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Table of Contents

**Principles of Mathematical Analysis PDF Book Details**

**Principles of Mathematical Analysis PDF Book Details**

Principles of Mathematical Analysis*Book Title:*3*Edition:*Walter Rudin*Author:*January 1st, 1976*Publication Date:*9780070542358*ISBN:**Formats:*352*No. of pages:*17 MB*Size:*Mathematics, Textbook*Genre:*English*Language:*Available for Download*File Status:*Free*Price:*

*Rudin Principles of Mathematical Analysis PDF Book Description*

*Rudin Principles of Mathematical Analysis PDF Book Description*

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.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

*Table Of Contents For Principles of Mathematical Analysis PDF*

*Table Of Contents For Principles of Mathematical Analysis PDF*

*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

Exercises

**Chapter 2: Basic Topology**

Finite, Countable, and Uncountable Sets

Metric Spaces

Compact Sets

Perfect Sets

Connected Sets

Exercises

**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

Exercises

**Chapter 4: Continuity**

Limits of Functions

Continuous Functions

Continuity and Compactness

Continuity and Connectedness

Discontinuities

Monotonic Functions

Infinite Limits and Limits at Infinity

Exercises

**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

Exercises

**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

Exercises

**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

Exercises

**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

Exercises

**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

Exercises

**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

Exercises

*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 *L*^{2}

Exercises

Bibliography

List of Special Symbols

Index

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