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Reviewer: Joan Catherine Horvath

This ambitious and well-written book is an excellent comprehensive review of what you need to know to evaluate or build a complex model or simulation of a physical process. Although the authors correctly note that users will need some significant mathematics to appreciate the entire book, a majority of it is more accessible than that. Although long (close to 800 pages) and dense, the book is organized in such a way that different users can easily use relevant parts of it and skim or skip the parts that are less so. As the authors note, the book develops the ideas needed to verify a simulation ("solving equations right") but also to validate it ("solving the right equations"). They do this with a mix of clear explanation, simple diagrams and flowcharts of good processes, a survey of necessary mathematics, and extensive references. The index is good, and allows readers to find concepts easily. This is a book about what can go wrong in a simulation, including what the authors call blind uncertainties: those errors that occur because no one thinks to allow for a particular phenomenon or error. This book admits that those types of errors exist, and discusses pragmatic ways to think about them. It covers many of the art aspects of developing a simulation: defining where your system begins and ends, prioritizing effort and fidelity where the system really needs it, and considering pragmatic human nature issues. Five major sections comprise the book. The first, on fundamental concepts, is a good review of terminology and concepts of verification, validation, and uncertainty. The next two sections move from verification of computer code to verification of the equations being solved. These sections start off with a rather general survey of the field of software engineering, and then move into a rather mathematically intense discussion. Those who are not concerned personally with issues of discretization and analysis of numerical and approximation errors can dip around in those 200 pages and read pieces that apply to their situations. The book is written modularly enough that this will not damage understanding of the big picture concepts later on. The last two sections discuss how to think about validating that a simulation reflects reality. One good discussion reviews how to think about using experimental data to validate software, given that sometimes software needs inputs that may not have been measured in a physical experiment, and what to consider if experimental data just is not practical to obtain. Finally, the book discusses project management issues. The book would be a good textbook for a senior-level engineering or physics undergraduate semester course, particularly a project-based one that develops requirements for a simple prototype numerical model of a system. Pure mathematicians might struggle with the examples that are mostly oriented toward aerospace systems. Students without some exposure to differential equations might panic when they see the solution verification chapters, but an instructor could easily skip that section and replace it with simpler metrics that are appropriate for a student project situation. If the book has a negative aspect, it is that it is somewhat skewed toward aerospace and a bit heavier on the acronyms than perhaps it needs to be. This is unfortunate, because it might scare off, say, biologists and others considering the issues in developing numerical models of their systems. A bit more diversity in the examples might be something that the authors could consider for a future edition. That said, one audience the authors do not mention in their discussion of potential readers is potential purchasers or users of a simulation system. This book would provide a manager who is not as familiar as he or she would like with the right questions to ask of technical staff, particularly since the authors close with a chapter on management responsibilities. An intense session of an afternoon or so with this book would be a good crash course or refresher for anyone who needs to deal with modeling or simulation issues. Online Computing Reviews Service