PRINCIPLES OF MATHEMATICAL ANALYSIS 3rd Edition by Walter Rudin ISBN 7111134176 9787111134176

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ISBN 10: 7111134176 
ISBN 13: 9787111134176
Author: Walter Rudin

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind’s construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.

PRINCIPLES OF MATHEMATICAL ANALYSIS 3rd Table of contents:

Chapter 1: The Real and Complex Number Systems

• Introduction

• Ordered Sets

• Fields

• The Real Field

• The Extended Real Number System

• The Complex Field

• Euclidean Spaces

• Appendix: Dedekind Cuts

Chapter 2: Basic Topology

• Finite, Countable, and Uncountable Sets

• Metric Spaces

• Compact Sets

• Perfect Sets

• Connected Sets

Chapter 3: Numerical Sequences and Series

• Convergent Sequences

• Subsequences

• Cauchy Sequences

• Upper and Lower Limits

• Some Special Sequences

• Series

• Series of Nonnegative Terms

• The Number e

• The Root and Ratio Tests

• Power Series

• Summation by Parts

• Absolute Convergence

• Addition and Multiplication of Series

• Rearrangements

Chapter 4: Continuity

• Limits of Functions

• Continuous Functions

• Continuity and Compactness

• Continuity and Connectedness

• Discontinuities

• Monotonic Functions

• Infinite Limits and Limits at Infinity

Chapter 5: Differentiation

• The Derivative of a Real Function

• Mean Value Theorems

• The Continuity of Derivatives

• L’Hospital’s Rule

• Derivatives of Higher Order

• Taylor’s Theorem

• Differentiation of Vector-valued Functions

Chapter 6: The Riemann-Stieltjes Integral

• Definition and Existence of the Integral

• Properties of the Integral

• Integration and Differentiation

• Integration of Vector-valued Functions

• Rectifiable Curves

Chapter 7: Sequences and Series of Functions

• Discussion of Main Problem

• Uniform Convergence

• Uniform Convergence and Continuity

• Uniform Convergence and Integration

• Uniform Convergence and Differentiation

• Equicontinuous Families of Functions

• The Stone-Weierstrass Theorem

Chapter 8: Some Special Functions

• Power Series

• The Exponential and Logarithmic Functions

• The Trigonometric Functions

• The Algebraic Completeness of the Complex Field

• Fourier Series

• The Gamma Function

Chapter 9: Functions of Several Variables

• Linear Transformations

• Differentiation

• The Contraction Principle

• The Inverse Function Theorem

• The Implicit Function Theorem

• The Rank Theorem

• Determinants

• Derivatives of Higher Order

• Differentiation of Integrals

Chapter 10: Integration of Differential Forms

• Integration

• Primitive Mappings

• Partitions of Unity

• Change of Variables

• Differential Forms

• Simplexes and Chains

• Stokes’ Theorem

• Closed Forms and Exact Forms

• Vector Analysis

Chapter 11: The Lebesgue Theory

• Set Functions

• Construction of the Lebesgue Measure

• Measure Spaces

• Measurable Functions

• Simple Functions

• Integration

• Comparison with the Riemann Integral

• Integration of Complex Functions

• Functions of Class L²

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