chapter 3 - Bentham Science

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PREFACE
This e-book is devoted to the use of spreadsheets in the service of education in a broad spectrum
of disciplines: science, mathematics, engineering, business, and general education. The effort is
aimed at collecting the works of prominent researchers and educators that make use of spreadsheets
as a means to communicate concepts with high educational value.
Spreadsheets have been around since the late 70s. They were initially conceived as office
productivity tools, most notably in accounting applications. Over time, spreadsheets evolved to incorporate
a wealth of functions to appeal to the scientific community. Applications of spreadsheets
in different branches of science and engineering are continually being reported in many scholarly
journals.
In recent years, a shift in learning paradigms towards a more constructivist education has incited
researchers and educators to find new approaches to education in science, mathematics, and
engineering. This trend is not confined to the USA only, but it seems that it is more widespread
around the globe. It is in this context, that applications of spreadsheets in education, from primary
to university levels, are gaining marked prominence, as evidenced by the number of journal
publications and presentations at technical conferences.
This e-book brings some of the most recent applications of spreadsheets in education and research
to the fore. We assume that the reader is already familiar with the basics of electronic
spreadsheets. To offer the reader a broad overview of the diversity of applications, carefully chosen
examples from different areas have been included. Applications have been organized in four parts,
each containing three chapters:
• Part I: Engineering
Chapter 1 presents fault analysis in power systems, a common topic in power system courses.
Symmetrical and unsymmetrical short circuit currents are computed using a spreadsheet. The
determination of these currents provides valuable information for selecting the appropriate
protection equipment in a power system.
Chapter 2 shows how to implement spreadsheets for structural analysis. The topic is relevant
to many branches of engineering, namely, civil, mechanical, aerospace, and structural
engineering. Spreadsheet models for analyzing beams, walls, frames, and multi-degree-offreedom
systems are presented.
Chapter 3 discusses optimal control of dynamical systems. The minimum principle of Pontryagin
and the numerical solution of differential equations are illustrated with spreadsheets.
In addition, an interesting example motivated by research (control of a flexible structure via
command shaping) is presented in this chapter.