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    Julie Schumacher 9780385538138

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This title in other editions

A First Course in Real Analysis (Undergraduate Texts in Mathematics)

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A First Course in Real Analysis (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means.

Table of Contents

1: Axioms for the Field (R) of Real Numbers. 2: First Properties of (R). 3: Sequences of Real Numbers, Convergence. 4: Special Subsets of (R). 5: Continuity. 6: Continuous Functions on an Interval. 7: Limits of Functions. 8: Derivatives. 9: Riemann Integral. 10: Infinite Series. 11: Beyond the Riemann Integral.

Product Details

ISBN:
9780387942179
Author:
Berberian, Sterling K.
Publisher:
Springer
Subject:
History
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Numbers, Real
Subject:
Functional Analysis
Subject:
Real functions
Subject:
Mathematics-Calculus
Copyright:
Edition Number:
1
Edition Description:
1994. Corr. 2nd
Series:
Undergraduate Texts in Mathematics
Series Volume:
20
Publication Date:
19940624
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
251
Dimensions:
235 x 155 mm 549 gr

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Related Subjects

Reference » Science Reference » General
Science and Mathematics » History of Science » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General

A First Course in Real Analysis (Undergraduate Texts in Mathematics) New Hardcover
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