Complex Analysis

Author: Eberhard Freitag,Rolf Busam

Publisher: Springer Science & Business Media

ISBN: 3540939830

Category: Mathematics

Page: 532

View: 3821

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included
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Complex Analysis 2

Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions

Author: Eberhard Freitag

Publisher: Springer Science & Business Media

ISBN: 9783642205545

Category: Mathematics

Page: 506

View: 6548

The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̀„rst volume. There is no comparable treatment in the literature.
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Complex Analysis

A Functional Analysis Approach

Author: D.H. Luecking,L.A. Rubel

Publisher: Springer Science & Business Media

ISBN: 1461382955

Category: Mathematics

Page: 176

View: 2620

The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.
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Complex Variables

An Introduction

Author: Carlos A. Berenstein,Roger Gay

Publisher: Springer Science & Business Media

ISBN: 1461230241

Category: Mathematics

Page: 652

View: 7751

Textbooks, even excellent ones, are a reflection of their times. Form and content of books depend on what the students know already, what they are expected to learn, how the subject matter is regarded in relation to other divisions of mathematics, and even how fashionable the subject matter is. It is thus not surprising that we no longer use such masterpieces as Hurwitz and Courant's Funktionentheorie or Jordan's Cours d'Analyse in our courses. The last two decades have seen a significant change in the techniques used in the theory of functions of one complex variable. The important role played by the inhomogeneous Cauchy-Riemann equation in the current research has led to the reunification, at least in their spirit, of complex analysis in one and in several variables. We say reunification since we think that Weierstrass, Poincare, and others (in contrast to many of our students) did not consider them to be entirely separate subjects. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other subjects from the classic theory of functions of one complex variable. This ongoing reconsideration led us to think that a textbook incorporating some of these new perspectives and techniques had to be written.
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Complex Analysis

Author: Ian Stewart,David Tall

Publisher: Cambridge University Press

ISBN: 110843679X

Category: Mathematics

Page: 330

View: 6404

A new edition of a classic textbook on complex analysis with an emphasis on translating visual intuition to rigorous proof.
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Introductory Complex Analysis

Author: Richard A. Silverman

Publisher: Courier Corporation

ISBN: 0486318524

Category: Mathematics

Page: 400

View: 5837

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.
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COMPLEX VARIABLES

THEORY AND APPLICATIONS

Author: H. S. KASANA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120326415

Category: Mathematics

Page: 504

View: 3562

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.
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Complex Analysis

Author: Joseph Bak,Donald J. Newman

Publisher: Springer Science & Business Media

ISBN: 9781441972880

Category: Mathematics

Page: 328

View: 7896

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-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.
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Mathematical Analysis I

Author: V. A. Zorich

Publisher: Springer

ISBN: 3662487926

Category: Mathematics

Page: 616

View: 7506

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.
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Function Theory of Several Complex Variables

Author: Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821827243

Category: Mathematics

Page: 564

View: 2005

The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.
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Functions of One Complex Variable I

Author: John B. Conway

Publisher: Springer Science & Business Media

ISBN: 1461263131

Category: Mathematics

Page: 322

View: 731

"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET
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Analysis

Author: Elliott H. Lieb,Michael Loss

Publisher: American Mathematical Soc.

ISBN: 0821827839

Category: Mathematics

Page: 346

View: 9980

This is an excellent textbook on analysis and it has several unique features: Proofs of heat kernel estimates, the Nash inequality and the logarithmic Sobolev inequality are topics that are seldom treated on the level of a textbook. Best constants in several inequalities, such as Young's inequality and the logarithmic Sobolev inequality, are also included. A thorough treatment of rearrangement inequalities and competing symmetries appears in book form for the first time. There is an extensive treatment of potential theory and its applications to quantum mechanics, which, again, is unique at this level. Uniform convexity of $L^p$ space is treated very carefully. The presentation of this important subject is highly unusual for a textbook. All the proofs provide deep insights into the theorems. This book sets a new standard for a graduate textbook in analysis. --Shing-Tung Yau, Harvard University For some number of years, Rudin's ``Real and Complex'', and a few other analysis books, served as the canonical choice for the book to use, and to teach from, in a first year grad analysis course. Lieb-Loss offers a refreshing alternative: It begins with a down-to-earth intro to measure theory, $L^p$ and all that ... It aims at a wide range of essential applications, such as the Fourier transform, and series, inequalities, distributions, and Sobolev spaces--PDE, potential theory, calculus of variations, and math physics (Schrodinger's equation, the hydrogen atom, Thomas-Fermi theory ... to mention a few). The book should work equally well in a one-, or in a two-semester course. The first half of the book covers the basics, and the rest will be great for students to have, regardless of whether or not it gets to be included in a course. --Palle E. T. Jorgensen, University of Iowa
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A First Course in Discrete Dynamical Systems

Author: Richard A. Holmgren

Publisher: Springer Science & Business Media

ISBN: 1441987320

Category: Mathematics

Page: 223

View: 496

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.
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Complex Analysis and Applications, Second Edition

Author: Alan Jeffrey

Publisher: CRC Press

ISBN: 158488553X

Category: Mathematics

Page: 592

View: 5764

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 theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.
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Complex Analysis

Author: Dennis G. Zill,Patrick D. Shanahan

Publisher: Jones & Bartlett Publishers

ISBN: 1449694624

Category: Mathematics

Page: 475

View: 4210

Complex Analysis: A First Course with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section devoted exclusively to the applications of complex analysis to science and engineering, providing students with the opportunity to develop a practical and clear understanding of complex analysis. New and Key Features: Clarity of exposition supported by numerous examples Extensive exercise sets with a mix of computational and conceptual problems Applications to science and engineering throughout the text New and revised problems and exercise sets throughout Portions of the text and examples have been revised or rewritten to clarify or expand upon the topics at hand The Mathematica syntax from the second edition has been updated to coincide with version 8 of the software.
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Complex Geometry

An Introduction

Author: Daniel Huybrechts

Publisher: Springer Science & Business Media

ISBN: 3540266879

Category: Mathematics

Page: 309

View: 2335

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
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Classical Complex Analysis

Author: Liang-shin Hahn,Bernard Epstein

Publisher: Royal Society of Chemistry

ISBN: 9780867204940

Category: Computers

Page: 411

View: 8948

Classic Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter on power series gives the reader concrete examples of analytic functions and a review of calculus. Mobius transformations are presented with emphasis on the geometric aspect, and the Cauchy theorem is covered in the classical manner. The remaining chapters provide an elegant and solid overview of special topics such as Entire and Meromorphic Functions, Analytic Continuation, Normal Families, Conformal Mapping, and Harmonic Functions.
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Complex Manifolds without Potential Theory

(With an Appendix on the Geometry of Characteristic Classes)

Author: Shiing-shen Chern

Publisher: Springer

ISBN: 9780387904221

Category: Mathematics

Page: 172

View: 4969

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#
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