Classical Complex Analysis

Suitable for upper-level undergraduates and graduate students, this treatment of complex analysis focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes do

This 2007 book provides a systematic and self-contained account of the fast-developing theory of complex social networks. Social networks are central to the understanding of most socio-economic phenomena in the modern world. The classical approach to studying them relies on a methodology that abstracts from their size and complexity. In contrast, the approach taken in this book keeps complexity at the core, whilst integrating it with the incentive considerations that are preeminent in traditional economic analysis. The treatment starts with a detailed discussion of the basic models that act as 'benchmarks' for the complex-network literature: random networks, small worlds, and scale-free networks, before studying three different forces that underlie almost all network phenomena in social contexts: diffusion, search, and play. Finally, these forces are combined into a unified framework that is brought to bear on the issue of network formation and the coevolution of agents' behaviour and

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tens

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

Presented from the point of view of modern work in the field, this book addresses advanced topics in complex analysis that verge on current areas of research. It adroitly weaves through a variety of t

In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of m

Large surveys are becoming increasingly available for public use, and researchers are often faced with the need to analyse complex survey data to address key scientific issues. For proper analysis it

The intricacies of Chinese classical theater receive expert analysis in this reliable and practical handbook. Beginning with an introduction to the history and development of the Peking Theater, the

All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at underg

A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more comp

This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

A comprehensive introduction to syntactical analysis of Classical Chinese, focusing on the language of the high classical period and particularly the Mencius , the L·nyu , and the Zuozhuan texts.

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.

A number of monographs of various aspects of complex analysis in several variables have appeared since the first version of this book was published, but none of them uses the analytic techniques based

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

An international conference on complex analysis was held in Canterbury in July 1973. Some of the world's most prominent complex analysts attended and some outstanding open problems had their first solutions announced there. These are reflected in this set of Proceedings. Almost all of the contributions are abstracts of talks given at the symposium. The final part of this volume is a section on research problems contributed by members of the conference and a report on a previous collection of problems edited by Professor W. K. Hayman after an earlier conference in 1964. This book is essential reading for research workers and graduate students interested in complex analysis.

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and

This book presents the statistical analysis of compositional data using the log-ratio approach. It includes a wide range of classical and robust statistical methods adapted for compositional data anal

Explores and brings together the existent body of knowledge on building performance analysis Building performance is an important yet surprisingly complex concept. This book presents a comprehensive a

This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses

Quantitative analysis of outcomes vs PMs at the individual level Leading Complex Projects takes a unique approach to post-mortem analysis to provide project managers with invaluable insight. For the f

This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts develop

Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with r

This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was

This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the the

Introducing a revolutionary new model for the statistical analysis of experimental data In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical ana

This monograph contains expert knowledge on complex fluid-flows in microfluidic devices. The topical spectrum includes, but is not limited to, aspects such as the analysis, experimental characterizati

This book is the first to combine principles from analytics, complex systems theory, multi-disciplinary diagnostics and sport performance analysis. It considers athletes, teams, and sport organization

This book examines and critiques classical approaches to strategic analysis, whilst exploring alternative methods which utilise ecosystem and platform concepts, as well as chaos and complexity theorie

The frames of classical art are often seen as marginal to the images that they surround. Traditional art history has tended to view framing devices as supplementary 'ornaments'. Likewise, classical archaeologists have often treated them as tools for taxonomic analysis. This book not only argues for the integral role of framing within Graeco-Roman art, but also explores the relationship between the frames of classical antiquity and those of more modern art and aesthetics. Contributors combine close formal analysis with more theoretical approaches: chapters examine framing devices across multiple media (including vase and fresco painting, relief and free-standing sculpture, mosaics, manuscripts and inscriptions), structuring analysis around the themes of 'framing pictorial space', 'framing bodies', 'framing the sacred' and 'framing texts'. The result is a new cultural history of framing - one that probes the sophisticated and playful ways in which frames could support, delimit, shape and

As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theor

Animals were omnipresent in the everyday life of classical Greece, and its culture was not merely anthropocentric. Through close textual analysis of ancient Greek literature, the authors present a nua

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

Inequalities in Analysis and Probability is a must for graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and

This book introduces a theory of music analysis that one can use to explore aspects of segmentation and associative organization in a wide range of repertoire including Western classical music from th

This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical

Going beyond performing simple analyses, researchers involved in the highly dynamic field of computational intelligent data analysis design algorithms that solve increasingly complex data problems in