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principles Of mathematical analysis 3ed; walter rudin [pdf]

### Principles of Mathematical Analysis (3E) by Walter Rudin

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Principles of Mathematical Analysis (3E) written by Walter Rudin, Professor of Mathematics, University of Wisconsin-Madison. Publish by McGR1\W-HILL. This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics.

Principles of Mathematical Analysis (3E) written by Walter Rudin cover the following topics.

• 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

• 2: Basic Topology Finite, Countable, and Uncountable Sets
Metric Spaces
Compact Sets
Perfect Sets
Connected Sets
Exercises

• 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
Rearrangements
Exercises

• 4: Continuity
Limits of Functions
Continuous Functions
Continuity and Compactness
Continuity and Connectedness
Discontinuities
Monotonic Functions
Infinite Limits and Limits at Infinity
Exercises

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• ##### other Math Books of Mathematical Analysis

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