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Principles of Mathematics Analysis (Cloth)

Principles of Mathematics Analysis (Cloth) - 3rd edition

ISBN13: 978-0070542358

Cover of Principles of Mathematics Analysis (Cloth) 3RD 76 (ISBN 978-0070542358)
ISBN13: 978-0070542358
ISBN10: 007054235X
Cover type: Hardback
Edition/Copyright: 3RD 76
Publisher: McGraw-Hill Publishing Company
Published: 1976
International: No
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Principles of Mathematics Analysis (Cloth) - 3RD 76 edition

ISBN13: 978-0070542358

Walter Rudin

ISBN13: 978-0070542358
ISBN10: 007054235X
Cover type: Hardback
Edition/Copyright: 3RD 76
Publisher: McGraw-Hill Publishing Company

Published: 1976
International: No
Summary

Explains set theory, sequences, continuity, differentiation, integrals, and vector-space concepts.

Author Bio

Rudin, Walter : University of Wisconsin

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
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