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Elements of Real Analysis (87 Edition)

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Elements of Real Analysis (87 Edition) Cover

 

Synopses & Reviews

Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.

Publisher Comments:

This classic text in introductory analysis delineates and explores the intermediate steps between the basics of calculus and the ultimate stage of mathematics: abstraction and generalization.

Since many abstractions and generalizations originate with the real line, the author has made it the unifying theme of the text, constructing the real number system from the point of view of a Cauchy sequence (a step which Dr. Sprecher feels is essential to learn what the real number system is).

The material covered in Elements of Real Analysis should be accessible to those who have completed a course in calculus. To help give students a sound footing, Part One of the text reviews the fundamental concepts of sets and functions and the rational numbers. Part Two explores the real line in terms of the real number system, sequences and series of number and the structure of point sets. Part Three examines the functions of a real variable in terms of continuity, differentiability, spaces of continuous functions, measure and integration, and the Fourier series.

An especially valuable feature of the book is the exercises which follow each section. There are over five hundred, ranging from the simple to the highly difficult, each focusing on a concept previously introduced.

Synopsis:

Classic text covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, much more. Over 500 exercises.

Synopsis:

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.

Synopsis:

Classic text delineates and explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Examines sets and functions, rational numbers, the real line in terms of the real number system, sequences and functions of a real variable in terms of continuity, differentiability, more. Over 500 exercises.

Table of Contents

  Preface

Part I. Fundamental Concepts

  1. Sets and Functions

    1. Sets

    2. The Algebra of Sets

    3. Functions

    4. Countability

  2. The Rational Numbers

    5. Alebraic Properties

    6. Decimal Expansions

Part II. The Real Line

  3. The Real Number System

    7. Cauchy Sequences and Their Equivalence Classes

    8. The Real Number System

    9. Completeness Properties of R

    10. The Extended Real Line

  4. Sequences and Series of Number

    11. Sequences: Basic Limit Theorems

    12. Upper and Lower Limits

    13. Basic Properties of Series

    14. Series with Nonnegative Terms

    15. Alternating Series

    16. Absolute Convergence

  5. The Structure of Point Sets

    17. Basic Notions

    18. Closed Sets

    19. Open Sets

    20. Perfect Sets

    21. Distance between Point Sets

    22. Connected Sets

  3. Functions of a Real Variable

    23. Continuity; Limits of Functions

    24. Continuous Functions

    25. The Nature of Discontinuities

    26. Monotonic Functions

    27. Uniform Continuity

  7. Differentiability

    28 The Derivative at a Point

    29. A Continuous Nowhere Differentiable Function

    30. Properties of the Derivative

    31. Taylor's Theorem

  8. Spaces of Continuous Functions

    32. The Problems of Separability and Convergence

    33. Uniform Convergence

    34. Power Series

    35. The Approximation of Functions

    36. Equicontinuity

    37. Summary

  9. Measure and Integration

    38. Measurable Sets

    39. Properties of Measurable Sets

    40. Measurable Functions

    41. The Lebesgue Integral of Simple Functions

    42. The Lebesgue Integral

    43. Theorems on Limits under the Integral Sign

    44. The Riemann Integral

  10. Fourier Series

    45. Basic Facts

    46. The Space £ superscript 2

    47. The Question of Convergence

  Bibliography; Glossary of Symbols; Index

Product Details

ISBN:
9780486653853
Author:
Sprecher, David A.
Publisher:
Dover Publications
Author:
Mathematics
Author:
David A. Spre
Author:
Cher
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Advanced
Subject:
Functions of real variables
Subject:
General Mathematics
Subject:
Functional Analysis
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
1954
Publication Date:
20100731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
368
Dimensions:
8.5 x 5.38 in 0.88 lb

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Elements of Real Analysis (87 Edition) Used Trade Paper
0 stars - 0 reviews
$8.00 In Stock
Product details 368 pages Dover Publications - English 9780486653853 Reviews:
"Synopsis" by , Classic text covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, much more. Over 500 exercises.

"Synopsis" by ,
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.

"Synopsis" by ,
Classic text delineates and explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Examines sets and functions, rational numbers, the real line in terms of the real number system, sequences and functions of a real variable in terms of continuity, differentiability, more. Over 500 exercises.
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