is used to solve a series of problems, including 1-D initial value problems (Runge-Kutta methods), 1-D boundary value

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Blanchard, J. P. (1997, June), Using Spreadsheets To Teach Engineering Problem Solving: Differential And Integral Equations Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6885