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Introduction to real analysis / Robert G. Bartle and Donald R. Sherbert.

By: Contributor(s): Material type: TextTextPublication details: New Delhi : Wiley, 2015.Edition: 4th edDescription: xiii, 402 pages : illustrations ; 24 cmISBN:
  • 9788126551811
Subject(s): DDC classification:
  • 515 23 B289
Contents:
Ch. 1. Preliminaries -- Ch. 2. The Real Numbers -- Ch. 3. Sequences and series -- Ch. 4. Limits -- Ch. 5. Continuous functions -- Ch. 6. Differentiation -- Ch. 7. The Riemann integral -- Ch. 8. Sequences of functions -- Ch. 9. Infinite series -- Ch. 10. The generalized Riemann integral -- Ch. 11. A glimpse into topology -- Appendix A. Logic and proofs -- Appendix B. Finite and countable sets -- Appendix C. The Riemann and Lebesgue criteria -- Appendix D. Approximate integration -- Appendix E. Two examples.
Summary: This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals and drawing student attention to possible applications wherever possible.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515 B289 (Browse shelf(Opens below)) Available C26540
Total holds: 0

Includes index.

Ch. 1. Preliminaries --
Ch. 2. The Real Numbers --
Ch. 3. Sequences and series --
Ch. 4. Limits --
Ch. 5. Continuous functions --
Ch. 6. Differentiation --
Ch. 7. The Riemann integral --
Ch. 8. Sequences of functions --
Ch. 9. Infinite series --
Ch. 10. The generalized Riemann integral --
Ch. 11. A glimpse into topology --
Appendix A. Logic and proofs --
Appendix B. Finite and countable sets --
Appendix C. The Riemann and Lebesgue criteria --
Appendix D. Approximate integration --
Appendix E. Two examples.

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals and drawing student attention to possible applications wherever possible.

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