Advanced Analysis

on the Real Line

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Author: R. Kannan,Carole K. Krueger

Publisher: Springer Science & Business Media

ISBN: 1461384745

Category: Mathematics

Page: 260

View: 6080

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p-adic Numbers

An Introduction

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Author: Fernando Gouvea

Publisher: Springer Science & Business Media

ISBN: 9783540629115

Category: Mathematics

Page: 306

View: 2047

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE

Analysis in Beispielen und Gegenbeispielen

Eine Einführung in die Theorie reeller Funktionen

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Author: Jürgen Appell

Publisher: Springer-Verlag

ISBN: 3540889035

Category: Mathematics

Page: 470

View: 6804

Das Buch führt in die Theorie der reellen Funktionen einer und mehrerer Variablen ein. Im Vordergrund stehen weniger abstrakte Ergebnisse als vielmehr die zahlreichen Beispiele und Gegenbeispiele, anhand derer die Bedeutung mathematischer Sätze deutlich gemacht wird. Kapitel 1 – 3 sind den wesentlichen Ergebnissen über stetige, differenzierbare und integrierbare Funktionen gewidmet, Kapitel 4 geht mit „merkwürdigen" Teilmengen der reellen Achse etwas über den üblichen Stoff hinaus. Funktionen mehrerer Variablen werden in Kapitel 5 bzw. 6 behandelt.

Elements of Advanced Mathematical Analysis for Physics and Engineering

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Author: Filippo Gazzola,Maurizio Zanotti,Alberto Ferrero

Publisher: Società Editrice Esculapio

ISBN: 8874886454

Category: Mathematics

Page: 328

View: 5895

Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary to achieve such a knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Universit`a del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The three Authors, for the variety of their skills, decided to join their expertises to write this book. One of the reasons that should encourage its reading is that the presentation turns out to be a reasonable compromise among the essential mathematical rigor, the importance of the applications and the clearness, which is necessary to make the reference work pleasant to the readers, even to the inexperienced ones. The range of treated topics is quite wide and covers the main basic notions of the scientific research which is based upon mathematical models. We start from vector spaces and Lebesgue integral to reach the frontier of theoretical research such as the study of critical exponents for semilinear elliptic equations and recent problems in fluid dynamics. This long route passes through the theory of Banach and Hilbert spaces, Sobolev spaces, differential equations, Fourier and Laplace transforms, before which we recall some appropriate tools of Complex Analysis. We give all the proofs that have some didactic or applicative interest, while we omit the ones which are too technical or require too high level knowledge. This book has the ambitious purpose to be useful to a broad variety of readers. The first possible beneficiaries are of course the second or third year students of a scientific course of degree: in what follows they will find the topics that are necessary to approach more advanced studies in Mathematics and in other fields, especially Physics and Engineering. This text could be also useful to graduate students who want to start a Ph.D. course: indeed it contains the matter of a multidisciplinary Ph.D. course given by Filippo Gazzola for several years at Politecnico di Milano. Finally, this book could be addressed also to the ones who have already left education far-back but occasionally need to use mathematical tools: we refer both to university professors and their research, and to professionals and designers who want to model a certain phenomenon, but also to the nostalgics of the good old days when they were students. It is precisely for this last type of reader that we have also reported some elementary topics, such as the properties of numerical sets and of the integrals; moreover, every chapter is provided with examples and specific exercises aimed at the involvement of the reader. Let us start immediately inviting the reader to find an “anomaly” among the six formulas appearing in the cover. This book is the translation from Italian of the book ”Elementi di Analisi Superiore per la Fisica e l’Ingegneria”. The translation is due to Ilaria Lucardesi.

Advanced Risk Analysis in Engineering Enterprise Systems

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Author: Cesar Ariel Pinto,Paul R. Garvey

Publisher: CRC Press

ISBN: 1439826153

Category: Business & Economics

Page: 464

View: 5562

Since the emerging discipline of engineering enterprise systems extends traditional systems engineering to develop webs of systems and systems-of-systems, the engineering management and management science communities need new approaches for analyzing and managing risk in engineering enterprise systems. Advanced Risk Analysis in Engineering Enterprise Systems presents innovative methods to address these needs. With a focus on engineering management, the book explains how to represent, model, and measure risk in large-scale, complex systems that are engineered to function in enterprise-wide environments. Along with an analytical framework and computational model, the authors introduce new protocols: the risk co-relationship (RCR) index and the functional dependency network analysis (FDNA) approach. These protocols capture dependency risks and risk co-relationships that may exist in an enterprise. Moving on to extreme and rare event risks, the text discusses how uncertainties in system behavior are intensified in highly networked, globally connected environments. It also describes how the risk of extreme latencies in delivering time-critical data, applications, or services can have catastrophic consequences and explains how to avoid these events. With more and more communication, transportation, and financial systems connected across domains and interfaced with an infinite number of users, information repositories, applications, and services, there has never been a greater need for analyzing risk in engineering enterprise systems. This book gives you advanced methods for tackling risk problems at the enterprise level.

Mathematical Analysis II

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Author: V. A. Zorich

Publisher: Springer

ISBN: 3662489937

Category: Mathematics

Page: 720

View: 5879

This second English 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 English 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. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

Analysis II

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Author: Vladimir A. Zorich

Publisher: Springer

ISBN: 9783540462316

Category: Mathematics

Page: 708

View: 9588

Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.

Nonsmooth Analysis

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Author: Winfried Schirotzek

Publisher: Springer

ISBN: 9783540713326

Category: Mathematics

Page: 378

View: 9812

This book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and then presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed: this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. Each chapter ends with bibliographic notes and exercises.

Real Functions

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Author: Ján Borsík,Ján Haluška

Publisher: N.A

ISBN: N.A

Category: Functions of real variables

Page: 188

View: 9646

Analysis with Ultrasmall Numbers

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Author: Karel Hrbacek,Olivier Lessmann,Richard O'Donovan

Publisher: CRC Press

ISBN: 149870266X

Category: Mathematics

Page: 316

View: 9238

Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms

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Author: Jingshan Zhao,Zhijing Feng,Fulei Chu,Ning Ma

Publisher: Academic Press

ISBN: 0124202233

Category: Computers

Page: 496

View: 2586

Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms provides a complete analytical approach to the invention of new robot mechanisms and the analysis of existing designs based on a unified mathematical description of the kinematic and geometric constraints of mechanisms. Beginning with a high level introduction to mechanisms and components, the book moves on to present a new analytical theory of terminal constraints for use in the development of new spatial mechanisms and structures. It clearly describes the application of screw theory to kinematic problems and provides tools that students, engineers and researchers can use for investigation of critical factors such as workspace, dexterity and singularity. Combines constraint and free motion analysis and design, offering a new approach to robot mechanism innovation and improvement Clearly describes the use of screw theory in robot kinematic analysis, allowing for concise representation of motion and static forces when compared to conventional analysis methods Includes worked examples to translate theory into practice and demonstrate the application of new analytical methods to critical robotics problems

Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

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Author: Matthew A. Pons

Publisher: Springer Science & Business Media

ISBN: 1461496381

Category: Mathematics

Page: 409

View: 5128

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

Analysis on h-Harmonics and Dunkl Transforms

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Author: Feng Dai,Yuan Xu

Publisher: Birkhäuser

ISBN: 3034808879

Category: Mathematics

Page: 118

View: 1824

​This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. Graduate students and researchers working in approximation theory, harmonic analysis, and functional analysis will benefit from this book.

The Real Numbers

An Introduction to Set Theory and Analysis

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Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 331901577X

Category: Mathematics

Page: 244

View: 2700

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Advanced Real Analysis

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Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

ISBN: 9780817644420

Category: Mathematics

Page: 466

View: 7181

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician