A First Course in Real Analysis / Edition 1

A First Course in Real Analysis / Edition 1

by Sterling K. Berberian
     
 

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

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Overview

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.

Product Details

ISBN-13:
9780387942179
Publisher:
Springer New York
Publication date:
06/24/1994
Series:
Undergraduate Texts in Mathematics Series
Edition description:
1st ed. 1994. Corr. 2nd printing 1998
Pages:
240
Product dimensions:
9.21(w) x 6.14(h) x 0.69(d)

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.

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