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Analysis
has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function.[1] It also includes the theories of differentiation, integration and measure, infinite series[2], and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or more specifically "distance" (a metric space).
Mathematical analysis includes the following subfields
Real analysis
the rigorous study of derivatives and integrals of functions of real variables. This includes the study of sequences and their limits, series, and measures.
Functional analysis
studies spaces of functions and introduces concepts such as Banach spaces and Hilbert spaces.
Harmonic analysis
deals with Fourier series and their abstractions.
Complex analysis
the study of functions from the complex plane to the complex plane which are complex differentiable.
Differential geometry and topology, the application of calculus to abstract mathematical spaces that possess a complicated internal structure.
p-adic analysis
the study of analysis within the context of p-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts.
Non-standard analysis
which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers. It is normally classed as model theory.
Numerical analysis
the study of algorithms for approximating the problems of continuous mathematics. ​

Classical analysis would normally be understood as any work not using functional analysis techniques, and is sometimes also called hard analysis; it also naturally refers to the more traditional topics. The study of differential equations is now shared with other fields such as dynamical systems, though the overlap with conventional analysis is large​
 
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Product Description​

Basic_Real_Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.​

Key topics and features of Basic Real Analysis:​

* Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations
* Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces
* The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments
* The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems​

requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician.​

Product Details​


Hardcover: 650 pages ​

1 edition​

(July 29, 2005)

Language: English
​

Download from here
رابط منتهي​
 


Advanced Real Analysis

by Anthony W. Knapp
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Product Description
​

Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.

Key topics and features of Advanced Real Analysis:

* Develops Fourier analysis and functional analysis with an eye toward partial differential equations
* Includes chapters on Sturm–Liouville theory, compact self-adjoint operators, Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, and aspects of partial differential equations
* Contains chapters about analysis on manifolds and foundations of probability
* Proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
* Includes many examples and nearly two hundred problems, and a separate 45-page section gives hints or complete solutions for most of the problems
* Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds

Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.

Product Details

Hardcover: 468 pages
Publisher: Birkhäuser Boston; 1 edition
(July 27, 2005)
Language: English
ISBN-10: 0817643826
ISBN-13: 978-0817643829
Product Dimensions: 9.3 x 6.1 x 1.1 inches
Shipping Weight: 1.8 pounds​



Download from here
http://ifile.it/sjl41kg/0817643826.rar​
 


Real Analysis

(3rd Edition)

by Halsey Royden
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The publisher, Prentice-Hall Engineering/Science/Mathematics
This is the classic introductory graduate text.

Product Details

Hardcover: 434 pages
Publisher: Prentice Hall; 3 edition
(February 12, 1988)
Language: English
ISBN-10: 0024041513
ISBN-13: 978-0024041517
Product Dimensions: 9.3 x 6.3 x 1.6 inches
Shipping Weight: 2.1 pounds ​


Download from here
http://ifile.it/c8osye/t02266.rar​
 


المهاجر قال:
جزاك الله كل خير و كل عام و أنتم بخير ....
أنقر للتوسيع...
مشكور على المرور العطر مستشارنا العزيز ....وأبارك لك الرمضان وعلى كل المسلمين, وأتمنى من الله ان هذا الشهر يكون شهر الخير والبركة
خالص تحياتي و تقديري لك ​
 


جزاك الله خيرا أستاذنا الفاضل الأخ عبدالجبار لشكري على مشاركاتك الأكثر من رائعه​

أشعر وكأني أسعد عضو في المنتدى بهذا التقسيم الفرعي داخل قسم الرياضيات ​

نسأل الله ان يبارك في هذا المنتدى الطيب والقائمين عليه وأن يجعل هذا العمل خالصا لوجهه​

و لي رأي و هو تغيير اسم هذا القسم الفرعي
من
Analysis
إلى
Topology and Analysis​

هذا مجرد اقتراح أرى أنه الأفضل والأمر معروض للمناقشة​
 


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Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
By Peter D. Lax



  • Publisher: Wiley-Interscience
  • Number Of Pages: 608
  • Publication Date: 2002-04-04
  • ISBN-10 / ASIN: 0471556041
  • ISBN-13 / EAN: 9780471556046
  • Binding: Hardcover


Product Description:
Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.
* Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.
* Includes an appendix on the Riesz representation theorem.


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Problems in Real Analysis: A Workbook with Solutions
By Charalambos D. Aliprantis, Owen Burkinshaw



  • Publisher: Academic Press
  • Number Of Pages: 403
  • Publication Date: 1999-01-15
  • ISBN-10 / ASIN: 0120502534
  • ISBN-13 / EAN: 9780120502530
  • Binding: Hardcover


Product Description:
A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior [COLOR=orange ! important][COLOR=orange ! important]science[/color][/color] and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.
Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.



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Principles of Real Analysis, Third Edition
By Charalambos D. Aliprantis



  • Publisher: Academic Press
  • Number Of Pages: 451
  • Publication Date: 1998-09-15
  • ISBN-10 / ASIN: 0120502577
  • ISBN-13 / EAN: 9780120502578
  • Binding: Hardcover


Product Description:
With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians


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