Society for Industrial and Applied Mathematics (COR)

In order to emphasize the relationships and cohesion between analytical and numerical techniques, this book presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.

This monograph offers a systematic quantitative approach to the analysis, evaluation, and design of electoral systems. Today, electoral reform is of concern to newborn democracies as well as many old ones. The authors use mathematical models and automatic procedures, when possible, to solve some of the problems that arise in the comparison of existing systems as well as in the construction of new ones. One distinctive feature of the book is the emphasis on single- and multiple-criteria optimization methods. This powerful tool kit will help political researchers evaluate and choose an appropriate electoral system. A general formal model is included as well as a coding system to describe, identify, and classify electoral systems. Evaluation criteria and the corresponding performance indicators are discussed. A treatment of electoral formulas as algorithms to minimize actual cost functions or disproportionality indexes is also included. Neutral automatic procedures for political districting are presented, and the process of electoral reform is analyzed from historical and political points of view.

One of the main accomplishments of control in the 1980s was the development of H? techniques. This book teaches control system design using H? methods. Students will find this book easy to use because it is conceptually simple. They will find it useful because of the widespread appeal of classical frequency domain methods. Classical control has always been presented as trial and error applied to specific cases; Helton and Merino provide a much more precise approach. This has the tremendous advantage of converting an engineering problem to one that can be put directly into a mathematical optimization package. After completing this course, students will be familiar with how engineering specs are coded as precise mathematical constraints.

American industry is becoming more aware of the importance of applying statistical methods to improve its competitive edge in the world market. Examples of real industrial applications can serve as a major motivator for industries that want to increase their use of statistical methods. This book contains a broad selection of case studies written by professionals in the semiconductor industry that illustrate the use of statistical methods to improve manufacturing processes. These case studies offer engineers, scientists, technicians, and managers numerous examples of best-in-class practices by their peers. Because of the universal nature of statistical applications, the methods described here can be applied to a wide range of industries, including the chemical, biotechnology, automotive, steel, plastics, textile, and food industries. Many industries already benefit from the use of statistical methods, although the semiconductor industry is considered both a leader in and a model for the wide application and effective use of statistics. Specific case studies address the following statistical methods: gauge studies, passive data collection (sources of variation studies), design of experiments, statistical process control, and equipment reliability. Readers familiar with the statistical methodologies that comprise the Six Sigma(R) tool box will find a wealth of applications. Czitrom has written an introduction to each statistical method, which, along with a glossary, gives basic definitions of frequently occurring statistical terms and suggestions for further reading. The case studies, which can be used in industrial training as well as in academia, are an extremely useful classroom supplement and will remain a rich source of used and useful approaches to real industrial problems for years to come.