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Mathematical Methods in Physics, Engineering, and Chemistry
by James Luscombe Brett BordenA concise and up-to-date introduction to mathematical methods for students in the physical sciences Mathematical Methods in Physics, Engineering and Chemistry offers an introduction to the most important methods of theoretical physics. Written by two physics professors with years of experience, the text puts the focus on the essential math topics that the majority of physical science students require in the course of their studies. This concise text also contains worked examples that clearly illustrate the mathematical concepts presented and shows how they apply to physical problems. This targeted text covers a range of topics including linear algebra, partial differential equations, power series, Sturm-Liouville theory, Fourier series, special functions, complex analysis, the Green’s function method, integral equations, and tensor analysis. This important text: Provides a streamlined approach to the subject by putting the focus on the mathematical topics that physical science students really need Offers a text that is different from the often-found definition-theorem-proof scheme Includes more than 150 worked examples that help with an understanding of the problems presented Presents a guide with more than 200 exercises with different degrees of difficulty Written for advanced undergraduate and graduate students of physics, materials science, and engineering, Mathematical Methods in Physics, Engineering and Chemistry includes the essential methods of theoretical physics. The text is streamlined to provide only the most important mathematical concepts that apply to physical problems.
Non-Equilibrium Statistical Mechanics
by James H. LuscombeStatistical mechanics provides a framework for relating the properties of macroscopic systems (large collections of atoms, such as in a solid) to the microscopic properties of its parts. However, what happens when macroscopic systems are not in thermal equilibrium, where time is not only a relevant variable, but also essential?That is the province of nonequilibrium statistical mechanics – there are many ways for systems to be out of equilibrium! The subject is governed by fewer general principles than equilibrium statistical mechanics and consists of a number of different approaches for describing nonequilibrium systems.Financial markets are analyzed using methods of nonequilibrium statistical physics, such as the Fokker-Planck equation. Any system of sufficient complexity can be analyzed using the methods of nonequilibrium statistical mechanics. The Boltzmann equation is used frequently in the analysis of systems out of thermal equilibrium, from electron transport in semiconductors to modeling the early Universe following the Big Bang.This book provides an accessible yet very thorough introduction to nonequilibrium statistical mechanics, building on the author's years of teaching experience. Covering a broad range of advanced, extension topics, it can be used to support advanced courses on statistical mechanics, or as a supplementary text for core courses in this field.Key Features: Features a clear, accessible writing style which enables the author to take a sophisticated approach to the subject, but in a way that is suitable for advanced undergraduate students and above Presents foundations of probability theory and stochastic processes and treats principles and basic methods of kinetic theory and time correlation functions Accompanied by separate volumes on thermodynamics and equilibrium statistical mechanics, which can be used in conjunction with this book
Basic Concepts of String Theory (Theoretical and Mathematical Physics)
by Dieter Lüst Ralph Blumenhagen Stefan TheisenThe purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.
Modern Algebra Essentials
by Lufti A. LutfiyyaREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.
Rigid Geometry of Curves and Their Jacobians
by Werner LütkebohmertThis book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Integrodifference Equations in Spatial Ecology (Interdisciplinary Applied Mathematics #49)
by Frithjof LutscherThis book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.
Pricing of Derivatives on Mean-Reverting Assets
by Björn LutzThe topic of this book is the development of pricing formulae for European style derivatives on assets with mean-reverting behavior, especially commodity derivatives. For this class of assets, convenience yield effects lead to mean-reversion under the risk-neutral measure. Mean-reversion in the log-price process is combined with other stochastic factors such as stochastic volatility, jumps in the underlying and the price process and a stochastic target level as well as with deterministic seasonality effects. Another focus is on numerical algorithms to calculate the Fourier integral as well as to integrate systems of ordinary differential equations.
Description Logic, Theory Combination, and All That: Essays Dedicated to Franz Baader on the Occasion of His 60th Birthday (Lecture Notes in Computer Science #11560)
by Carsten Lutz Uli Sattler Cesare Tinelli Anni-Yasmin Turhan Frank WolterThis Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that readers will enjoy the articles gathered in Franz's honour and appreciate the breadth and depth of his favourite areas of computer science.
Diagnose und Förderung in der elementaren Algebra: Entwicklung eines Diagnoseinstrumentes und Vorbereitung eines Förderkonzeptes (Landauer Beiträge zur mathematikdidaktischen Forschung)
by Tim LutzDieser Band berichtet die Ergebnisse des Projektes aldiff, das sich mit der Erstellung automatisiert auswertbarer Diagnose- und Fördermaterialien am Übergang Schule-Hochschule beschäftigt. Kenntnisse der elementaren Algebra sind zentrale Befähigungsvoraussetzungen für Studierende des Bereichs MINT. Universitäten und Hochschulen bereiten seit Langem Studenten in eigens konzipierten Vorbereitungs- und Unterstützungskursen studienbegleitend vor. Bislang steht dabei eher die Vermittlung "kalküllastiger" Fertigkeiten im Vordergrund als die Erlangung verstehensorientierter Fähigkeiten. An dieser Problematik setzt das Projekt aldiff mit fachdidaktischer Forschung an. Auf Basis eines theoretischen Fähigkeitsmodells für die elementare Algebra und eines Aufgabenpools werden empirische Modelle entwickelt. Das vorgeschlagene Förderkonzept ermöglicht differenzierende adaptive Unterstützungsmaßnahmen zum Einsatz am Übergang Schule-Hochschule.
The Future Population of the World: What can we assume today (Health and Population Set)
by Wolfgang LutzThe highly acclaimed The Future Population of the World contains the most authoritative assessment available of the extent to which population is likely to grow over the next 50 to 100 years. The book provides a thorough analysis of all the components of population change and translates these factors into a series of projections for the population of the world's regions. This revised and updated version incorporates completely new scenario projections based on updating starting values and revised assumptions, plus several methodological improvements. It also contains the best currently available information on global trends in AIDS mortality and the first ever fully probabilistic world population projections. The projections, given up to 2100, add important additional features to those of the UN and the World Bank: they show the impacts of alternative assumptions for all three components (mortality and migration, as well as fertility); they explicitly take into account possible environmental limits to growth; and, for the first time, they define confidence levels for global populations. Combining methodological innovation with overviews of the most recent data and literature, this updated edition of The Future Population of the World is sure to conform its reputation as the most comprehensive and essential publication in the field.
Quantitative and Qualitative Methods in Psychotherapy Research (Explorations in Mental Health)
by Wolfgang Lutz Sarah KnoxIn this collection, international contributors come together to discuss how qualitative and quantitative methods can be used in psychotherapy research. The book considers the advantages and disadvantages of each approach, and recognises how each method can enhance our understanding of psychotherapy. Divided into two parts, the book begins with an examination of quantitative research and discusses how we can transfer observations into numbers and statistical findings. Chapters on quantitative methods cover the development of new findings and the improvement of existing findings, identifying and analysing change, and using meta-analysis. The second half of the book comprises chapters considering how qualitative and mixed methods can be used in psychotherapy research. Chapters on qualitative and mixed methods identify various ways to strengthen the trustworthiness of qualitative findings via rigorous data collection and analysis techniques. Adapted from a special issue of Psychotherapy Research, this volume will be key reading for researchers, academics, and professionals who want a greater understanding of how a particular area of research methods can be used in psychotherapy.
Intelligent Systems and Applications in Business and Finance (Studies in Fuzziness and Soft Computing #415)
by Pasi Luukka Jan StoklasaThis book presents a selection of current research results in the field of intelligent systems and draws attention to their practical applications and issues connected with the areas of decision-making, economics, business and finance. The nature of the contributions is interdisciplinary – combining psychological and behavioural aspects with the theory and practice of decision-support, design of intelligent systems and development of machine learning tools. The authors, among other topics, discuss the multi-expert evaluation with intangible criteria, suggest a redefinition of the standard multiple-criteria decision-making framework, propose novel methods for causal map analysis and new feature selection methods. The topics are selected to stress the potential of the up-to-date intelligent methods to deal with practical problems relevant in these areas and to provide inspiration for advanced students, researchers and practitioners in the respective fields.
Iterative Dynamic Programming (Monographs and Surveys in Pure and Applied Mathematics)
by Rein LuusDynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast computer resources, modifications to his original schem
Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences
by Maksym Luz Mikhail MoklyachukEstimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
Up for Debate!: Exploring Math Through Argument
by Chris LuzniakIn Up for Debate!: Exploring Math Through Argument, high school math teacher and debate coach Chris Luzniak shares stories, examples, and step-by-step routines that will help you build a classroom culture where students do the talking, explain their thinking, and critique each other's reasoning, all in the context of the math content you're expected to teach. Inside, you'll find: Inspirational stories of students debating math in real classroomsConcrete structures and routines that will get your students talking, listening, and debatingSpecific techniques you can use to transform existing math problems into debatable ones You'll begin with short speaking and listening routines that take just a few minutes to introduce. When you and your students are ready, you can layer on additional debate routines, until your class is engaged in full-class debates using mathematical reasoning. With this easy-to-read guide, you don't need to wait any longer. You will be able to start debating in your classroom, tomorrow.
Power-Based Study of Boundary Layer Ingestion for Aircraft Application (SpringerBriefs in Applied Sciences and Technology)
by Peijian LvThis book presents research on Boundary Layer Ingestion (BLI). BLI is an aircraft-engine integration technique that aims at integrating the aircraft and the propulsion system such that the overall aircraft fuel consumption can be reduced. In this research, theoretical analysis suggests that the minimization of total power consumption should be used as a design criterion for aircraft utilizing BLI rather than focusing on the minimization of drag. Numerical simulations are performed, and the simulation results are processed using the PBM to support the theoretical analysis. Furthermore, an experimental study is carried out with a focus on the power conversion processes involved for a propulsor operating in the wake. Stereoscopic PIV is employed in order to visualize the flow and understand the physics. The so-called Power-based Method is used to quantify the power conversion mechanisms. The results prove that the dominant mechanism responsible for the efficiency enhancement is due to the utilization of body wake energy by the wake ingesting propeller. In short, the importance of wake energy flow rate in understanding the BLI phenomenon is highlighted. This book will be useful for researchers in the field of aircraft propulsion, aircraft aerodynamics, and airframe propulsion integration.
Digital Twins: Basics and Applications
by Zhihan Lv Elena FersmanThis book comprehensively introduces readers to Digital Twins, from the basic concepts, core technologies and technical architecture, to application scenarios and other aspects. Readers will gain a profound understanding of the emerging discipline of Digital Twins. Covering the latest and cutting-edge application technologies of Digital Twins in various fields, the book offers practitioners concrete problem-solving strategies. At the same time, it helps those working in Digital Twins-related fields to deepen their understanding of the industry and enhance their professional knowledge and skills. Given its scope, the book can also be used as teaching material or a reference book for teachers and students of product design, industrial design, design management, design marketing and related disciplines at colleges and universities. Covering a variety of groundbreaking Digital Twins technologies, it can also provide new directions for researchers.
Economic Systems Analysis: Statistical Indicators (Studies in Systems, Decision and Control #158)
by Innara R. Lyapina Lilia A. Mikheykina Lyudmila V. Oveshnikova Elena V. SibirskayaThis book explores a wide range of issues related to the methodology, organization, and technologies of analytical work, showing the potential of using analytical tools and statistical indicators for studying socio-economic processes, forecasting, organizing effective companies, and improving managerial decisions. At the level of “living knowledge” in the broad context, it describes the essence of analytical technologies and means of applying analytical and statistical work. The book is of interest to readers regardless of their specialization: scientific research, medicine, pedagogics, law, administrative work, or economic practice. Starting from the premise that readers are familiar with the theory of statistics, which has formulated the general methods and principles of establishing the quantitative characteristics of mass phenomena and processes, it describes the concepts, definitions, indicators and classifications of socio-economic statistics, taking into consideration the international standards and the present-day practice of statistics in Russia. Although concise, the book provides plenty of study material as well as questions at the end of each chapter It is particularly useful for those interested in self-study or remote education, as well as business leaders who are interested in gaining a scientific understanding of their financial and economic activities.
Survey Measurement and Process Quality
by Lars Lyberg Paul Biemer Martin Collins Edith De Leeuw Cathryn Dippo Norbert Schwarz Dennis TrewinAn in-depth look at current issues, new research findings, and interdisciplinary exchange in survey methodology and processing Survey Measurement and Process Quality extends the marriage of traditional survey issues and continuous quality improvement further than any other contemporary volume. It documents the current state of the field, reports new research findings, and promotes interdisciplinary exchange in questionnaire design, data collection, data processing, quality assessment, and effects of errors on estimation and analysis. The book's five sections discuss a broad range of issues and topics in each of five major areas, including * Questionnaire design--conceptualization, design of rating scales for effective measurement, self-administered questionnaires, and more * Data collection--new technology, interviewer effects, interview mode, children as respondents * Post-survey processing and operations--modeling of classification operations, coding based on such systems, editing, integrating processes * Quality assessment and control--total quality management, developing current best methods, service quality, quality efforts across organizations * Effects of misclassification on estimation, analysis, and interpretation--misclassification and other measurement errors, new variance estimators that account for measurement error, estimators of nonsampling error components in interview surveys Survey Measurement and Process Quality is an indispensable resource for survey practitioners and managers as well as an excellent supplemental text for undergraduate and graduate courses and special seminars.
Numerical Linear Algebra and Matrix Factorizations (Texts in Computational Science and Engineering #22)
by Tom LycheAfter reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Exercises in Computational Mathematics with MATLAB
by Tom Lyche Jean-Louis MerrienDesigned to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.
Splines and PDEs: Cetraro, Italy 2017 (Lecture Notes in Mathematics #2219)
by Tom Lyche Giancarlo Sangalli Stefano Serra-Capizzano Angela Kunoth Carla Manni Hendrik SpeleersThis book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.
For Better or For Worse? Collaborative Couples in the Sciences
by Annette Lykknes Donald L. Opitz Brigitte Van TiggelenIn this volume, a distinguished set of international scholars examine the nature of collaboration between life partners in the sciences, with particular attention to the ways in which personal and professional dynamics can foster or inhibit scientific practice. Breaking from traditional gender analyses which focus on divisions of labor and the assignment of credit, the studies scrutinize collaboration as a variable process between partners living in the nineteenth and twentieth centuries who were married and divorced, heterosexual and homosexual, aristocratic and working-class and politically right and left. The contributors analyze cases shaped by their particular geographical locations, ranging from retreat settings like the English countryside and Woods Hole, Massachusetts, to university laboratories and urban centers in Berlin, Stockholm, Geneva and London. The volume demonstrates how the terms and meanings of collaboration, variably shaped by disciplinary imperatives, cultural mores, and the agency of the collaborators themselves, illuminate critical intellectual and institutional developments in the modern sciences.
Math Matters 3
by Chicha Lynch Eugene OlmsteadThis textbook is different from other math books because MathMatters combines mathematic topics in an integrated program. Number sense, algebra, geometry, statistics, and logic are presented as tools for investigating phenomena and exploring new math concepts. Each chapter has a theme. This theme is the focus of many application problems, the chapter career features, the chapter data activity and the chapter investigation.
