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Produktbild: Principles of Mathematical Analysis
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Principles of Mathematical Analysis

Aus der Reihe Higher Math

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Beschreibung

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...

Beschreibung

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.

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

01.11.2026
Verlag McGraw-Hill Education Ltd
Seitenzahl

342

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

01.11.2026
Verlag McGraw-Hill Education Ltd
Seitenzahl

342
Maße (L/B/H)

22,7/15,1/1,5 cm
Gewicht

440 g
Auflage

3. Auflage
Sprache

Englisch
ISBN

978-0-07-085613-4
Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Principles of Mathematical Analysis

  • 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