| 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) |
|
