An Introduction To Modern Analysis
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Author | : Vicente Montesinos |
Publisher | : Springer |
Total Pages | : 884 |
Release | : 2015-05-04 |
Genre | : Mathematics |
ISBN | : 3319124811 |
Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.
Author | : Shmuel Kantorovitz |
Publisher | : Oxford Graduate Texts in Mathe |
Total Pages | : 447 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0198526563 |
This text is based on lectures given by the author in measure theory, functional analysis, Banach algebras, spectral theory (of bounded and unbounded operators), semigroups of operators, probability and mathematical statistics, and partial differential equations.
Author | : E. T. Whittaker |
Publisher | : Cambridge University Press |
Total Pages | : 620 |
Release | : 1927 |
Genre | : Mathematics |
ISBN | : 9780521588072 |
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Author | : Nikolaos Katzourakis |
Publisher | : CRC Press |
Total Pages | : 558 |
Release | : 2018-01-02 |
Genre | : Mathematics |
ISBN | : 1351765337 |
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
Author | : E.T. Whittaker |
Publisher | : Courier Dover Publications |
Total Pages | : 624 |
Release | : 2020-07-15 |
Genre | : Mathematics |
ISBN | : 048684286X |
Historic text by two great mathematicians consists of two parts, The Processes of Analysis and The Transcendental Functions. Geared toward students of analysis and historians of mathematics. 1920 third edition.
Author | : Avner Friedman |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 1982-01-01 |
Genre | : Mathematics |
ISBN | : 9780486640624 |
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
Author | : Voxman |
Publisher | : CRC Press |
Total Pages | : 700 |
Release | : 1981-03-01 |
Genre | : Mathematics |
ISBN | : 9780824769499 |
Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts and applied results ofsignificance that serves to bridge the gap between the two- or three-cemester calculus sequence andsenior/graduate level courses in the theory and appplications of ordinary and partial differentialequations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalizedfunctions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, andbrachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensiveproblem sets found throughout the book test the student's understanding of the topics andhelp develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-levelundergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in thistext will increase students' mathematical maturity and prepare them solidly for senior/graduatelevel topics. The wealth of materials in the text allows the instructor to select topics that are ofspecial interest to the student. A two- or three ll?lester calculus sequence is required for successfuluse of this book.
Author | : Norman R. Howes |
Publisher | : Springer Science & Business Media |
Total Pages | : 434 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208335 |
The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.
Author | : Wolfgang Tutschke |
Publisher | : CRC Press |
Total Pages | : 476 |
Release | : 2004-06-25 |
Genre | : Mathematics |
ISBN | : 1420057219 |
Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork
Author | : William J. Terrell |
Publisher | : American Mathematical Soc. |
Total Pages | : 607 |
Release | : 2019-10-21 |
Genre | : Education |
ISBN | : 1470451352 |
A Passage to Modern Analysis is an extremely well-written and reader-friendly invitation to real analysis. An introductory text for students of mathematics and its applications at the advanced undergraduate and beginning graduate level, it strikes an especially good balance between depth of coverage and accessible exposition. The examples, problems, and exposition open up a student's intuition but still provide coverage of deep areas of real analysis. A yearlong course from this text provides a solid foundation for further study or application of real analysis at the graduate level. A Passage to Modern Analysis is grounded solidly in the analysis of R and Rn, but at appropriate points it introduces and discusses the more general settings of inner product spaces, normed spaces, and metric spaces. The last five chapters offer a bridge to fundamental topics in advanced areas such as ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. Thus, the book introduces interesting and useful developments beyond Euclidean space where the concepts of analysis play important roles, and it prepares readers for further study of those developments.