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Introduction To Real Analysis | By Robert G. Bartle, Donald R. Sherbert | 4th Edition | Wiley Publisher Pvt. Ltd ( English medium)
Introduction To Real Analysis | By Robert G. Bartle, Donald R. Sherbert | 4th Edition | Wiley Publisher Pvt. Ltd ( English medium).
ABOUT THE BOOK:
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, analyze 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 additional 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.
TABLE OF CONTENTS :
CHAPTER 1 PRELIMINARIES.
1.1 Sets and Functions.
1.2 Mathematical Induction.
1.3 Finite and Infinite Sets.
CHAPTER 2 THE REAL NUMBERS.
2.1 The Algebraic and Order Properties of R.
2.2 Absolute Value and the Real Line.
2.3 The Completeness Property of R.
2.4 Applications of the Supremum Property.
2.5 Intervals.
CHAPTER 3 SEQUENCES AND SERIES.
3.1 Sequences and Their Limits.
3.2 Limit Theorems.
3.3 Monotone Sequences.
3.4 Subsequences and the Bolzano-Weierstrass Theorem.
3.5 The Cauchy Criterion.
3.6 Properly Divergent Sequences.
3.7 Introduction to Infinite Series.
CHAPTER 4 LIMITS.
4.1 Limits of Functions.
4.2 Limit Theorems.
4.3 Some Extensions of the Limit Concept.
CHAPTER 5 CONTINUOUS FUNCTIONS.
5.1 Continuous Functions.
5.2 Combinations of Continuous Functions.
5.3 Continuous Functions on Intervals.
5.4 Uniform Continuity.
5.5 Continuity and Gauges.
5.6 Monotone and Inverse Functions.
CHAPTER 6 DIFFERENTIATION.
6.1 The Derivative.
6.2 The Mean Value Theorem.
6.3 L’Hospital’s Rules.
6.4 Taylor’s Theorem.
CHAPTER 7 THE RIEMANN INTEGRAL.
7.1 Riemann Integral.
7.2 Riemann Integrable Functions.
7.3 The Fundamental Theorem.
7.4 The Darboux Integral.
7.5 Approximate Integration.
CHAPTER 8 SEQUENCES OF FUNCTIONS.
8.1 Pointwise and Uniform Convergence.
8.2 Interchange of Limits.
8.3 The Exponential and Logarithmic Functions.
8.4 The Trigonometric Functions.
CHAPTER 9 INFINITE SERIES.
9.1 Absolute Convergence.
9.2 Tests for Absolute Convergence.
9.3 Tests for Nonabsolute Convergence.
9.4 Series of Functions.
CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL.
10.1 Definition and Main Properties.
10.2 Improper and Lebesgue Integrals.
10.3 Infinite Intervals.
10.4 Convergence Theorems.
CHAPTER 11 A GLIMPSE INTO TOPOLOGY.
11.1 Open and Closed Sets in R.
11.2 Compact Sets.
11.3 Continuous Functions.
11.4 Metric Spaces.
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.
REFERENCES.
PHOTO CREDITS.
HINTS FOR SELECTED EXERCISES.
INDEX.
SEARCH KEY: Introduction To Real Analysis, By Robert G. Bartle, Donald R. Sherbert, 4th Edition, Fourth Edition, Wiley India Pvt. Ltd Publisher, English medium, Introduction To Real Analysis 4th edition, Introduction To Real Analysis Bartle & Sherbert, Analysis Book, Mathematical Induction, Bartle & Sherbert Analysis Book, Wiley India Edition, book for undergraduate students of Mathematics, Mathematics Book, Analysis Book, Mathematics Students, Genre Science.
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Product Details
| SKU, Publisher | Wiley-Intro-to-Real-Analy-(E) |
| Publisher | Wiley Publisher Pvt. Ltd. |
| Author, Edition | Robert G. Bartle, Donald R. Sherbert, 4th Editon. |
| Binding, Type | Paperback, New |
| No. of Pages | 416 |
Product Description
Introduction To Real Analysis | By Robert G. Bartle, Donald R. Sherbert | 4th Edition | Wiley Publisher Pvt. Ltd ( English medium).
SEARCH KEY: Introduction To Real Analysis, By Robert G. Bartle, Donald R. Sherbert, 4th Edition, Fourth Edition, Wiley India Pvt. Ltd Publisher, English medium, Introduction To Real Analysis 4th edition, Introduction To Real Analysis Bartle & Sherbert, Analysis Book, Mathematical Induction, Bartle & Sherbert Analysis Book, Wiley India Edition, book for undergraduate students of Mathematics, Mathematics Book, Analysis Book, Mathematics Students, Genre Science.
ABOUT THE BOOK:
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, analyze 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 additional 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.
TABLE OF CONTENTS :
CHAPTER 1 PRELIMINARIES.
1.1 Sets and Functions.
1.2 Mathematical Induction.
1.3 Finite and Infinite Sets.
CHAPTER 2 THE REAL NUMBERS.
2.1 The Algebraic and Order Properties of R.
2.2 Absolute Value and the Real Line.
2.3 The Completeness Property of R.
2.4 Applications of the Supremum Property.
2.5 Intervals.
CHAPTER 3 SEQUENCES AND SERIES.
3.1 Sequences and Their Limits.
3.2 Limit Theorems.
3.3 Monotone Sequences.
3.4 Subsequences and the Bolzano-Weierstrass Theorem.
3.5 The Cauchy Criterion.
3.6 Properly Divergent Sequences.
3.7 Introduction to Infinite Series.
CHAPTER 4 LIMITS.
4.1 Limits of Functions.
4.2 Limit Theorems.
4.3 Some Extensions of the Limit Concept.
CHAPTER 5 CONTINUOUS FUNCTIONS.
5.1 Continuous Functions.
5.2 Combinations of Continuous Functions.
5.3 Continuous Functions on Intervals.
5.4 Uniform Continuity.
5.5 Continuity and Gauges.
5.6 Monotone and Inverse Functions.
CHAPTER 6 DIFFERENTIATION.
6.1 The Derivative.
6.2 The Mean Value Theorem.
6.3 L’Hospital’s Rules.
6.4 Taylor’s Theorem.
CHAPTER 7 THE RIEMANN INTEGRAL.
7.1 Riemann Integral.
7.2 Riemann Integrable Functions.
7.3 The Fundamental Theorem.
7.4 The Darboux Integral.
7.5 Approximate Integration.
CHAPTER 8 SEQUENCES OF FUNCTIONS.
8.1 Pointwise and Uniform Convergence.
8.2 Interchange of Limits.
8.3 The Exponential and Logarithmic Functions.
8.4 The Trigonometric Functions.
CHAPTER 9 INFINITE SERIES.
9.1 Absolute Convergence.
9.2 Tests for Absolute Convergence.
9.3 Tests for Nonabsolute Convergence.
9.4 Series of Functions.
CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL.
10.1 Definition and Main Properties.
10.2 Improper and Lebesgue Integrals.
10.3 Infinite Intervals.
10.4 Convergence Theorems.
CHAPTER 11 A GLIMPSE INTO TOPOLOGY.
11.1 Open and Closed Sets in R.
11.2 Compact Sets.
11.3 Continuous Functions.
11.4 Metric Spaces.
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.
REFERENCES.
PHOTO CREDITS.
HINTS FOR SELECTED EXERCISES.
INDEX.
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We practice Easy Return/Exchange policy for Buyer Protection, So if you experience any difficulties like (Wrong Item delivered ) with any of the product received, you can raise request under Return / Exchange Policy through written E-mail at exam360.in@gmail.com with valid Footage. Once we validate the case in details we will initiate as per the Policy Standard & we will be more than happy to help you to solve your issues ASAP.
While receiving the item from any of our courier partner, users are requested to check the packaging item properly, If you feel any tampering we request not to accept the packet & instantly make a call to the below mentioned HELPLINE with your Order Details. And, If you purchased an item that was not Satisfactory, in such cases we will issue Return/ Refund if case is genuine!
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