Fault analysis is an important consideration in power system planning, protection equipment selection, and overall system reliability assessment. At the heart of today’s power generation and distribution are high-voltage transmission and distribution networks. When a fault (e.g., a short circuit) occurs at some point in the network, the normal operating conditions of the system are upset; if the fault is per-sistent severe loss of load, property damage due to fire or explosion, and steep eco-nomic losses can arise as undesirable consequences. Therefore, the correct modeling of components and the correct fault analysis in power systems are critical to ensur-ing safety and reliability. In this chapter fault analysis is illustrated via spreadsheets. Spreadsheets are widely accessible and the ease of programming is the hallmark feature that renders them appealing to many users. This simple tool is employed to analyze both symmetrical and unsymmetrical faults in powersystems. The determi-nation of fault currents aids the power engineer in the selection and coordination of protective equipment to ensure the safe and reliable operation of the system.

Structural engineering is a branch of engineering that is concerned with the analysis and design of elements such as beams, frames, trusses, and other me-chanical structures whose principal function is to providethe necessary supporting feature to withstand the mechanical loads, or related operating conditions, normally associated with structures such as buildings, bridges, cranes, airplanes, and so on.

This chapter concentrates on the analysis of beams, wall frames, and buildings. More specifically, the analyses of these structures are illustrated via Microsoft Ex-cel spreadsheets. Spreadsheets may be used to develop quitesophisticated applica-tions that can automate the intensive calculations commonly encountered in struc-tural analysis.

Optimal control techniques have numerous applications in engineering, economics, finance, biology, medicine, and many other fields. In spite of the util-ity of these techniques, the presentation of the topic of optimal control is normally reserved for graduate studies within specialties (e.g., systems engineering). In this chapter we present some illustrative examples in optimal control whose numerical solutions are obtained using the built-in solver capabilities of spreadsheets. Our hope is that the important and interesting topic of optimal control can be introduced to undergraduate students in a less intimidating manner when spreadsheets are used

Modular arithmetic has often been regarded as something of amathemat-ical curiosity, at least by those unfamiliar with its importance to both abstract algebra and number theory, and with its numerous applications. However, with the ubiquity of fast digital computers, and the need for reliable digitalsecurity systems such as RSA, this important branch of mathematics is now consideredessential knowledge for many professionals. Indeed, computer arithmetic itself is, ipso facto, modular. This chapter describes how the modern graphical spreadsheet may be used to clearly illustrate the basics of modular arithmetic, and to solve certain classes of problems. Students may then gain structural insight and the foundations laid for applications to such areas as hashing, random number generation, and public-key cryptography.

The learning of mathematical concepts can be aided by the useof tech-nology and graphical visualization. The use of modern toolscan greatly enhance the learning experience by encouraging inquiry and deepening one’s understanding. In this chapter triangular, square, and polygonal-like numbers are explored in context using spreadsheets. The context provides the element of relevance that learners need in order to appreciate concepts that might otherwise seem abstract in nature.

Through an interactive Excel spreadsheet and accompanying activity, first-year college students explore enzyme kinetics, experimental error, and the be-havior of inhibitors. Many “what if” questions drive students to discover how a variety of parameters influence results.

This chapter seeks to illustrate how simple spreadsheets can be used cre-atively with amazing outcomes. This will be demonstrated through a project man-agement game, built entirely using standard spreadsheet features and functions. The project management game is designed as a teaching tool to allow players to experi-ence project management in an interactive and fun atmosphere. In the game, players learn to respond to unforeseen events, make appropriate decisions to resolve issues, keep the project team motivated, and take corrective measures to keep the project on track and on target. This chapter is aimed at providing an overview of the game, dis-cussing how it should be played, and explaining the underlying principles behind the rules of the game. It is not meant to be technical, although some amount of logical relationship between variables and mathematical functions will be discussed.

Mean-variance portfoliotheory being part of the core curriculum of mod-ern finance in business education, this chapter presents an asset pricing model based on it in an equilibrium setting. Here, equilibrium pertains to matching of supply and demand of individual assets in an investment market for rational portfolio decisions. An example utilizing various Microsoft Excel features in matrix operations is pro-vided to illustrate the computational task involved. This chapter is intended to make the model less abstract, thus complementing the textbook materials on the model. With computational issues no longer a concern, students can focus their attention on the concepts involved.

Managers have long been concerned about new product development and the life cycle of these products. Because many products do not sell at constant levels throughout their lives, product life cycles must be considered when developing sales forecasts. Innovation diffusion models have successfully been employed to investigate the rate at which goods and/or services pass through the product life cycle. This research investigates innovation diffusion models and their relation to the product life cycle. The model is developed and then tested using modem sales from 1994–2009. Each successive generation of modem innovation, from 14.4k, 28.8k, 56k, broadband less than 3.6Mbps, to broadband greater than 3.6Mbps, is examined.

The use of computers is pervasive in education at both the secondary and university levels. Learner-oriented computer programs have the potential to motivate students to learn mathematics. One such computer program is Microsoft Excel, which for many years has been embraced by educators as the ideal platform for providing students with hands-on activities that enhance their learning. By design, Excel (or spreadsheets in general) lends itself to transparent problem formulation and minimal programming requirements.

In this chapter I will present several spreadsheet applications that I have devel-oped over the years. The applications are aimed at introducing concepts in the teach-ing of mathematics at the secondary level and introductory calculus as well.

Auniversity education in actuarial studies and related areas prepares graduates for a wide range of careers. This study demonstrates that recent gradu-ates working in the financial services industry make significant use of spreadsheet software. We found that all 76 respondents use spreadsheet software, and more than half spend at least 60% of their time using spreadsheets. Graduates also use a range of statistical, database, mathematical, financial, and actuarial software. This signifi-cant time spent in front of the computer has implications for universities wishing to design curriculum to prepare students for careers in the financial services industry.

Thischapter presents a case study illustrating the physical dispatch al-gorithm used by Australia’s electricity market operator (AEMO) to determine which power plants to dispatch into the grid and the resultant electricity spot price. The models are similar to case studies applied by the author in professional development for training a disparate audience about the nature of the deregulated Australian Na-tional Electricity Market (NEM). This chapter addresses the particular experiences of the author in delivering professional development education to an area of industry focusing in energy and finance. It has been found that the commonality amongst a diverse range of workshop participants is their understanding of Excel, and it forms an ideal mechanism to communicate technical and mathematical concepts. Although highly simplified, the implementation exhibits the key concepts of price-setting and dispatch instructions in the Australian electricity market (NEM).