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Walter Rudin's Principles of Mathematical Analysis (3E) by Roger Cooke



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Walter Rudin's Principles of Mathematical Analysis (3E) Solution Manual written by Roger Cooke, University of Vermont. Walter Rudin is Professor of Mathematicsf form University of Wisconsin-Madison and his book is 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 st udents who study mathematics.

Walter Rudin's Principles of Mathematical Analysis (3E) written by Roger Cooke 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
    Addition and Multiplication of Series
    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

  • Open
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