Rudin Principles of Mathematical Analysis PDF

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What else would you pick if you want to understand analysis at a higher level? Well, Anyone who wants to begin studying analysis could use this book to establish the necessary fundamentals in his head.¬†This book Rudin Principles of Mathematical Analysis PDF forms the basis for the first class in real analysis (in a single variable) for countless thousands of hapless students who decide to concentrate on math. It’s chosen by professors who have had decades of experience as university mathematicians, and have achieved a certain Zen-like understanding of the knowledge contained within. It’s one of the clearest introductory level analysis textbooks out there that you should try using.

Principles of Mathematical Analysis PDF Book Details

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

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

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 L2
Exercises

Bibliography
List of Special Symbols
Index

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