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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
    Ordered Sets
    The Real Field
    The Extended Real Number System
    The Complex Field
    Euclidean Spaces

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

  • 3: Numerical Sequences and Series
    Convergent Sequences
    Subsequences Cauchy Sequences
    Upper and Lower Limits
    Some Special Sequences
    Series of Nonnegative Terms
    The Number e
    The Root and Ratio Tests
    Power Series
    Summation by Parts Absolute Convergence
    Addition and Multiplication of Series

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

  • 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

  • 6: The Riemann-Stieltjes Integral
    Definition and Existence of the Integral
    Properties of the Integral
    Integration and Differentiation
    Integration of Vector-valued
    Functions Rectifiable

  • 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

  • 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

  • 9: Functions of Several Variables Linear Transformations
    The Contraction Principle
    The Inverse Function Theorem
    The Implicit Function Theorem
    The Rank Theorem Determinants
    Derivatives of Higher Order
    Differentiation of Integrals

  • 10: Integration of Differential Forms
    Primitive Mappings
    Partitions of Unity
    Change of Variables
    Differential Forms
    Simplexes and Chains
    Stokes` Theorem
    Closed Forms and Exact Forms
    Vector Analysis

  • 11: The Lebesgue Theory
    Set Functions
    Construction of the Lebesgue Measure
    Measure Spaces
    Measurable Functions
    Simple Functions
    Comparison with the Riemann Integral
    Integration of Complex Functions
    Functions of Class L2

  • Bibliography

  • List of Special Symbols

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