Advanced Topics in Mathematical Analysis

Advanced Topics in Mathematical Analysis
Title Advanced Topics in Mathematical Analysis PDF eBook
Author Michael Ruzhansky
Publisher CRC Press
Pages 588
Release 2019-01-08
Genre Mathematics
ISBN 1351142119

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Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

Advanced Real Analysis

Advanced Real Analysis
Title Advanced Real Analysis PDF eBook
Author Anthony W. Knapp
Publisher Springer Science & Business Media
Pages 484
Release 2008-07-11
Genre Mathematics
ISBN 0817644423

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* 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

Advances in Algebra and Analysis

Advances in Algebra and Analysis
Title Advances in Algebra and Analysis PDF eBook
Author V. Madhu
Publisher Springer
Pages 473
Release 2019-01-23
Genre Mathematics
ISBN 3030011208

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This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.

Advanced Mathematical Analysis

Advanced Mathematical Analysis
Title Advanced Mathematical Analysis PDF eBook
Author R. Beals
Publisher Springer Science & Business Media
Pages 241
Release 2013-12-01
Genre Mathematics
ISBN 146849886X

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Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi neering" from what might be called "advanced mathematical analysis for mathematicians." It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass ing different examples.

Basic Real Analysis

Basic Real Analysis
Title Basic Real Analysis PDF eBook
Author Anthony W. Knapp
Publisher Springer Science & Business Media
Pages 671
Release 2007-10-04
Genre Mathematics
ISBN 0817644415

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Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.

A Course in Advanced Calculus

A Course in Advanced Calculus
Title A Course in Advanced Calculus PDF eBook
Author Robert S. Borden
Publisher Courier Corporation
Pages 421
Release 2012-09-11
Genre Mathematics
ISBN 0486150380

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This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.

A Course in Complex Analysis

A Course in Complex Analysis
Title A Course in Complex Analysis PDF eBook
Author Wolfgang Fischer
Publisher Springer Science & Business Media
Pages 280
Release 2011-10-21
Genre Mathematics
ISBN 3834886610

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This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.