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Book
Author Beardon, Alan F.

Title Limits : a new approach to real analysis / Alan F. Beardon
Published New York : Springer, [1997]
©1997

Copies

Location Call no. Vol. Availability
 MELB  515.222 Bea/Lan  DUE 11-10-22
Description ix, 189 pages : illustrations ; 25 cm
Series Undergraduate texts in mathematics
Undergraduate texts in mathematics.
Contents Partial Ch. 1. Sets and Functions -- Ch. 2. Real and Complex Numbers -- Ch. 3. Limits -- Ch. 4. Bisection Arguments -- Ch. 5. Infinite Series -- Ch. 6. Periodic Functions -- Ch. 7. Sequences -- Ch. 8. Continuous Functions -- Ch. 9. Derivatives -- Ch. 10. Integration -- Ch. 11. [pi], [gamma], e, and n! -- App. Mathematical Induction
Ch. 1. Sets and Functions -- Ch. 2. Real and Complex Numbers -- Ch. 3. Limits -- Ch. 4. Bisection Arguments -- Ch. 5. Infinite Series -- Ch. 6. Periodic Functions -- Ch. 7. Sequences -- Ch. 8. Continuous Functions -- Ch. 9. Derivatives -- Ch. 10. Integration -- Ch. 11. [pi], [gamma], e, and n! -- App. Mathematical Induction
Summary This book is intended as an undergraduate text on real analysis and includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a unique and novel approach to the subject matter that has not previously appeared in book form. The author defines what is meant by a limit just once, and all of the subsequent limiting processes are viewed as special cases of this one definition. In this way the subject matter attains a unity and coherence that is missing in the traditional approach, and students will be able to fully appreciate and understand the common source of the topics they are studying. These topics are presented as "variations on a theme" rather than essentially different ideas, and this leads to a clearer global view of the subject
Bibliography Includes bibliographical references (page186) and index
Subject Mathematical analysis.
LC no. 97020490
ISBN 0387982744 (hardcover : acid-free paper)
(hardcover : acid-free paper)