Methods

Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Volterra equations, although attractive to treat theoretically, arise less often in practical problems and so have been given less emphasis. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. This book should serve as a valuable text for final year undergraduate or postgraduate courses, and as an introduction or reference work for practisin

This book discusses a broad range of statistical design and analysis methods that are particularly well suited to pollution data. It explains key statistical techniques in easy-to-comprehend terms and

In this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. Although the discussion is mathematically self-contained, it assumes that the reader has a firm background in calculus and differential equations. Each chapter contains a number of worked examples plus exercises designed to allow the student to put concepts into practice. The author writes in a mathematically elegant yet relaxed and readable style, and provides interesting historical notes along the way. Undergraduate students of electrical engineering, applied mathematics, and related disciplines - and their teachers - will welcome this book.

This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those de

Compendium of Organic Synthetic Methods Volume III Louis S. Hegedus & Leroy G. Wade, Jr. Presents the new synthetic methods for preparation of monofunctional compounds for 1974, 1975, and 1976. Sectio

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

Describes various commonly used methods of initial factoring and factor rotation. In addition to a full discussion of exploratory factor analysis, confirmatory factor analysis and various methods of

Analyses of Theories and Methods of Physics and Psychology was first published in 1970. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are

This book is designed to provide students, teachers, and researchers with a text that includes a full range of statistical methods available to address commonly encountered research problems. Many textbooks for introductory, intermediate, and advanced statistics courses focus heavily on parametric methods. However, in practice the assumptions underlying these methods are frequently not met, therefore calling into question their use. This book addresses this issue by presenting parametric, nonparametric, robust, and Bayesian techniques that are appropriate for research scenarios often encountered in practice and typically found in statistics courses. For each of these major topics, the standard parametric approach is presented, along with the assumptions underlying it and the methods used to assess the viability of these assumptions. Next, a set of alternative techniques for the research scenario is presented and applied to the motivating example that begins each chapter. Each chapter c

This second edition guides readers through experimental and computational techniques on the study of tissue morphogenesis, with a specific focus on techniques to image, manipulate, model and analyze tissue morphogenesis. Chapters focus on imagining analysis of tissue morphogenesis, culture models of tissue morphogenesis, manipulating cells and tissues in vivo, novel model systems to investigate issue morphogenesis and computational models. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and key tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Tissue Morphogenesis: Methods and Protocols serves as a primary resource for both fundamental and practical understanding of the techniques used to uncover the basis of tissue morphogenesis.

This second edition details new and updated protocols for experimental approaches that are currently used to study the formation of flowers. Chapters guide readers on genetic methods, phenotypic analyses, genome-wide experiments, modeling, and system-wide approaches. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and key tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Flower Development: Methods and Protocols, Second Edition aims to be a useful and practical guide to new researchers and experts looking to expand their knowledge.

The A to Z of Creative Writing Methods is an alphabetical collection of essays to prompt consideration of method within creative writing research and practice.Almost sixty contributors from a range of writing traditions and across multiple forms and genre are represented in this volume: from poets, essayists, novelists and performance writers, to graphic novelists, illustrators, and those engaged in multi-media writing or writing-related arts activism. Contributors bring to this collection their distinct and diverse literary and cultural contexts, defining, expanding and enacting the methods they describe, and providing new possibilities for creative writing practice.Accessible and provocative, A to Z of Creative Writing Methods lays bare new developments and directions in the field, making it an invaluable resource for the teachers, research students and scholar-practitioners in the field of creative writing studies.

The A to Z of Creative Writing Methods is an alphabetical collection of essays to prompt consideration of method within creative writing research and practice.Almost sixty contributors from a range of writing traditions and across multiple forms and genre are represented in this volume: from poets, essayists, novelists and performance writers, to graphic novelists, illustrators, and those engaged in multi-media writing or writing-related arts activism. Contributors bring to this collection their distinct and diverse literary and cultural contexts, defining, expanding and enacting the methods they describe, and providing new possibilities for creative writing practice.Accessible and provocative, A to Z of Creative Writing Methods lays bare new developments and directions in the field, making it an invaluable resource for the teachers, research students and scholar-practitioners in the field of creative writing studies.

Intended for researchers and practitioners in interaction design, this book shows how Bayesian models can be brought to bear on problems of interface design and user modelling. It introduces and motivates Bayesian modelling and illustrates how powerful these ideas can be in thinking about human-computer interaction, especially in representing and manipulating uncertainty. Bayesian methods are increasingly practical as computational tools to implement them become more widely available, and offer a principled foundation to reason about interaction design. The book opens with a self-contained tutorial on Bayesian concepts and their practical implementation, tailored for the background and needs of interaction designers. The contributed chapters cover the use of Bayesian probabilistic modelling in a diverse set of applications, including improving pointing-based interfaces; efficient text entry using modern language models; advanced interface design using cutting-edge techniques in Bayesia

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author's focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding.Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in t

Qualitative comparative methods – and specifically controlled qualitative comparisons – are central to the study of politics. They are not the only kind of comparison, though, that can help us better understand political processes and outcomes. Yet there are few guides for how to conduct non-controlled comparative research. This volume brings together chapters from more than a dozen leading methods scholars from across the discipline of political science, including positivist and interpretivist scholars, qualitative methodologists, mixed-methods researchers, ethnographers, historians, and statisticians. Their work revolutionizes qualitative research design by diversifying the repertoire of comparative methods available to students of politics, offering readers clear suggestions for what kinds of comparisons might be possible, why they are useful, and how to execute them. By systematically thinking through how we engage in qualitative comparisons and the kinds of insights those comparis

Qualitative comparative methods – and specifically controlled qualitative comparisons – are central to the study of politics. They are not the only kind of comparison, though, that can help us better understand political processes and outcomes. Yet there are few guides for how to conduct non-controlled comparative research. This volume brings together chapters from more than a dozen leading methods scholars from across the discipline of political science, including positivist and interpretivist scholars, qualitative methodologists, mixed-methods researchers, ethnographers, historians, and statisticians. Their work revolutionizes qualitative research design by diversifying the repertoire of comparative methods available to students of politics, offering readers clear suggestions for what kinds of comparisons might be possible, why they are useful, and how to execute them. By systematically thinking through how we engage in qualitative comparisons and the kinds of insights those comparis

Handbook of Statistical Methods for Randomized Controlled Trials

Covers the entire breadth of work in intermittent demand forecasting and the very latest research findings in the following topics: time series (parametric) methods bootstrapping, both parametric and

This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions.

This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using di

The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.

This book discusses one of the most recent developments in interior-point methods, the arc-search techniques. Introducing these techniques result in an efficient interior-point algorithm with the lowe

Learn about the state-of-the-art at the interface between information theory and data science with this first unified treatment of the subject. Written by leading experts in a clear, tutorial style, and using consistent notation and definitions throughout, it shows how information-theoretic methods are being used in data acquisition, data representation, data analysis, and statistics and machine learning. Coverage is broad, with chapters on signal acquisition, data compression, compressive sensing, data communication, representation learning, emerging topics in statistics, and much more. Each chapter includes a topic overview, definition of the key problems, emerging and open problems, and an extensive reference list, allowing readers to develop in-depth knowledge and understanding. Providing a thorough survey of the current research area and cutting-edge trends, this is essential reading for graduate students and researchers working in information theory, signal processing, machine le

The successful collection of data is a key challenge to obtaining reliable and valid results in applied linguistics research. Data Collection Research Methods in Applied Linguistics investigates how r

Methods of Research on Human Development and Families is an introduction to quantitative and qualitative research methods that teaches students how to be intelligent and critical consumers of research

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questi

Get 12 months FREE access to the Digital Methods Manual (the abridged, interactive eBook that provides handy step-by-step guidance to your phone, tablet, laptop or reading device) when purchasing ISBN

This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for

Multi-dimensional Analysis: Research Methods and Current Issues provides a comprehensive guide both to the statistical methods in Multi-dimensional Analysis (MDA) and its key elements, such as corpus

This volume presents modern and enhanced methods that detail techniques to perform proteomics analyses dedicated to biomarker discovery for human health. Chapters guide readers through pre/post analyt