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This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton–type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed numerically. Theorems on the existence of solutions will be presented for all examples discussed. In using various constitutive equations the restrictions following from the second law of thermodynamics will be implemented. Finally, the physical implications of obtained solutions will be discussed in detail.

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Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including: Concepts of function, continuity, and derivative Properties of exponential and logarithmic function Inverse trigonometric functions and their properties Derivatives of higher order Methods to find maximum and minimum values of a function Hyperbolic functions and their properties Readers are equipped with the necessary tools to quickly learn how to understand a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.

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Praise for the First Edition “…extremely well written…a comprehensive and up-to-date overview of this important field.” – Journal of Environmental Quality Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition provides comprehensive coverage of recent advancements in microarray data analysis. A cutting-edge guide, the Second Edition demonstrates various methodologies for analyzing data in biomedical research and offers an overview of the modern techniques used in microarray technology to study patterns of gene activity. The new edition answers the need for an efficient outline of all phases of this revolutionary analytical technique, from preprocessing to the analysis stage. Utilizing research and experience from highly-qualified authors in fields of data analysis, Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition features: A new chapter on the interpretation of findings that includes a discussion of signatures and material on gene set analysis, including network analysis New topics of coverage including ABC clustering, biclustering, partial least squares, penalized methods, ensemble methods, and enriched ensemble methods Updated exercises to deepen knowledge of the presented material and provide readers with resources for further study The book is an ideal reference for scientists in biomedical and genomics research fields who analyze DNA microarrays and protein array data, as well as statisticians and bioinformatics practitioners. Exploration and Analysis of DNA Microarray and Other High-Dimensional Data, Second Edition is also a useful text for graduate-level courses on statistics, computational biology, and bioinformatics.

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This book explores two combined approaches (strategy and accounting) from a cross-disciplinary perspective in order to improve knowledge of value creation in various contexts. Existing studies on this topic have generally adopted a purely account-based or strategy-oriented approach to address this issue. However, this book draws upon a number of well-defined theoretical and empirical backgrounds and methodologies. Since the 1980s, many changes have occurred and companies have increasingly focused their strategies on value creation. Consequently, new strategic directions have emerged, especially for managerial accounting. Management accounting and alignment with strategy could thus improve performance. This book encourages further thought and reflection on these issues which should be pursued in the future as firms face new challenges associated with the acceleration of digital transformation.

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Introduction to Statistical Analysis of Laboratory Data presents a detailed discussion of important statistical concepts and methods of data presentation and analysis Provides detailed discussions on statistical applications including a comprehensive package of statistical tools that are specific to the laboratory experiment process Introduces terminology used in many applications such as the interpretation of assay design and validation as well as “fit for purpose” procedures including real world examples Includes a rigorous review of statistical quality control procedures in laboratory methodologies and influences on capabilities Presents methodologies used in the areas such as method comparison procedures, limit and bias detection, outlier analysis and detecting sources of variation Analysis of robustness and ruggedness including multivariate influences on response are introduced to account for controllable/uncontrollable laboratory conditions

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Solutions Manual to accompany Introduction to Quantitative Methods in Business: With Applications Using Microsoft® Office Excel®

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A well-balanced and accessible introduction to the elementary quantitative methods and Microsoft® Office Excel® applications used to guide business decision making Featuring quantitative techniques essential for modeling modern business situations, Introduction to Quantitative Methods in Business: With Applications Using Microsoft® Office Excel® provides guidance to assessing real-world data sets using Excel. The book presents a balanced approach to the mathematical tools and techniques with applications used in the areas of business, finance, economics, marketing, and operations. The authors begin by establishing a solid foundation of basic mathematics and statistics before moving on to more advanced concepts. The first part of the book starts by developing basic quantitative techniques such as arithmetic operations, functions and graphs, and elementary differentiations (rates of change), and integration. After a review of these techniques, the second part details both linear and nonlinear models of business activity. Extensively classroom-tested, Introduction to Quantitative Methods in Business: With Applications Using Microsoft® Office Excel® also includes: Numerous examples and practice problems that emphasize real-world business quantitative techniques and applications Excel-based computer software routines that explore calculations for an assortment of tasks, including graphing, formula usage, solving equations, and data analysis End-of-chapter sections detailing the Excel applications and techniques used to address data and solutions using large data sets A companion website that includes chapter summaries, Excel data sets, sample exams and quizzes, lecture slides, and an Instructors’ Solutions Manual Introduction to Quantitative Methods in Business: With Applications Using Microsoft® Office Excel® is an excellent textbook for undergraduate-level courses on quantitative methods in business, economics, finance, marketing, operations, and statistics. The book is also an ideal reference for readers with little or no quantitative background who require a better understanding of basic mathematical and statistical concepts used in economics and business. Bharat Kolluri, Ph.D., is Professor of Economics in the Department of Economics, Finance, and Insurance at the University of Hartford. A member of the American Economics Association, his research interests include econometrics, business statistics, quantitative decision making, applied macroeconomics, applied microeconomics, and corporate finance. Michael J. Panik, Ph.D., is Professor Emeritus in the Department of Economics, Finance, and Insurance at the University of Hartford. He has served as a consultant to the Connecticut Department of Motor Vehicles as well as to a variety of health care organizations. In addition, Dr. Panik is the author of numerous books, including Growth Curve Modeling: Theory and Applications and Statistical Inference: A Short Course, both published by Wiley. Rao N. Singamsetti, Ph.D., is Associate Professor in the Department of Economics, Finance, and Insurance at the University of Hartford. A member of the American Economics Association, his research interests include the status of war on poverty in the United States since the 1960s and forecasting foreign exchange rates using econometric methods.

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Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.

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A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.

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An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) – method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.

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