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A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

This book aims to enable readers to understand and implement, via the widely used statistical software package Minitab (Release 16), statistical methods fundamental to the Six Sigma approach to the continuous improvement of products, processes and services. The second edition includes the following new material: Pareto charts and Cause-and-Effect diagrams Time-weighted control charts cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) Multivariate control charts Acceptance sampling by attributes and variables (not provided in Release 14) Tests of association using the chi-square distribution Logistic regression Taguchi experimental designs

How do you draw a map of 100,000 places, of more than a million flows of people, of changes over time and space, of different kinds of spaces, surfaces and volumes, from human travel time to landscapes of hopes, fears, migration, manufacturing and mortality? How do you turn the millions of numbers concerning some of the most important moments of our lives into images that allow us to appreciate the aggregate while still remembering the detail? The visualization of spatial social structure means, literally, making visible the geographical patterns to the way our lives have come to be socially organised, seeing the geography in society. To a statistical readership visualization implies using data. More widely defined it implies freeing our imaginations. The Visualization of Spatial Social Structure introduces the reader to new ways of thinking about how to look at social statistics, particularly those about people in places. The author presents a unique combination of statistical focus and understanding of social structures and innovations in visualization, describing the rationale for, and development of, a new way of visualizing information in geographical research. These methods are illustrated through extensive full colour graphics; revealing mistakes, techniques and discoveries which present a picture of a changing political and social geography. More complex aspects on the surface of social landscapes are revealed with sculptured symbols allowing us to see the relationships between the wood and the trees of social structure. Today's software can be so flexible that these techniques can now be emulated without coding. This book centres on a particular place and time; 1980s Britain, and a particular set of records; routine social statistics. A great deal of information about the 80s' social geography of Britain is contained within databases such as the population censuses, surveys and administrative data. Following the release of the 2011 census, now is a good time to look back at the past to introduce many new visualization techniques that could be used by future researchers.

Introduces the graphical capabilities of R to readers new to the software Due to its flexibility and availability, R has become the computing software of choice for statistical computing and generating graphics across various fields of research. Guidebook to R Graphics Using Microsoft® Windows offers a unique presentation of R, guiding new users through its many benefits, including the creation of high-quality graphics. Beginning with getting the program up and running, this book takes readers step by step through the process of creating histograms, boxplots, strip charts, time series graphs, steam-and-leaf displays, scatterplot matrices, and map graphs. In addition, the book presents: Tips for establishing, saving, and printing graphs along with essential base-package plotting functions Interactive R programs for carrying out common tasks such as inputting values, moving data on a natural spline, adjusting three-dimensional graphs, and understanding simple and local linear regression Various external packages for R that help to create more complex graphics like rimage, gplots, ggplot2, tripack, rworldmap, and plotrix packages Throughout the book, concise explanations of key concepts of R graphics assist readers in carrying out the presented procedures, and any coverage of functions is clearly written out and displayed in the text as demos. The discussed techniques are accompanied by a wealth of screenshots and graphics with related R code available on the book's FTP site, and numerous exercises allow readers to test their understanding of the presented material. Guidebook to R Graphics Using Microsoft® Windows is a valuable resource for researchers in the fields of statistics, public health, business, and the life and social sciences who use or would like to learn how to use R to create visual representations of data. The book can also be used as a supplement for courses on statistical analysis at the upper-undergraduate level.

Utilizing the latest software, this book presents the essential statistical procedures for drawing valuable results from data in the social sciences. Mobilizing interesting real-world examples from the field of education, Understanding Educational Statistics Using Microsoft Excel and SPSS supplies a seamless presentation that identifies valuable connections between statistical applications and research design. Class-tested to ensure an accessible presentation, the book combines clear, step-by-step explanations and the use of software packages that are accessible to both the novice and professional alike to present the fundamental statistical practices for organizing, understanding, and drawing conclusions from educational research data. The book begines with an introduction to descriptive and inferential statistics and then proceeds to acquaint readers with the various functions for working with quantitative data in the Microsoft Excel environment, such as spreadsheet navigation; sorting and filtering; and creating pivot tables. Subsequent chapters treat the procedures that are commonly-employed when working with data across various fields of social science research, including: Single-sample tests Repeated measure tests Independent t-tests One way ANOVA and factorial ANOVA Correlation Bivariate regression Chi square Multiple regression Individual chapters are devoted to specific procedures, each ending with a lab exercise that highlights the importance of that procedure by posing a research question, examining the question through its application in Excel and SPSS, and concluding with a brief research report that outlines key findings drawn from the results. Real-world examples and data from modern educational research are used throughout the book, and a related Web site features additional data sets, examples, and labs, allowing readers to reinforce their comprehension of the material. Bridging traditional statistical topics with the latest software and applications in the field of education, Understanding Educational Statistics Using Microsoft Excel and SPSS is an excellent book for courses on educational research methods and introductory statistics in the social sciences at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and practitioners in the fields of education, psychology, and the social sciences who require a statistical background to work with data in their everyday work.

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task – a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers. The content focuses on the modeling of a class of dynamic systems usually called “discrete event systems” where the timing of the events is crucial. Events are viewed as sudden changes in a process which is, essentially, a man-made system, such as automated manufacturing lines or transportation systems. Its main advantage is its formalism which allows us to clearly describe complex notions and the possibilities to transpose theoretical results between dioids and practical applications.

Introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book. Financial Risk Modelling and Portfolio Optimization with R: Demonstrates techniques in modelling financial risks and applying portfolio optimization techniques as well as recent advances in the field. Introduces stylized facts, loss function and risk measures, conditional and unconditional modelling of risk; extreme value theory, generalized hyperbolic distribution, volatility modelling and concepts for capturing dependencies. Explores portfolio risk concepts and optimization with risk constraints. Enables the reader to replicate the results in the book using R code. Is accompanied by a supporting website featuring examples and case studies in R. Graduate and postgraduate students in finance, economics, risk management as well as practitioners in finance and portfolio optimization will find this book beneficial. It also serves well as an accompanying text in computer-lab classes and is therefore suitable for self-study.

A comprehensive treatment on the use of quantitative modeling for decision making and best practices in the service industries Making up a significant part of the world economy, the service sector is a rapidly evolving field that is relied on to dictate the public's satisfaction and success in various areas of everyday life, from banking and communications to education and healthcare. Service Science provides managers and students of the service industries with the quantitative skills necessary to model key decisions and performance metrics associated with services, including the management of resources, distribution of goods and services to customers, and the analysis and design of queueing systems. The book begins with a brief introduction to the service sector followed by an introduction to optimization and queueing modeling, providing the methodological background needed to analyze service systems. Subsequent chapters present specific topics within service operations management, including: Location modeling and districting Resource allocation problems Short- and long-term workforce management Priority services, call center design, and customer scheduling Inventory modeling Vehicle routing The author's own specialized software packages for location modeling, network optimization, and time-dependent queueing are utilized throughout the book, showing readers how to solve a variety of problems associated with service industries. These programs are freely available on the book's related web site along with detailed appendices and online spreadsheets that accompany the book's «How to Do It in Excel» sections, allowing readers to work hands-on with the presented techniques. Extensively class-tested to ensure a comprehensive presentation, Service Science is an excellent book for industrial engineering and management courses on service operations at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers in the fields of business, management science, operations research, engineering, and economics. This book was named the 2010 Joint Publishers Book of the Year by the Institute of Industrial Engineers.

Throughout the social, medical and other sciences the importance of understanding complex hierarchical data structures is well understood. Multilevel modelling is now the accepted statistical technique for handling such data and is widely available in computer software packages. A thorough understanding of these techniques is therefore important for all those working in these areas. This new edition of Multilevel Statistical Models brings these techniques together, starting from basic ideas and illustrating how more complex models are derived. Bayesian methodology using MCMC has been extended along with new material on smoothing models, multivariate responses, missing data, latent normal transformations for discrete responses, structural equation modeling and survival models. Key Features: Provides a clear introduction and a comprehensive account of multilevel models. New methodological developments and applications are explored. Written by a leading expert in the field of multilevel methodology. Illustrated throughout with real-life examples, explaining theoretical concepts. This book is suitable as a comprehensive text for postgraduate courses, as well as a general reference guide. Applied statisticians in the social sciences, economics, biological and medical disciplines will find this book beneficial.

We all face risks in a variety of ways, as individuals, businesses and societies. The discipline of risk assessment and risk management is growing rapidly and there is an enormous drive for the implementation of risk assessment methods and risk management in organizations. There are great expectations that these tools provide suitable frameworks for obtaining high levels of performance and balance different concerns such as safety and costs. The analysis and management of risk are not straightforward. There are many challenges. The risk discipline is young and there area a number of ideas, perspectives and conceptions of risk out there. For example many analysts and researchers consider it appropriate to base their risk management policies on the use of expected values, which basically means that potential losses are multiplied with their associated consequences. However, the rationale for such a policy is questionable. A number of such common conceptions of risk are examined in the book, related to the risk concept, risk assessments, uncertainty analyses, risk perception, the precautionary principle, risk management and decision making under uncertainty. The Author discusses these concepts, their strenghts and weaknesses, and concludes that they are often better judged as misconceptions of risk than conceptions of risk. Key Features: Discusses common conceptions of risk with supporting examples. Provides recommendations and guidance to risk analysis and risk management. Relevant for all types of applications, including engineering and business. Presents the Author’s overall conclusions on the issues addressed throughout the book. All those working with risk-related problems need to understand the fundamental ideas and concepts of risk. Professionals in the field of risk, as well as researchers and graduate sutdents will benefit from this book. Policy makers and business people will also find this book of interest.

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems. Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries. The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics. Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.

This book provides a comprehensive introduction to actuarial mathematics, covering both deterministic and stochastic models of life contingencies, as well as more advanced topics such as risk theory, credibility theory and multi-state models. This new edition includes additional material on credibility theory, continuous time multi-state models, more complex types of contingent insurances, flexible contracts such as universal life, the risk measures VaR and TVaR. Key Features: Covers much of the syllabus material on the modeling examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society. (SOA-CIA exams MLC and C, CSA exams 3L and 4.) Extensively revised and updated with new material. Orders the topics specifically to facilitate learning. Provides a streamlined approach to actuarial notation. Employs modern computational methods. Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study. An ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modeling examinations of the major North American actuarial associations. Furthermore, this book is highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions.