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Author : Murray H. Protter,Charles Bradfield Morrey
Publisher : Addison Wesley Publishing Company
Page : 830 pages
File Size : 55,7 Mb
Release : 1964
Category : Mathematics
ISBN : UOM:39015009820542
Author : William P. Ziemer
Publisher : Springer
Page : 382 pages
File Size : 51,9 Mb
Release : 2017-11-30
Category : Mathematics
ISBN : 9783319646299
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.
Author : Gerald B. Folland
Publisher : John Wiley & Sons
Page : 309 pages
File Size : 51,8 Mb
Release : 2013-06-11
Category : Mathematics
ISBN : 9781118626399
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: * Revised material on the n-dimensional Lebesgue integral. * An improved proof of Tychonoff's theorem. * Expanded material on Fourier analysis. * A newly written chapter devoted to distributions and differential equations. * Updated material on Hausdorff dimension and fractal dimension.
Author : E. T. Whittaker,George Neville Watson,G. N. Watson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 42,6 Mb
Release : 1927
Category : Mathematics
ISBN : 0521588073
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,Eugen Varvaruca
Publisher : CRC Press
Page : 558 pages
File Size : 40,6 Mb
Release : 2018-01-02
Category : Mathematics
ISBN : 9781351765336
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 : Ernst Hairer,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 42,5 Mb
Release : 2008-05-30
Category : Mathematics
ISBN : 9780387770369
This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.
Author : Nader Vakil
Publisher : Cambridge University Press
Page : 587 pages
File Size : 48,9 Mb
Release : 2011-02-17
Category : Mathematics
ISBN : 9781107002029
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Author : Vladimir A. Zorich
Publisher : Krishna Prakashan Media
Page : 792 pages
File Size : 46,6 Mb
Release : 2010-11-16
Category : Mathematics
ISBN : 8210379456XXX
The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.
Author : Murray H. Protter,Charles Bradfield Morrey
Publisher : Unknown
Page : 790 pages
File Size : 53,9 Mb
Release : 1969
Category : Mathematical analysis
ISBN : LCCN:69016938
Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer
Page : 521 pages
File Size : 52,8 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319743257
A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.
Author : Vicente Montesinos,Peter Zizler,Václav Zizler
Publisher : Springer
Page : 863 pages
File Size : 44,6 Mb
Release : 2015-05-04
Category : Mathematics
ISBN : 9783319124810
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 University Press on Demand
Page : 447 pages
File Size : 43,8 Mb
Release : 2003
Category : Psychology
ISBN : 9780198526568
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 : Nicola Fusco,Paolo Marcellini,Carlo Sbordone
Publisher : Springer Nature
Page : 678 pages
File Size : 50,7 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031041518
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions. The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect. The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Author : Michael Reed,Barry Simon
Publisher : Gulf Professional Publishing
Page : 417 pages
File Size : 40,6 Mb
Release : 1980
Category : Functional analysis
ISBN : 9780125850506
"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description.
Author : Bernard R. Gelbaum
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 51,6 Mb
Release : 2011-02-25
Category : Mathematics
ISBN : 9781118030806
Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis. While maintaining the strictest standards ofrigor, Professor Gelbaum's approach is designed to appeal tointuition whenever possible. Modern Real and Complex Analysisprovides up-to-date treatment of such subjects as the Daniellintegration, differentiation, functional analysis and Banachalgebras, conformal mapping and Bergman's kernels, defectivefunctions, Riemann surfaces and uniformization, and the role ofconvexity in analysis. The text supplies an abundance of exercisesand illustrative examples to reinforce learning, and extensivenotes and remarks to help clarify important points.