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Analytical Geometry of Three Dimensions: Second Revised Version
by William H. McCreaBrief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.
Analytical Groundwater Modeling: Theory and Applications using Python
by Mark Bakker Vincent PostThis book provides a detailed description of how Python can be used to give insight into the flow of groundwater based on analytic solutions. Starting with simple problems to illustrate the basic principles, complexity is added step by step to show how one-dimensional and two-dimensional models of one or two aquifers can be implemented. Steady and transient flow problems are discussed in confined, semi-confined, and unconfined aquifers that may include wells, rivers, and areal recharge. Special consideration is given to coastal aquifers, including the effect of tides and the simulation of interface flow. Application of Python allows for compact and readable code, and quick visualization of the solutions. Python scripts are provided to reproduce all results. The scripts are also available online so that they can be altered to meet site-specific conditions. This book is intended both as training material for the next generation of university students and as a useful resource for practitioners. A primer is included for those who are new to Python or as a refresher for existing users.
Analytical Mechanics: A Concise Textbook (UNITEXT for Physics)
by Sergio CecottiThis textbook is based on the author's lecture notes held at Qiuzhen College, Tsinghua University, Beijing, renowned for its rapid scientific growth of its excellent students. The book offers a remarkable combination of characteristics that are both exceptional and seemingly contradictory. It is designed to be entirely self-contained, starting from the basics and building a strong foundation in geometric and algebraic tools. Simultaneously, topics are infused with mathematical elegance and profundity, employing contemporary language and techniques. From a physicist's perspective, the content delves deeply into the physical aspects, emphasizing the underlying principles. This book bridges the gap between students and cutting-edge research, with a special focus on symplectic geometry, integrability, and recent developments in the field. It is designed to engage and captivate the reader. A conscious selection of topics ensures a more relevant and contemporary approach compared to traditional textbooks. The book addresses common misconceptions, offering clarity and precision. In its quest for brevity, this book is tailored for a one-semester course, offering a comprehensive and concise resource. The author's dedication is evident throughout this volume, encapsulating these goals within roughly 300 pages.
An Analytical Mechanics Framework for Flow-Oscillator Modeling of Vortex-Induced Bluff-Body Oscillations (Solid Mechanics and Its Applications #260)
by Sohrob Mottaghi Rene Gabbai Haym BenaroyaThis self-contained book provides an introduction to the flow-oscillator modeling of vortex-induced bluff-body oscillations. One of the great challenges in engineering science also happens to be one of engineering design – the modeling, analysis and design of vibrating structures driven by fluid motion. The literature on fluid–structure interaction is vast, and it can be said to comprise a large fraction of all papers published in the mechanical sciences. This book focuses on the vortex-induced oscillations of an immersed body, since, although the importance of the subject has long been known, it is only during the past fifty years that there have been concerted efforts to analytically model the general behavior of the coupling between vortex shedding and structural oscillations. At the same time, experimentalists have been gathering data on such interactions in order to help define the various regimes of behavior. This data is critical to our understanding and to those who develop analytical models, as can be seen in this book. The fundamental bases for the modeling developed in this book are the variational principles of analytical dynamics, in particular Hamilton’s principle and Jourdain’s principle, considered great intellectual achievements on par with Newton’s laws of motion. Variational principles have been applied in numerous disciplines, including dynamics, optics and quantum mechanics. Here, we apply variational principles to the development of a framework for the modeling of flow-oscillator models of vortex-induced oscillations.
Analytical Mechanics (Seventh Edition)
by Grant R. Fowles George L. CassidayThis textbook is intended for an undergraduate course in classical mechanics taken by students majoring in physics, physical science, or engineering.
Analytical Methods for Kolmogorov Equations (Chapman & Hall/CRC Monographs and Research Notes in Mathematics #25)
by Luca LorenziThe second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.
Analytical Methods for Risk Management: A Systems Engineering Perspective (Statistics: A Series of Textbooks and Monographs)
by Paul R. GarveyA Text on the Foundation Processes, Analytical Principles, and Implementation Practices of Engineering Risk ManagementDrawing from the author's many years of hands-on experience in the field, Analytical Methods for Risk Management: A Systems Engineering Perspectivepresents the foundation processes and analytical practices
Analytical Methods in Applied Mathematics (Problem Books in Mathematics)
by Edmundo Capelas de Oliveira José Emílio MaiorinoThis book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering. The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green's function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented. With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.
Analytical Methods In Corrosion Science and Engineering (Corrosion Technology)
by Philippe Marcus Florian MansfeldDamage from corrosion costs billions of dollars per year. Controlling corrosion requires a fundamental, in-depth understanding of the mechanisms and phenomena involved, and this understanding is best achieved through advanced analytical methods. The first book to treat both surface analytical and electrochemical techniques in a single reference, An
Analytical Methods in Physics
by Luiza AnghelutaThis textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo. This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.
Analytical Methods in Rotor Dynamics: Second Edition (Mechanisms and Machine Science #9)
by Thomas G. Chondros Stefanos A. Paipetis Andrew D. DimarogonasThe design and construction of rotating machinery operating at supercritical speeds was, in the 1920s, an event of revolutionary importance for the then new branch of dynamics known as rotor dynamics. In the 1960s, another revolution occurred: In less than a decade, imposed by operational and economic needs, an increase in the power of turbomachinery by one order of magnitude took place. Dynamic analysis of complex rotor forms became a necessity, while the importance of approximate methods for dynamic analysis was stressed. Finally, the emergence of fracture mechanics, as a new branch of applied mechanics, provided analytical tools to investigate crack influence on the dynamic behavior of rotors. The scope of this book is based on all these developments. No topics related to the well-known classical problems are included, rather the book deals exclusively with modern high-power turbomachinery.
Analytical Methods in Statistics: AMISTAT, Liberec, Czech Republic, September 2019 (Springer Proceedings in Mathematics & Statistics #329)
by Matúš Maciak Michal Pešta Martin SchindlerThis book collects peer-reviewed contributions on modern statistical methods and topics, stemming from the third workshop on Analytical Methods in Statistics, AMISTAT 2019, held in Liberec, Czech Republic, on September 16-19, 2019. Real-life problems demand statistical solutions, which in turn require new and profound mathematical methods. As such, the book is not only a collection of solved problems but also a source of new methods and their practical extensions. The authoritative contributions focus on analytical methods in statistics, asymptotics, estimation and Fisher information, robustness, stochastic models and inequalities, and other related fields; further, they address e.g. average autoregression quantiles, neural networks, weighted empirical minimum distance estimators, implied volatility surface estimation, the Grenander estimator, non-Gaussian component analysis, meta learning, and high-dimensional errors-in-variables models.
Analytical Methods of Optimization (Dover Books on Mathematics)
by D. F. LawdenSuitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. It takes the approach most appropriate for applications to problems of optimizing the behavior of engineering systems. Two of these problem areas have strongly influenced this presentation: the design of the control systems and the choice of rocket trajectories to be followed by terrestrial and extraterrestrial vehicles.Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Prerequisites include a course in the analysis of functions of many real variables and a familiarity with the elementary theory of ordinary differential equations, especially linear equations. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. Solutions to the exercises are available from the publisher upon request.
Analytical Properties of Nonlinear Partial Differential Equations: with Applications to Shallow Water Models (CMS/CAIMS Books in Mathematics #10)
by Shanghai Maritime University Alexei CheviakovNonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Analytical Similarity Assessment in Biosimilar Product Development
by Shein-Chung ChowThis book focuses on analytical similarity assessment in biosimilar product development following the FDA’s recommended stepwise approach for obtaining totality-of-the-evidence for approval of biosimilar products. It covers concepts such as the tiered approach for assessment of similarity of critical quality attributes in the manufacturing process of biosimilar products, models/methods like the statistical model for classification of critical quality attributes, equivalence tests for critical quality attributes in Tier 1 and the corresponding sample size requirements, current issues, and recent developments in analytical similarity assessment.
Analytical Solutions for Transport Processes: Fluid Mechanics, Heat and Mass Transfer (Mathematical Engineering)
by Günter BrennThis monograph provides analytical solutions to a number of classical problems in transport processes, i. e. in fluid mechanics, heat and mass transfer. Increasing computing power and efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results. This is why the analytical solutions are of high value. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena of a given process than the corresponding numerical solution. The target audience primarily comprises researcher and practitioners but the book may also be beneficial for graduate students who want to enter the field.
Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs (Lecture Notes in Mathematics #2334)
by Dinh Dũng Van Kien Nguyen Christoph Schwab Jakob ZechThe present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered.Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain.The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.
Analytics and Data Science: Advances in Research and Pedagogy (Annals of Information Systems #21)
by Ashish Gupta Lakshmi S. Iyer Amit V. Deokar Mary C. JonesThis book explores emerging research and pedagogy in analytics and data science that have become core to many businesses as they work to derive value from data. The chapters examine the role of analytics and data science to create, spread, develop and utilize analytics applications for practice. Selected chapters provide a good balance between discussing research advances and pedagogical tools in key topic areas in analytics and data science in a systematic manner. This book also focuses on several business applications of these emerging technologies in decision making, i. e. , business analytics. The chapters in Analytics and Data Science: Advances in Research and Pedagogy are written by leading academics and practitioners that participated at the Business Analytics Congress 2015. Applications of analytics and data science technologies in various domains are still evolving. For instance, the explosive growth in big data and social media analytics requires examination of the impact of these technologies and applications on business and society. As organizations in various sectors formulate their IT strategies and investments, it is imperative to understand how various analytics and data science approaches contribute to the improvements in organizational information processing and decision making. Recent advances in computational capacities coupled by improvements in areas such as data warehousing, big data, analytics, semantics, predictive and descriptive analytics, visualization, and real-time analytics have particularly strong implications on the growth of analytics and data science.
Analytics and Knowledge Management (Data Analytics Applications)
by Suliman Hawamdeh and Hsia-Ching ChangThe process of transforming data into actionable knowledge is a complex process that requires the use of powerful machines and advanced analytics technique. Analytics and Knowledge Management examines the role of analytics in knowledge management and the integration of big data theories, methods, and techniques into an organizational knowledge management framework. Its chapters written by researchers and professionals provide insight into theories, models, techniques, and applications with case studies examining the use of analytics in organizations. The process of transforming data into actionable knowledge is a complex process that requires the use of powerful machines and advanced analytics techniques. Analytics, on the other hand, is the examination, interpretation, and discovery of meaningful patterns, trends, and knowledge from data and textual information. It provides the basis for knowledge discovery and completes the cycle in which knowledge management and knowledge utilization happen. Organizations should develop knowledge focuses on data quality, application domain, selecting analytics techniques, and on how to take actions based on patterns and insights derived from analytics. Case studies in the book explore how to perform analytics on social networking and user-based data to develop knowledge. One case explores analyze data from Twitter feeds. Another examines the analysis of data obtained through user feedback. One chapter introduces the definitions and processes of social media analytics from different perspectives as well as focuses on techniques and tools used for social media analytics. Data visualization has a critical role in the advancement of modern data analytics, particularly in the field of business intelligence and analytics. It can guide managers in understanding market trends and customer purchasing patterns over time. The book illustrates various data visualization tools that can support answering different types of business questions to improve profits and customer relationships. This insightful reference concludes with a chapter on the critical issue of cybersecurity. It examines the process of collecting and organizing data as well as reviewing various tools for text analysis and data analytics and discusses dealing with collections of large datasets and a great deal of diverse data types from legacy system to social networks platforms.
Analytics And Modern Warfare: Dominance by the Numbers
by Michael TaillardThis book details very simply and for even the most novice of potential analysts not only how to perform analytics which describe what is happening, predict what is going to happen, and optimize responses, but also places these analytics in the context of proactive strategy development.
Analytics for Managers: With Excel
by Gregory S. Zaric Peter C. BellAnalytics is one of a number of terms which are used to describe a data-driven more scientific approach to management. Ability in analytics is an essential management skill: knowledge of data and analytics helps the manager to analyze decision situations, prevent problem situations from arising, identify new opportunities, and often enables many millions of dollars to be added to the bottom line for the organization. The objective of this book is to introduce analytics from the perspective of the general manager of a corporation. Rather than examine the details or attempt an encyclopaedic review of the field, this text emphasizes the strategic role that analytics is playing in globally competitive corporations today. The chapters of this book are organized in two main parts. The first part introduces a problem area and presents some basic analytical concepts that have been successfully used to address the problem area. The objective of this material is to provide the student, the manager of the future, with a general understanding of the tools and techniques used by the analyst.
Analytics, Machine Learning, and Artificial Intelligence: Second Analytics Global Conference, AGC 2024, Kolkata, India, March 6–7, 2024, Revised Selected Papers (Communications in Computer and Information Science #2224)
by Suparna Dhar Sanjay Goswami Dinesh Kumar Unni Krishnan Indranil Bose Rameshwar Dubey Chandan MazumdarThis book constitutes the refereed proceedings of the Second Analytics Global Conference on Analytics, Machine Learning, and Artificial Intelligence, AGC 2024, held in Kolkata, India, during March 6-7, 2024. The 15 full papers and 3 short papers presented in these proceedings were carefully reviewed and selected from 60 submissions. The papers are organized in these topical sections: applications of analytics in business; analytics methods, tools & techniques.
Analytics Modeling in Reliability and Machine Learning and Its Applications (Springer Series in Reliability Engineering)
by Hoang PhamThis book presents novel research and application chapters on topics in reliability, statistics, and machine learning. It has an emphasis on analytical models and techniques and practical applications in reliability engineering, data science, manufacturing, health care, and industry using machine learning, AI, optimization, and other computational methods. Today, billions of people are connected to each other through their mobile devices. Data is being collected and analysed more than ever before. The era of big data through machine learning algorithms, statistical inference, and reliability computing in almost all applications has resulted in a dramatic shift in the past two decades. Data analytics in business, finance, and industry is vital. It helps organizations and business to achieve better results and fact-based decision-making in all aspects of life. The book offers a broad picture of current research on the analytics modeling and techniques and its applications in industry. Topics include: l Reliability modeling and methods. l Software reliability engineering. l Maintenance modeling and policies. l Statistical feature selection. l Big data modeling. l Machine learning: models and algorithms. l Data-driven models and decision-making methods. l Applications and case studies in business, health care, and industrial systems. Postgraduates, researchers, professors, scientists, engineers, and practitioners in reliability engineering and management, machine learning engineering, data science, operations research, industrial and systems engineering, statistics, computer science and engineering, mechanical engineering, and business analytics will find in this book state-of-the-art analytics, modeling and methods in reliability and machine learning.
Analytische Transmissionselektronenmikroskopie: Eine praxisbezogene Einführung
by Jürgen Thomas Thomas GemmingDas Buch wendet sich an alle, egal ob im Studium, in technischen Berufen, oder in der Wissenschaft, die die sich für die analytische Transmissionselektronenmikroskopie interessieren und einen Überblick über diese Methode erhalten möchten. Insbesondere betrifft dies Personen, die an einem Transmissionselektronenmikroskop arbeiten wollen oder müssen, die aber noch keine spezielle elektronenmikroskopische Ausbildung durchlaufen haben. Das Buch basiert auf den Erfahrungen der Autoren bei der Unterrichtung von Studierenden, Promovierenden und in technischen Berufen Tätigen. Der Überblick über die analytische Transmissionselektronenmikroskopie umfasst die Schwerpunkte Optische Abbildung, Elektronenwellen, magnetische Linsen, Abbildungsfehler, Aufbau eines Transmissionselektronenmikroskops, Präparation dünner Proben, Justage des Mikroskops, Elektronenbeugung, Kontrastentstehung, Höchstauflösungselektronenmikroskopie, Rastertransmissionselektronenmikroskopie sowie Analytik mittels energiedispersiver Röntgenspektroskopie und Elektronenenergieverlust-Spektroskopie. Ein mathematischer Anhang erklärt grundlegende Formalismen zur Thematik.
Analyzing and Modeling Rank Data (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by John I MardenThis book is the first single source volume to fully address this prevalent practice in both its analytical and modeling aspects. The information discussed presents the use of data consisting of rankings in such diverse fields as psychology, animal science, educational testing, sociology, economics, and biology. This book systematically presents th