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Functions of Two Variables (Second Edition)
by Sean Dineen<p>Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background. There is another way-a highly engaging way that does not neglect readers' own intuition, experience, and excitement. One that presents the fundamentals of the subject in a two-variable context and was set forth in the popular first edition of Functions of Two Variables. <p>The second edition goes even further toward a treatment that is at once gentle but rigorous, atypical yet logical, and ultimately an ideal introduction to a subject important to careers both within and outside of mathematics. The author's style remains informal and his approach problem-oriented. He takes care to motivate concepts prior to their introduction and to justify them afterwards, to explain the use and abuse of notation and the scope of the techniques developed. <p>Functions of Two Variables, Second Edition includes a new section on tangent lines, more emphasis on the chain rule, a rearrangement of several chapters, refined examples, and more exercises. It maintains a balance between intuition, explanation, methodology, and justification, enhanced by diagrams, heuristic comments, examples, exercises, and proofs.</p>
Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods: FCMTCCT2 2022, Almería, Spain, July 11–15, Invited and Selected Contributions (Springer Proceedings in Mathematics & Statistics #450)
by Alexander MartsinkovskyThis volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almería, Spain, in July 2022.The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field.Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interestfor researchers, the volume will also be an invaluable resource for newcomers.
Fundamental and Applied Sciences in Asia: International Conference on Science Technology and Social Sciences (ICSTSS 2018)
by Nor Azizah Yacob Duratul Ain Tholibon Nor Yuziah Mohd Yunus Zadariana Jamil Syuhada Mohd TahirThis book gathers selected science and technology papers presented at the 2018 International Conference on Science Technology and Social Sciences (ICSTSS 2018), organised bi-annually by Universiti Teknologi MARA Pahang, Malaysia. Based on the theme “Redesigning Education for Industrial Revolution”, the papers in this book address a broad range of topics in the fundamental and applied sciences, including computer science, engineering, environmental and management, furniture, forestry, health and medicine, material science, mathematics, plantation and agrotechnology, sport science and statistics, covering theoretical, numerical and experimental studies. The book serves as a platform for disseminating research findings by academicians of local, regional and global prominence, as a catalyst to inspire positive innovations in the development of the region. It provides a significant point of reference for academicians and students: for academicians, it is a good source of information to conduct further research; for students, it is the latest point of reference on research conducted in their fields of study. The carefully reviewed papers intend to facilitate the creation of new knowledge through the exchange of ideas, strategies and innovations in various science and technology disciplines, and to contribute towards enhancing the learning environment.
Fundamental Aspects of Operational Risk and Insurance Analytics
by Marcelo G. Cruz Pavel V. Shevchenko Gareth W. PetersA one-stop guide for the theories, applications, andstatistical methodologies essential to operational riskProviding a complete overview of operational risk modeling andrelevant insurance analytics, Fundamental Aspects of OperationalRisk and Insurance Analytics: A Handbook of Operational Riskoffers a systematic approach that covers the wide range of topicsin 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 thefundamentals of operational risk, with a primary focus on BaselII/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 fourdata elements used in operational risk framework as well asprocessing risk taxonomy. The book then goes further in-depth intothe key topics in operational risk measurement and insurance, forexample diverse methods to estimate frequency and severity models.Finally, the book ends with sections on specific topics, such asscenario analysis; multifactor modeling; and dependence modeling. Aunique companion with Advances in Heavy Tailed Risk Modeling: AHandbook of Operational Risk, the handbook also features:Discussions on internal loss data and key risk indicators,which are both fundamental for developing a risk-sensitiveframeworkGuidelines for how operational risk can be inserted into afirm's strategic decisionsA model for stress tests of operational risk under the UnitedStates Comprehensive Capital Analysis and Review (CCAR)programA valuable reference for financial engineers, quantitativeanalysts, risk managers, and large-scale consultancy groupsadvising banks on their internal systems, the handbook is alsouseful for academics teaching postgraduate courses on themethodology of operational risk.
Fundamental Aspects of Plasma Chemical Physics
by Annarita Laricchiuta Domenico Bruno Mario CapitelliFundamental Aspects of Plasma Chemical Physics: Transport develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation. The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals. A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties. Throughout the book, worked examples are provided to clarify concepts and mathematical approaches. This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, Fundamental Aspects of Plasma Chemical Physics: Thermodynamics, is dedicated to plasma thermodynamics; and the third, Fundamental Aspects of Plasma Chemical Physics: Kinetics, deals with plasma kinetics.
Fundamental Concepts of Abstract Algebra
by Gertrude EhrlichA text in abstract algebra for undergraduate mathematics majors, this volume contains enough material for a two-semester course. It presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. Examples, definitions, theorems, and proofs appear throughout, along with numerous practice exercises at the end of each section. 1991 edition.
Fundamental Concepts of Geometry (Dover Books on Mathematics)
by Bruce E. MeserveFundamental Concepts of Geometry demonstrates in a clear and lucid manner the relationships of several types of geometry to one another. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts. Professor Meserve (University of Vermont) offers students and prospective teachers the broad mathematical perspective gained from an elementary treatment of the fundamental concepts of mathematics. The clearly presented text is written on an undergraduate (or advanced secondary-school) level and includes numerous exercises and a brief bibliography. An indispensable taddition to any math library, this helpful guide will enable the reader to discover the relationships among Euclidean plane geometry and other geometries; obtain a practical understanding of "proof"; view geometry as a logical system based on postulates and undefined elements; and appreciate the historical evolution of geometric concepts.
Fundamental Math and Physics for Scientists and Engineers
by Hannah Yevick David YevickThis text summarizes the core undergraduate physics curriculum together with the mathematics frequently encountered in engineering and physics calculations, focusing on content relevant to practical applications.Covers major undergraduate physics topics including the complete Physics GRE subject examination syllabusOverview of key results in undergraduate applied mathematics and introduces scientific programmingPresents simple, coherent derivations and illustrations of fundamental concepts
Fundamental Mathematical Analysis (Springer Undergraduate Mathematics Series)
by Robert MagnusThis textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout.Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function.Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
Fundamental Mathematical Modeling of Additive Manufacturing (Springer Tracts in Additive Manufacturing)
by Juha Jeronen Tero Tuovinen Matti KurkiThis book elucidates the fundamental thermomechanical behaviour inherent in the 3D printing process within a laser-based powder bed fusion (L-PBF) system. It presents foundational concepts and provides in-depth derivations of the governing equations. The analysis encompasses arbitrary anisotropic linear viscoelastic materials, accounting for thermal effects. The authors leverage the theory of axially moving materials, a framework previously employed in the analysis of production processes within the process industry. They introduce a coordinate frame that moves in tandem with the printing laser, adopting an Eulerian perspective towards the in-motion solid. Designed for graduate students and researchers, this book is poised to foster a profound comprehension and spur innovative technological advancements in the realm of additive manufacturing.
Fundamental Mathematical Structures of Quantum Theory: Spectral Theory, Foundational Issues, Symmetries, Algebraic Formulation
by Valter MorettiThis textbook presents in a concise and self-contained way the advanced fundamental mathematical structures in quantum theory. It is based on lectures prepared for a 6 months course for MSc students. The reader is introduced to the beautiful interconnection between logic, lattice theory, general probability theory, and general spectral theory including the basic theory of von Neumann algebras and of the algebraic formulation, naturally arising in the study of the mathematical machinery of quantum theories. Some general results concerning hidden-variable interpretations of QM such as Gleason's and the Kochen-Specker theorems and the related notions of realism and non-contextuality are carefully discussed. This is done also in relation with the famous Bell (BCHSH) inequality concerning local causality.Written in a didactic style, this book includes many examples and solved exercises.The work is organized as follows. Chapter 1 reviews some elementary facts and properties of quantum systems. Chapter 2 and 3 present the main results of spectral analysis in complex Hilbert spaces. Chapter 4 introduces the point of view of the orthomodular lattices' theory. Quantum theory form this perspective turns out to the probability measure theory on the non-Boolean lattice of elementary observables and Gleason's theorem characterizes all these measures. Chapter 5 deals with some philosophical and interpretative aspects of quantum theory like hidden-variable formulations of QM. The Kochen-Specker theorem and its implications are analyzed also in relation BCHSH inequality, entanglement, realism, locality, and non-contextuality. Chapter 6 focuses on the algebra of observables also in the presence of superselection rules introducing the notion of von Neumann algebra. Chapter 7 offers the idea of (groups of) quantum symmetry, in particular, illustrated in terms of Wigner and Kadison theorems. Chapter 8 deals with the elementary ideas and results of the so called algebraic formulation of quantum theories in terms of both *-algebras and C*-algebras.This book should appeal to a dual readership: on one hand mathematicians that wish to acquire the tools that unlock the physical aspects of quantum theories; on the other physicists eager to solidify their understanding of the mathematical scaffolding of quantum theories.
Fundamental Physics and Physics Education Research (Springer Proceedings In Physics Ser. #145)
by Burra G. Sidharth Jesús Carnicer Murillo Marisa Michelini Carmen PereaThis book highlights selected contributions presented at the 15th annual international symposium Frontiers of Fundamental Physics (FFP15), with the aim of informing readers about the most important recent advances in fundamental physics and physics education research. The FFP series offers a platform for physicists from around the world to present their latest theories and findings. The latest symposium was held in Orihuela, Spain and covered diverse fields of research, including gravitation, astronomy and astrophysics, physics of complex systems, high-energy physics, and mathematical physics. Considerable attention was also paid to physics education research, teacher education in physics, and the popularization of physics. In a knowledge-based society, research into fundamental physics plays a vital role in both the advancement of human knowledge and the development of new technologies. Presenting valuable new peer-reviewed contributions submitted from 15 countries, this book will appeal to a broad audience of scholars and researchers.
The Fundamental Rules of Risk Management
by Nigel LewisThe consequences of taking on risk can be ruinous to personal finances, professional careers, corporate survivability, and even nation states. Yet many risk managers do not have a clear understanding of the basics. Requiring no statistical or mathematical background, The Fundamental Rules of Risk Management gives you the knowledge to successfully h
Fundamental Solutions of Linear Partial Differential Operators
by Norbert Ortner Peter WagnerThis monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell's system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.
Fundamental Statistical Inference: A Computational Approach (Wiley Series in Probability and Statistics)
by Marc S. PaolellaA hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
Fundamental Statistics for the Behavioral Sciences 8th Edition
by David C. HowellFUNDAMENTAL STATISTICS FOR THE BEHAVIORAL SCIENCES focuses on providing the context of statistics in behavioral research, while emphasizing the importance of looking at data before jumping into a test. This practical approach provides readers with an understanding of the logic behind the statistics, so they understand why and how certain methods are used--rather than simply carry out techniques by rote. Readers move beyond number crunching to discover the meaning of statistical results and appreciate how the statistical test to be employed relates to the research questions posed by an experiment. An abundance of real data and research studies provide a real-life perspective and help you understand concepts as you learn about the analysis of data.
Fundamental Statistics for the Social and Behavioral Sciences
by Howard T. TokunagaFundamental Statistics for the Social and Behavioral Sciences, Second Edition places statistics within the research process, illustrating how they are used to answer questions and test ideas. Students learn not only how to calculate statistics, but also how to interpret and communicate the results of statistical analyses in light of a study’s research hypothesis. Featuring accessible writing and well-integrated research examples, the book gives students a greater understanding of how research studies are conceived, conducted, and communicated. New and Proven Features Updated data sets and research examples address real-world issues and topics across the social and behavioral sciences, illustrating the use of statistical procedures to test research questions and hypotheses. Significantly expanded discussion of linear and multiple regression and correlation now gives regression its own separate chapter. Thorough presentation of formulas, hand calculations, and the presentation of visual data enable mastery of key techniques and prove especially helpful in flipped or online classes. In-chapter learning checks and end-of-chapter exercises give students an opportunity to continually assess their understanding. Screenshots of statistical calculations using IBM® SPSS® Statistics at the end of chapters help students learn to use SPSS software and interpret output. Original SAGE videos for each chapter, featuring author Howard K. Tokunaga, bring concepts to life and appeal to diverse learners.
Fundamental Statistics for the Social and Behavioral Sciences
by Howard T. TokunagaFundamental Statistics for the Social and Behavioral Sciences, Second Edition places statistics within the research process, illustrating how they are used to answer questions and test ideas. Students learn not only how to calculate statistics, but also how to interpret and communicate the results of statistical analyses in light of a study’s research hypothesis. Featuring accessible writing and well-integrated research examples, the book gives students a greater understanding of how research studies are conceived, conducted, and communicated. New and Proven Features Updated data sets and research examples address real-world issues and topics across the social and behavioral sciences, illustrating the use of statistical procedures to test research questions and hypotheses. Significantly expanded discussion of linear and multiple regression and correlation now gives regression its own separate chapter. Thorough presentation of formulas, hand calculations, and the presentation of visual data enable mastery of key techniques and prove especially helpful in flipped or online classes. In-chapter learning checks and end-of-chapter exercises give students an opportunity to continually assess their understanding. Screenshots of statistical calculations using IBM® SPSS® Statistics at the end of chapters help students learn to use SPSS software and interpret output. Original SAGE videos for each chapter, featuring author Howard K. Tokunaga, bring concepts to life and appeal to diverse learners.
Fundamentals of Abstract Algebra (Textbooks in Mathematics)
by Mark J. DeBonisFundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained.Features Self-contained treatments of all topics Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course Copious exercises and examples Mark DeBonis received his PhD in Mathematics from the University of California, Irvine, USA. He began his career as a theoretical mathematician in the field of group theory and model theory, but in later years switched to applied mathematics, in particular to machine learning. He spent some time working for the US Department of Energy at Los Alamos National Lab as well as the US Department of Defense at the Defense Intelligence Agency, both as an applied mathematician of machine learning. He held a position as Associate Professor of Mathematics at Manhattan College in New York City, but later left to pursue research working for the US Department of Energy at Sandia National Laboratory as a Principal Data Analyst. His research interests include machine learning, statistics and computational algebra.
Fundamentals of Actuarial Mathematics
by S. David PromislowThis 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.
Fundamentals of Actuarial Mathematics
by S. David PromislowThis 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.
Fundamentals of Algebra Practice Book (Progress in Mathematics)
by Alfred S. Posamentier Catherine D. Le Tourneau Edward Wiliam Quinn*This textbook has been transcribed in UEB, formatted according to Braille textbook formats, proofread and corrected. <P><P> Progress in Mathematics 2009 Student Edition Practice Book Grade 7 In alignment with the Common Core State Standards, the scope and sequence of Fundamentals of Algebra is organized into bite-sized, manageable lessons allowing for deeper understanding of skills and concepts so students get the necessary skills for Algebra and beyond. Fundamentals of Algebra: • Focuses on conceptual development for all learners. • Builds knowledge lesson by lesson and across grade levels with coherent lessons. • Develops fluency and conceptual understanding in a multitude of ways. • Deepens understanding with vocabulary, cognitive rigor, and higher-level thinking skills. The Sourcebook allows students to focus on learning skills and concepts before moving onto independent practice in the Practice Book.
Fundamentals of Algebraic Microlocal Analysis (Chapman And Hall/crc Pure And Applied Mathematics Ser. #217)
by Goro Kato Daniele C Struppa"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Fundamentals of Applied Multidimensional Scaling for Educational and Psychological Research
by Cody S. DingThis book explores the fundamentals of multidimensional scaling (MDS) and how this analytic method can be used in applied setting for educational and psychological research. The book tries to make MDS more accessible to a wider audience in terms of the language and examples that are more relevant to educational and psychological research and less technical so that the readers are not overwhelmed by equations. The goal is for readers to learn the methods described in this book and immediately start using MDS via available software programs. The book also examines new applications that have previously not been discussed in MDS literature. It should be an ideal book for graduate students and researchers to better understand MDS. Fundamentals of Applied Multidimensional Scaling for Educational and Psychological Research is divided into three parts. Part I covers the basic and fundamental features of MDS models pertaining to applied research applications. Chapters in this section cover the essential features of data that are typically associated with MDS analysis such as preference ration or binary choice data, and also looking at metric and non-metric MDS models to build a foundation for later discussion and applications in later chapters. Part II examines specific MDS models and its applications for education and psychology. This includes spatial analysis methods that can be used in MDS to test clustering effect of items and individual differences MDS model (INDSCAL). Finally, Part III focuses on new applications of MDS analysis in these research fields. These new applications consist of profile analysis, longitudinal analysis, mean-level change, and pattern change. The book concludes with a historical review of MDS development as an analytical method and a look to future directions.
The Fundamentals of Atomic and Molecular Physics
by Robert L BrooksThe Fundamentals of Atomic and Molecular Physics is intended as an introduction to the field for advanced undergraduates who have taken quantum mechanics. Each chapter builds upon the previous, using the same tools and methods throughout. As the students progress through the book, their ability to use these tools will steadily increase, along with their confidence in their efficacy. The book treats the two-electron atom as the simplest example of the many-electron atom--as opposed to using techniques that are not applicable to many-electron atoms--so that it is unnecessary to develop additional equations when turning to multielectron atoms, such as carbon. External fields are treated using both perturbation theory and direct diagonalization and spontaneous emission is developed from first principles. Only diatomic molecules are considered with the hydrogen molecular ion and neutral molecule treated in some detail. This comprehensive coverage of the quantum mechanics of complex atoms and simple diatomic molecules, developed from the very basic components, is extremely useful for students considering graduate studies in any area of physics.