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	Introduction To Real Analysis by Bartle R.G.
	Price : Rs 519.00
	Your Price : Rs 415.20

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, analyses 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.

Chapter 1 Preliminaries

Sets and Functions.
Mathematical Induction.
Finite and Infinite Sets.

Chapter 2 The Real Numbers

The Algebraic and Order Properties of R.
Absolute Value and the Real Line.
The Completeness Property of R.
Applications of the Supremum Property.
Intervals.

Chapter 3 Sequences and Series.

Sequences and Their Limits.
Limit Theorems.
Monotone Sequences.
Subsequences and the Bolzano-Weierstrass Theorem.
The Cauchy Criterion.
Properly Divergent Sequences.
Introduction to Infinite Series.

Chapter 4 Limits

Limits of Functions.
Limit Theorems.
Some Extensions of the Limit Concept.

Chapter 5 Continuous Functions

Continuous Functions.
Combinations of Continuous Functions.
Continuous Functions on Intervals.
Uniform Continuity.
Continuity and Gauges.
Monotone and Inverse Functions

Chapter 6 Differentiation

The Derivative.
The Mean Value Theorem.
L`Hospital`s Rules.
Taylor`s Theorem.

Chapter 7 The Riemann Integral

Riemann Integral.
Riemann Integrable Functions.
The Fundamental Theorem.
The Darboux Integral.
Approximate Integration.

Chapter 8 Sequences of Functions

Pointwise and Uniform Convergence.
Interchange of Limits.
The Exponential and Logarithmic Functions.
The Trigonometric Functions.

Chapter 9 Infinite Series

Absolute Convergence.
Tests for Absolute Convergence. Tests for Nonabsolute Convergence.
Series of Functions.

Chapter 10 The Generalized Rieman Integral

Definition and Main Properties.
Improper and Lebesgue Integrals.
Infinite Intervals.
Convergence Theorems.

Chapter 11 A Glimpse into Topology

Open and Closed Sets in R.
Compact Sets.
Continuous Functions.
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. ISBN - 9788126551811

Pages : 416

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Introduction To Real Analysis

by Bartle R.G.