Elementary Real and Complex Analysis

Author: Georgi E. Shilov
Publisher: Courier Corporation
ISBN: 0486135004
Format: PDF, Mobi
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DIVExcellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition. /div

Introductory Complex Analysis

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318524
Format: PDF, ePub
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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.

Complex Analysis with Applications

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 9780486647623
Format: PDF, ePub, Docs
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The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.

Hilbert Space and Quantum Mechanics

Author: Franco Gallone
Publisher: World Scientific Publishing Company
ISBN: 9814635855
Format: PDF, ePub
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The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Preface. The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparently distinct approaches employed in quantum theory.

Mathematical Principles of the Internet Volume 2

Author: Nirdosh Bhatnagar
Publisher: CRC Press
ISBN: 1351379119
Format: PDF, Kindle
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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

A Collection of Problems on Complex Analysis

Author: Lev Izrailevich Volkovyskiĭ
Publisher: Courier Dover Publications
ISBN:
Format: PDF, Kindle
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Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox
Publisher: Courier Corporation
ISBN: 9780486682938
Format: PDF, Mobi
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This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Elementary Functional Analysis

Author: Georgi E. Shilov
Publisher: Courier Corporation
ISBN: 0486318680
Format: PDF, ePub
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Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.

Anschauliche Funktionentheorie

Author: Tristan Needham
Publisher: Oldenbourg Wissenschaftsverlag
ISBN: 9783486709025
Format: PDF, ePub, Mobi
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Needhams neuartiger Zugang zur Funktionentheorie wurde von der Fachpresse begeistert aufgenommen. Mit über 500 zum großen Teil perspektivischen Grafiken vermittelt er im wahrsten Sinne des Wortes eine Anschauung von der sonst oft als trocken empfundenen Funktionentheorie. 'Anschauliche Funktionentheorie ist eine wahre Freude und ein Buch so recht nach meinem Herzen. Indem er ausschließlich seine neuartige geometrische Perspektive verwendet, enthüllt Tristan Needham viele überraschende und bisher weitgehend unbeachtete Facetten der Schönheit der Funktionentheorie.' (Sir Roger Penrose)

Introduction to Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Format: PDF, Kindle
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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.