Applied Complex Variables

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in 1982. It was intended be a synthesis of those topics and a broad introduction to the field. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a further knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts were designed to provide an introduction to the more advanced works in the subject.

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading exper

This book is designed as a textbook for a first course on functions of a complex variable. It introduces the fundamental idea of complex numbers and complex variables leading to different tools of com

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex ana

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex ana

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variabl

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variabl

This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single

Complex Systems and Applied Linguistics introduces key concepts in complexity theory to readers concerned with language, its learning, and its use. The book demonstrates the applicability and usefulne

This book moves systematically through the topic of applied probability from an introductory chapter to such topics as random variables and vectors, stochastic processes, estimation, testing and regre

Multivariate analysis plays an important role in the understanding of complex data sets requiring simultaneous examination of all variables. Breaking through the apparent disorder of the information,

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of math

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solut

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayas

Applied Theatre: Creative Ageing examines the complex social, political and cultural needs of a diverse group in our society and asks how contemporary applied theatre responds to those needs. For the

We live in a complex and dynamic world. Understanding how to monitor, manage and conserve species and habitats--the goal of applied ecology--is becoming increasingly important. Applied Ecology shows s

Complex software systems have been designed to efficiently handle large numbers of variables. In manufacturing, variables affect every part of the supply chain from inventory to production to delivery

Complex software systems have been designed to efficiently handle large numbers of variables. In manufacturing, variables affect every part of the supply chain from inventory to production to delivery

This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are

This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black–Merton–Schole

An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scient

Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the t

This book provides practical guidance on research methods and designs that can be applied to Complex Dynamic Systems Theory (CDST) research. It discusses the contribution of CDST to the field of appli

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

The Little Quick Fix on how to Identify Your Variables unlocks the gate to simple data analysis for any stats course. Packed with lively examples it shows students what variables a

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeco

As most econometricians will readily agree, the data used in applied econometrics seldom provide accurate measurements for the pertinent theory's variables. Here, Bernt Stigum offers the first systema

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappie, Koppelman, multidimensional logarithmic resid

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

Fourier Analysis with Complex Variables explains transform methods and their application to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space con

This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fund

Addressing a hugely diverse range of topics, both fundamental and applied, this anthology of papers from leading researchers in non-linear and complex dynamics honors the seminal contributions to the

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

Kapoor (U. of Hyderabad, India) finds the theory of functions of a complex variable to be one of those areas of mathematics that were created for reasons not even remotely connected to any practical,