Complex Variables

This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, d

This Book begins with the basics of geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, diffe

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Study faster, learn better, and get top grades Modified to conform to the current curriculum, Schaum's Outline of Probability, Random Variables, and Random Processes complements these courses in scop

Methods for more planet-friendly process engineering Our earth is just one big, complex Process Facility with limited air, water, and mineral resources. It responds to a number of process variables—a

Decision making is a critical element in the field of medicine that can lead to life-or-death outcomes, yet it is an element fraught with complex and conflicting variables, diagnostic and therapeutic

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

This graduate-level treatment of aerodynamic theory opens with a survey of vector analysis and complex variables that presents readers with the basic tools for handling subsequent chapters. Topics inc

Ecological and environmental research has increased in scope and complexity in the last few decades, from simple systems with a few managed variables to complex ecosystems with many uncontrolled vari

Ecological and environmental research has increased in scope and complexity in the last few decades, from simple systems with a few managed variables to complex ecosystems with many uncontrolled vari

Introduces the algebraic equation and variables using examples relating to flight.

Logistic Regression Models for Ordinal Response Variables provides applied researchers in the social, educational, and behavioral sciences with an accessible and comprehensive coverage of analyses fo

Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and

Governed by strict regulations and the intricate balance of complex interactions among variables, the application of mechanics to vehicle crashworthiness is not a simple task. It demands a solid under

This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book prese

The task of management has become increasingly complex in recent years. Chief executives and senior managers are confronted with the daunting challenge of making sense of a myriad of variables that

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

This book presents the econometric analysis of single-equation and simultaneous-equation models in which the jointly dependent variables can be continuous, categorical, or truncated. Despite the traditional emphasis on continuous variables in econometrics, many of the economic variables encountered in practice are categorical (those for which a suitable category can be found but where no actual measurement exists) or truncated (those that can be observed only in certain ranges). Such variables are involved, for example, in models of occupational choice, choice of tenure in housing, and choice of type of schooling. Models with regulated prices and rationing, and models for program evaluation, also represent areas of application for the techniques presented by the author.

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

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This book introduces the reader to a wide range of topics in the theory of holomorphic functions of several variables, with fairly complete proofs. It reviews the relevant properties of subharmonic fu

Production of world food supplies is related to more complicated socioeconomic variables than have previously been analyzed. Besides traditional inputs of land, labor, and fertilizer, the technologica

The upheavals of recent decades show us that traditional models of understanding processes of social and economic change are failing to capture real-world risk and volatility. This has resulted in flawed policy that seeks to capture change in terms of the rise or decline of regimes or regions. In order to comprehend current events, understand future risks and decide how to prepare for them, we need to consider economies and social orders as open, complex networks. This highly original work uses the tools of network analysis to understand great transitions in history, particularly those concerning economic development and globalisation. Hilton L. Root shifts attention away from particular agents – whether individuals, groups, nations or policy interventions – and toward their dynamic interactions. Applying insights from complexity science to often overlooked variables across European and Chinese history, he explores the implications of China's unique trajectory and ascendency, as a comp

Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this

Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtain

This book presents an overview of the different errors-in-variables (EIV) methods that can be used for system identification. Readers will explore the properties of an EIV problem. Such problems play

A concise monograph by two Russian experts provides an account of the operational calculus in two variables based on the two-dimensional Laplace transform. Suitable for advanced undergraduates and gra

This book introduces the reader to the vast area of research focusing on quantum mechanical systems described by continuous variables, such as positions and momenta of particles, which provide the the

What Makes Variables Random: Probability for the Applied Researcher provides an introduction to the foundations of probability that underlie the statistical analyses used in applied research. By expla

This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

This book offers a unified perspective on the study of complex systems for scholars of various disciplines, including mathematics, physics, computer science, biology, economics and social science. The contributions, written by leading scientists, cover a broad set of topics, including new approaches to data science, the connection between scaling limits and conformal field theories, and new ideas on the Legendre duality approach in statistical mechanics of disordered systems. The volume moreover explores results on extreme values of correlated random variables and their connection with the Riemann zeta functions, the relation between diffusion phenomena and complex systems, and the Brownian web, which appears as the universal scaling limit of several probabilistic models. Written for researchers from a broad range of scientific fields, this text examines a selection of recent developments in complex systems from a rigorous perspective.

This valuable compendium provides an overview of the variables and consequences of oceanic carbon cycling in the context of climate change. The chapters highlight the importance of marine plankton in

Seven of the eleven papers in this collection explain how to estimate discrete dependent variables with spatial dependence using maximum likelihood and how to estimate binary and count dependent va

Predictive modeling uses data to forecast future events. It exploits relationships between explanatory variables and the predicted variables from past occurrences to predict future outcomes. Forecasting financial events is a core skill that actuaries routinely apply in insurance and other risk-management applications. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used to gain a competitive advantage in situations with complex data. Volume 2 examines applications of predictive modeling. Where Volume 1 developed the foundations of predictive modeling, Volume 2 explores practical uses for techniques, focusing on property and casualty insurance. Readers are exposed to a variety of techniques in concrete, real-life contexts that demonstrate their value and the overall value of predictive modeling, for se

This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical syst

The first study of its kind, Regional Variation in Written American English takes a corpus-based approach to map over one hundred grammatical alternation variables across the United States. A multivariate spatial analysis of these maps shows that grammatical alternation variables follow a relatively small number of common regional patterns in American English, which can be explained based on both linguistic and extra-linguistic factors. Based on this rigorous analysis of extensive data, Grieve identifies five primary modern American dialect regions, demonstrating that regional variation is far more pervasive and complex in natural language than is generally assumed. The wealth of maps and data, and the groundbreaking implications of this volume, make it essential reading for students and researchers in linguistics, English language, geography, computer science, sociology and communication studies.

Measuring Non Cognitive Variables: Improving Admissions and Post Enrollment Services in Higher Education is written for admissions professionals, counselors, faculty and advisors who admit, teach, or

Measuring Non Cognitive Variables: Improving Admissions and Post Enrollment Services in Higher Education is written for admissions professionals, counselors, faculty and advisors who admit, teach, or

Principles of Measurement and Transduction of Biomedical Variables is a comprehensive text on biomedical transducers covering the principles of functioning, application examples and new technology sol

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in