This beautifully written text starts with proofs and sets in the first 40 pages and continues in the rest of Parts I and II to maintain an ongoing emphasis on the construction of proofs, demonstrating proper skills through detailed examples using the "forward-backward" method. *One of the texts greatest strengths are the problem sets, which are many and varied. *Offers a wide range of problem material guiding readers through large projects and allowing them to explore and develop interest in near research-level topics. *Presents the most abstract subject matter in terms that relate to students experience in calculus, rather than ignoring or downplaying the value of this experience. *Depicts the structure of the real number system as a collection of closely interrelated properties, rather than simply a list of theorems.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 22 mm
Gewicht
ISBN-13
978-0-13-229824-7 (9780132298247)
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Schweitzer Klassifikation
I. PRELIMINARIES. 1. Building Proofs. 2. Finite, Infinite and Even Bigger. 3. Algebra of Real Numbers. 4. Ordering, Intervals and Neighborhoods. II. THE STRUCTURE OF THE REAL NUMBER SYSTEM. 5. Upper Bounds and Suprema. 6. Nested Intervals. 7. Cluster Points. 8. Topology of the Real Numbers. 9. Sequences. 10. Sequences and the Big Theorem. 11. Compact Sets. 12. Connected Sets. III. TOPICS FROM CALCULUS. 13. Series. 14. Uniform Continuity. 15. Sequences and Series of Functions. 16. Differentiation. 17. Integration. 18. Interchanging Limit Processes. IV. SELECTED SHORTS. 19. Increasing Functions. 20. Continuous Functions and Differentiability. 21. Continuous Functions and Integrability. 22. We Build the Real Numbers. Index.
