Applied Functional Analysis

A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and «do» mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Applied Engineering Analysis Tai-Ran Hsu, San Jose State University, USA A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls. Drawing on the author’s extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors. Key features: Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student’s self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC). Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.

An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concepts and applications, offers a complete, easily accessible introduction to the fundamentals of regression analysis. Assuming only a basic knowledge of elementary statistics, Applied Regression Analysis, Third Edition focuses on the fitting and checking of both linear and nonlinear regression models, using small and large data sets, with pocket calculators or computers. This Third Edition features separate chapters on multicollinearity, generalized linear models, mixture ingredients, geometry of regression, robust regression, and resampling procedures. Extensive support materials include sets of carefully designed exercises with full or partial solutions and a series of true/false questions with answers. All data sets used in both the text and the exercises can be found on the companion disk at the back of the book. For analysts, researchers, and students in university, industrial, and government courses on regression, this text is an excellent introduction to the subject and an efficient means of learning how to use a valuable analytical tool. It will also prove an invaluable reference resource for applied scientists and statisticians.

THE MOST PRACTICAL, UP-TO-DATE GUIDE TO MODELLING AND ANALYZING TIME-TO-EVENT DATA—NOW IN A VALUABLE NEW EDITION Since publication of the first edition nearly a decade ago, analyses using time-to-event methods have increase considerably in all areas of scientific inquiry mainly as a result of model-building methods available in modern statistical software packages. However, there has been minimal coverage in the available literature to9 guide researchers, practitioners, and students who wish to apply these methods to health-related areas of study. Applied Survival Analysis, Second Edition provides a comprehensive and up-to-date introduction to regression modeling for time-to-event data in medical, epidemiological, biostatistical, and other health-related research. This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. It offers a clear and accessible presentation of modern modeling techniques supplemented with real-world examples and case studies. Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data. Features of the Second Edition include: Expanded coverage of interactions and the covariate-adjusted survival functions The use of the Worchester Heart Attack Study as the main modeling data set for illustrating discussed concepts and techniques New discussion of variable selection with multivariable fractional polynomials Further exploration of time-varying covariates, complex with examples Additional treatment of the exponential, Weibull, and log-logistic parametric regression models Increased emphasis on interpreting and using results as well as utilizing multiple imputation methods to analyze data with missing values New examples and exercises at the end of each chapter Analyses throughout the text are performed using Stata® Version 9, and an accompanying FTP site contains the data sets used in the book. Applied Survival Analysis, Second Edition is an ideal book for graduate-level courses in biostatistics, statistics, and epidemiologic methods. It also serves as a valuable reference for practitioners and researchers in any health-related field or for professionals in insurance and government.

From a preeminent authority—a modern and applied treatment of multiway data analysis This groundbreaking book is the first of its kind to present methods for analyzing multiway data by applying multiway component techniques. Multiway analysis is a specialized branch of the larger field of multivariate statistics that extends the standard methods for two-way data, such as component analysis, factor analysis, cluster analysis, correspondence analysis, and multidimensional scaling to multiway data. Applied Multiway Data Analysis presents a unique, thorough, and authoritative treatment of this relatively new and emerging approach to data analysis that is applicable across a range of fields, from the social and behavioral sciences to agriculture, environmental sciences, and chemistry. General introductions to multiway data types, methods, and estimation procedures are provided in addition to detailed explanations and advice for readers who would like to learn more about applying multiway methods. Using carefully laid out examples and engaging applications, the book begins with an introductory chapter that serves as a general overview of multiway analysis, including the types of problems it can address. Next, the process of setting up, carrying out, and evaluating multiway analyses is discussed along with commonly encountered issues, such as preprocessing, missing data, model and dimensionality selection, postprocessing, and transformation, as well as robustness and stability issues. Extensive examples are presented within a unified framework consisting of a five-step structure: objectives; data description and design; model and dimensionality selection; results and their interpretation; and validation. Procedures featured in the book are conducted using 3WayPack, which is software developed by the author, and analyses can also be carried out within the R and MATLAB systems. Several data sets and 3WayPack can be downloaded via the book's related Web site. The author presents the material in a clear, accessible style without unnecessary or complex formalism, assuring a smooth transition from well-known standard two-analysis to multiway analysis for readers from a wide range of backgrounds. An understanding of linear algebra, statistics, and principal component analyses and related techniques is assumed, though the author makes an effort to keep the presentation at a conceptual, rather than mathematical, level wherever possible. Applied Multiway Data Analysis is an excellent supplement for component analysis and statistical multivariate analysis courses at the upper-undergraduate and beginning graduate levels. The book can also serve as a primary reference for statisticians, data analysts, methodologists, applied mathematicians, and social science researchers working in academia or industry. Visit the Related Website: http://three-mode.leidenuniv.nl/, to view data from the book.

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. «Many examples drawn from the author’s experience of engineering applications are used to illustrate the theoretical results, which are presented in a cookbook fashion…it provides an excellent practical guide to the analysis of product-life data.» –T.M.M. Farley Special Programme of Research in Human Reproduction World Health Organization Geneva, Switzerland Review in Biometrics, September 1983 Now a classic, Applied Life Data Analysis has been widely used by thousands of engineers and industrial statisticians to obtain information from life data on consumer, industrial, and military products. Organized to serve practitioners, this book starts with basic models and simple informative probability plots of life data. Then it progresses through advanced analytical methods, including maximum likelihood fitting of advanced models to life data. All data analysis methods are illustrated with numerous clients' applications from the author's consulting experience.

A complete introduction to discriminant analysis–extensively revised, expanded, and updated This Second Edition of the classic book, Applied Discriminant Analysis, reflects and references current usage with its new title, Applied MANOVA and Discriminant Analysis. Thoroughly updated and revised, this book continues to be essential for any researcher or student needing to learn to speak, read, and write about discriminant analysis as well as develop a philosophy of empirical research and data analysis. Its thorough introduction to the application of discriminant analysis is unparalleled. Offering the most up-to-date computer applications, references, terms, and real-life research examples, the Second Edition also includes new discussions of MANOVA, descriptive discriminant analysis, and predictive discriminant analysis. Newer SAS macros are included, and graphical software with data sets and programs are provided on the book's related Web site. The book features: Detailed discussions of multivariate analysis of variance and covariance An increased number of chapter exercises along with selected answers Analyses of data obtained via a repeated measures design A new chapter on analyses related to predictive discriminant analysis Basic SPSS(r) and SAS(r) computer syntax and output integrated throughout the book Applied MANOVA and Discriminant Analysis enables the reader to become aware of various types of research questions using MANOVA and discriminant analysis; to learn the meaning of this field's concepts and terms; and to be able to design a study that uses discriminant analysis through topics such as one-factor MANOVA/DDA, assessing and describing MANOVA effects, and deleting and ordering variables.

Written for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in «Numerical Analysis» and «Numerical Methods.» It will combine the material of both these areas as well as special topics in modern applications. Included at the end of each chapter are a variety of theoretical and computational exercises.

This complete resource on the theory and applications of reliability engineering, probabilistic models and risk analysis consolidates all the latest research, presenting the most up-to-date developments in this field. With comprehensive coverage of the theoretical and practical issues of both classic and modern topics, it also provides a unique commemoration to the centennial of the birth of Boris Gnedenko, one of the most prominent reliability scientists of the twentieth century. Key features include: expert treatment of probabilistic models and statistical inference from leading scientists, researchers and practitioners in their respective reliability fields detailed coverage of multi-state system reliability, maintenance models, statistical inference in reliability, systemability, physics of failures and reliability demonstration many examples and engineering case studies to illustrate the theoretical results and their practical applications in industry Applied Reliability Engineering and Risk Analysis is one of the first works to treat the important areas of degradation analysis, multi-state system reliability, networks and large-scale systems in one comprehensive volume. It is an essential reference for engineers and scientists involved in reliability analysis, applied probability and statistics, reliability engineering and maintenance, logistics, and quality control. It is also a useful resource for graduate students specialising in reliability analysis and applied probability and statistics. Dedicated to the Centennial of the birth of Boris Gnedenko, renowned Russian mathematician and reliability theorist