COMPLEX VARIABLES

THEORY AND APPLICATIONS

Author: H. S. KASANA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120326415

Category: Mathematics

Page: 504

View: 3801

The second edition of this comprehensive and accessible text continues to offer students a challenging and enjoyable study of complex variables that is infused with perfect balanced coverage of mathematical theory and applied topics. The author explains fundamental concepts and techniques with precision and introduces the students to complex variable theory through conceptual develop-ment of analysis that enables them to develop a thorough understanding of the topics discussed. Geometric interpretation of the results, wherever necessary, has been inducted for making the analysis more accessible. The level of the text assumes that the reader is acquainted with elementary real analysis. Beginning with the revision of the algebra of complex variables, the book moves on to deal with analytic functions, elementary functions, complex integration, sequences, series and infinite products, series expansions, singularities and residues. The application-oriented chapters on sums and integrals, conformal mappings, Laplace transform, and some special topics, provide a practical-use perspective. Enriched with many numerical examples and exercises designed to test the student's comprehension of the topics covered, this book is written for a one-semester course in complex variables for students in the science and engineering disciplines.
Posted in Mathematics

Fundamentals of Complex Analysis for Mathematics, Science, and Engineering

Author: E. B. Saff,Arthur David Snider

Publisher: N.A

ISBN: N.A

Category: Functions of complex variables.

Page: 468

View: 7774

Covers complex numbers, analytic functions, integration, residue theory, conformal mapping, and Fourier and Laplace transforms.
Posted in Functions of complex variables.

Schaum's Outline of Theory and Problems of Complex Variables

With an Introduction to Conformal Mapping and Its Applications

Author: Murray R. Spiegel

Publisher: McGraw Hill Professional

ISBN: 9780070602304

Category: Mathematics

Page: 313

View: 7630

This work is an introduction to the theory and practice of Business Statistics, a core course in business colleges, 4-year institutions, and MBA programmes. This updated edition includes more focus on Excel to reflect upon the change in the curriculum.
Posted in Mathematics

Holomorphic Operator Functions of One Variable and Applications

Methods from Complex Analysis in Several Variables

Author: Israel Gohberg,Jürgen Leiterer

Publisher: Springer Science & Business Media

ISBN: 3034601263

Category: Mathematics

Page: 424

View: 6595

This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.
Posted in Mathematics

The Implicit Function Theorem

History, Theory, and Applications

Author: Steven George Krantz,Harold R. Parks

Publisher: Springer Science & Business Media

ISBN: 9780817642853

Category: Mathematics

Page: 163

View: 2549

The implicit function theorem, part of the bedrock of mathematical analysis and geometry, has important implications in the theories of partial differential equations, differential geometry, and geometric analysis. Its history is lively and complex, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics.
Posted in Mathematics

Complex Variable Theory and Transform Calculus

With Technical Applications

Author: M. W. McLachlan

Publisher: Cambridge University Press

ISBN: 0521154154

Category: Mathematics

Page: 388

View: 8061

This book, first published in 1939, updated in 1953, explores the applications to mathematical problems in various branches of technology.
Posted in Mathematics

Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Author: Tianyou Fan

Publisher: Springer Science & Business Media

ISBN: 3642146430

Category: Technology & Engineering

Page: 350

View: 2657

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.
Posted in Technology & Engineering

Complex Analysis with Applications to Flows and Fields

Author: Luis Manuel Braga da Costa Campos

Publisher: CRC Press

ISBN: 1420071203

Category: Mathematics

Page: 1029

View: 2361

Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.
Posted in Mathematics

Clifford Algebras and Their Application in Mathematical Physics

Aachen 1996

Author: Volker Dietrich,Klaus Habetha,Gerhard Jank

Publisher: Springer Science & Business Media

ISBN: 9780792350378

Category: Mathematics

Page: 441

View: 6185

Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics. This book will appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.
Posted in Mathematics

Integral Theorems for Functions and Differential Forms in C(m)

Author: Reynaldo Rocha-Chavez,Michael Shapiro,Frank Sommen

Publisher: CRC Press

ISBN: 1420035517

Category: Mathematics

Page: 216

View: 1292

The theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories. The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain. In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.
Posted in Mathematics

Mathematical Techniques and Physical Applications

Author: J Killingbeck

Publisher: Elsevier

ISBN: 0323142826

Category: Science

Page: 736

View: 6301

Mathematical Techniques and Physical Applications provides a wide range of basic mathematical concepts and methods, which are relevant to physical theory. This book is divided into 10 chapters that cover the different branches of traditional mathematics. This book deals first with the concept of vector, matrix, and tensor analysis. These topics are followed by discussions on several theories of series relevant to physics; the fundamentals of complex variables and analytic functions; variational calculus for presenting the basic laws of many branches of physics; and the applications of group representations. The final chapters explore some partial and integral equations and derivatives of physics, as well as the concept and application of probability theory. Physics teachers and students will greatly appreciate this book.
Posted in Science

Complex Analysis and Applications

Proceedings of the 13th International Conference on Finite Or Infinite Dimensional Complex Analysis and Applications, Shantou University, China, 8-12 August 2005

Author: Yuefei Wang

Publisher: World Scientific

ISBN: 9812568689

Category: Mathematics

Page: 337

View: 8540

This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, Teichmller theory and Klainian groups, several complex variables, and value distribution theory.
Posted in Mathematics

Supermanifolds

Theory and Applications

Author: Alice Rogers

Publisher: World Scientific

ISBN: 9812708855

Category: Mathematics

Page: 251

View: 3762

This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory. The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory. Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.
Posted in Mathematics

Functional Equations: History, Applications and Theory

Author: J. Aczél

Publisher: Springer Science & Business Media

ISBN: 9781402003295

Category: Mathematics

Page: 246

View: 3933

Approach your problems from It isn't that they can't see the right end and begin with the solution. It is that they the answers. Then one day, can't see the problem. perhaps you will find the G.K. Chesterton. The Scandal of final question. Father Brown 'The Point of a Pin' . 'The Hermit Clad ~n Crane Feathers' in R. van Gulik's The Chinese Haze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) ~n re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are rele vant to filtering; and prediction and electrical en~ineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existinf, classifi~ation schemes. They draw upon widely different sections of mathematics.
Posted in Mathematics

History of Functional Analysis

Author: J. Dieudonne

Publisher: Elsevier

ISBN: 9780080871608

Category: Mathematics

Page: 311

View: 9574

History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition—one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the ""crypto-integral"" equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics.
Posted in Mathematics

Conformal Field Theories and Tensor Categories

Proceedings of a Workshop Held at Beijing International Center for Mathematical Research

Author: Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert

Publisher: Springer Science & Business Media

ISBN: 3642393837

Category: Mathematics

Page: 279

View: 5881

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Posted in Mathematics

Application of Holomorphic Functions in Two and Higher Dimensions

Author: Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig

Publisher: Springer

ISBN: 3034809646

Category: Mathematics

Page: 390

View: 952

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
Posted in Mathematics

Multidimensional Systems Theory and Applications

Author: N.K. Bose

Publisher: Springer Science & Business Media

ISBN: 9781402016233

Category: Technology & Engineering

Page: 269

View: 2523

The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.
Posted in Technology & Engineering

Microeconomics: Theory And Applications

Author: D. N. Dwivedi

Publisher: Pearson Education India

ISBN: 9788177586480

Category: Cost

Page: 644

View: 7316

This book is intended to be a comprehensive and standard textbook for undergraduate students of Microeconomics. Apart from providing students with sufficient study material for examination purpose, it aims at making them understand economics. An effort has been made to explain abstract and complex microeconomic theories in a simple and lucid language without sacrificing analytical sophistication. The subject matter has been structured in a systematic manner without leaving gaps for the readers to fill in. Though the approach is non-mathematical, simple algebra has been used to give a concrete view of economic concepts and theories and to show the applicability of economic theories in decision making.
Posted in Cost

Linear Theory of Colombeau Generalized Functions

Author: M Nedeljkov,S Pilipovic,D Scarpalezos

Publisher: CRC Press

ISBN: 9780582356832

Category: Mathematics

Page: 168

View: 2863

Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.
Posted in Mathematics