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First Course in Real Analysis 2ND Edition

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First Course in Real Analysis 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

This book is designed for a first course in real analysis following the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors have included such elementary topics as the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits. The pace is deliberate, and the proofs are detailed. The emphasis of the presentation is on theory, but the book also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many exercises that enable the student to learn the techniques of proofs and the standard tools of analysis. In this second edition, improvements have been made in the exposition, and many of the proofs have been simplified. Additionally, this new edition includes an assortment of new exercises and provides answers for the odd-numbered problems.

Book News Annotation:

For students who have completed a standard course in calculus. Most notable among the changes that been made in this edition (first, 1977) are the addition of many problems and the inclusion of answers to most of the odd-numbered exercises (there are now more than a thousand exercises in all).
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

This work is designed for a first course in real analysis following the standard course in elementary calculus. It contains a treatment (with many illustrative samples and exercises) of the standard topics in infinite metric spaces, and vector field theory. It includes an assortment of exercises and provides answers for the odd-numbered problems.

Synopsis:

This book is designed for a first course in real analysis following the standard course in elementary calculus. Included in this edition are the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits.

Synopsis:

Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.

Table of Contents

1: The Real Number System. 2: Continuity and Limits. 3: Basic Properties of Functions on R. 4: Elementary Theory of Differentiation. 5: Elementary Theory of Integration. 6: Elementary Theory of Metric Spaces. 7: Differentiation in R. 8: Integration in R. 9: Infinite Sequences and Infinite Series. 10: Fourier Series. 11: Functions Defined by Integrals; Improper Integrals. 12: The Riemann-Stieltjes Integral and Functions of Bounded Variation. 13: Contraction Mappings, Newton's Method, and Differential Equations. 14: Implicit Function Theorems and Lagrange Multipliers. 15: Functions on Metric Spaces; Approximation. 16: Vector Field Theory; the Theorems of Green and Stokes. Appendices.

Product Details

ISBN:
9780387974378
Editor:
Ewing, J. H.
Editor:
Gehring, F. W.
Editor:
Ewing, J. H.
Author:
Charles B. Jr. Morrey
Author:
Protter, Murray H.
Author:
Morrey, Charles B. Jr.
Author:
Morrey, Charles Bradfield Jr.
Author:
Gehring, F. W.
Publisher:
Springer
Location:
New York :
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Functional Analysis
Subject:
Analysis
Subject:
Differentialrechnung
Subject:
Integralrechnung
Subject:
Real functions
Subject:
Mathematics-Calculus
Copyright:
Edition Number:
2
Edition Description:
1991. Corr. 4th
Series:
Undergraduate Texts in Mathematics
Series Volume:
127
Publication Date:
19910801
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
554
Dimensions:
235 x 155 mm 957 gr

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First Course in Real Analysis 2ND Edition New Hardcover
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Product details 554 pages Springer-Verlag - English 9780387974378 Reviews:
"Synopsis" by , This work is designed for a first course in real analysis following the standard course in elementary calculus. It contains a treatment (with many illustrative samples and exercises) of the standard topics in infinite metric spaces, and vector field theory. It includes an assortment of exercises and provides answers for the odd-numbered problems.
"Synopsis" by , This book is designed for a first course in real analysis following the standard course in elementary calculus. Included in this edition are the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits.
"Synopsis" by , Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation.
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