Elements of Real Anyalsis

  • Filename: elements-of-real-anyalsis.
  • ISBN: 9788121903066
  • Release Date: 2003-06-01
  • Number of pages: 312
  • Author: M.D.Raisinghania
  • Publisher: S. Chand Publishing



This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.

The Elements of Real Analysis

  • Filename: the-elements-of-real-analysis.
  • ISBN: 0471063916
  • Release Date: 1982-01
  • Number of pages: 598
  • Author: Robert G. Bartle
  • Publisher: John Wiley & Sons Incorporated



Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

Elements of Real Analysis

  • Filename: elements-of-real-analysis.
  • ISBN: 9780763779474
  • Release Date: 2011-01-28
  • Number of pages: 739
  • Author: Charles G. Denlinger
  • Publisher: Jones & Bartlett Learning



Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.

Elements of Real Analysis

  • Filename: elements-of-real-analysis.
  • ISBN: 9780486153254
  • Release Date: 2012-04-25
  • Number of pages: 368
  • Author: David A. Sprecher
  • Publisher: Courier Corporation



Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Elements of Real Analysis

  • Filename: elements-of-real-analysis.
  • ISBN: 013897067X
  • Release Date: 1998
  • Number of pages: 501
  • Author: Herbert S. Gaskill
  • Publisher: Upper Saddle River, NJ : Prentice Hall



Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner. Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.

Elements of Real Analysis

  • Filename: elements-of-real-analysis.
  • ISBN: 9781584886617
  • Release Date: 2006-08-21
  • Number of pages: 436
  • Author: M.A. Al-Gwaiz
  • Publisher: CRC Press



Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.

Basic Elements of Real Analysis

  • Filename: basic-elements-of-real-analysis.
  • ISBN: 9780387227498
  • Release Date: 2006-05-02
  • Number of pages: 276
  • Author: Murray H. Protter
  • Publisher: Springer Science & Business Media



From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.

Elements of the Theory of Functions and Functional Analysis

  • Filename: elements-of-the-theory-of-functions-and-functional-analysis.
  • ISBN: 0486406830
  • Release Date: 1999
  • Number of pages: 288
  • Author: Andre? Nikolaevich Kolmogorov
  • Publisher: Courier Corporation



Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

Fundamentals of Real Analysis

  • Filename: fundamentals-of-real-analysis.
  • ISBN: 0387984801
  • Release Date: 1999
  • Number of pages: 479
  • Author: Sterling K. Berberian
  • Publisher: Springer Science & Business Media



"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

Elementary Real Analysis Second Edition

  • Filename: elementary-real-analysis-second-edition.
  • ISBN: 9781434843678
  • Release Date: 2008-04-07
  • Number of pages: 638
  • Author: Brian S. Thomson
  • Publisher: ClassicalRealAnalysis.com



This is the second edition of the text Elementary Real Analysis originally published by Prentice Hall (Pearson) in 2001.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. Differentiation Chapter 8. The IntegralChapter 9. Sequences and series of functionsChapter 10. Power seriesChapter 11. Euclidean Space R^nChapter 12. Differentiation on R^nChapter 13. Metric Spaces

Real Analysis Through Modern Infinitesimals

  • Filename: real-analysis-through-modern-infinitesimals.
  • ISBN: 9781107002029
  • Release Date: 2011-02-17
  • Number of pages: 565
  • Author: Nader Vakil
  • Publisher: Cambridge University Press



This series is devoted to significant topics orthemes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and Its Applications cover their subjects comprehensively. Less important results may be summarized as exercises at the ends of chapters. Each book contains an extensive bibliography. Thus the volumes are encyclopedic references or manageable guides to major subjects.

Real Analysis

  • Filename: real-analysis.
  • ISBN: 0521497566
  • Release Date: 2000-08-15
  • Number of pages: 401
  • Author: N. L. Carothers
  • Publisher: Cambridge University Press



This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists alike, including historical commentary, carefully chosen references, and plenty of exercises.

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