Vor Ort
Merkzettel Warenkorb
Produktbild: Elementary Classical Analysis

Elementary Classical Analysis

389,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

15.03.1993

Abbildungen

640 p.

Verlag

Macmillan Learning

Seitenzahl

752

Maße (L/B/H)

24,2/17,4/4 cm

Gewicht

1216 g

Auflage

2nd edition

Sprache

Englisch

ISBN

978-0-7167-2105-5

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

15.03.1993

Abbildungen

640 p.

Verlag

Macmillan Learning

Seitenzahl

752

Maße (L/B/H)

24,2/17,4/4 cm

Gewicht

1216 g

Auflage

2nd edition

Sprache

Englisch

ISBN

978-0-7167-2105-5

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

Noch keine Bewertungen vorhanden

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.

Kundinnen und Kunden meinen

Bewertungen (0)
  • Produktbild: Elementary Classical Analysis



  • 1. Introduction: Sets and Functions
        Supplement on the Axioms of Set Theory

        

      
    2. The Real Line and Euclidean Space
        Ordered Fields and the Number Systems

        Completeness and the Real Number System

        Least Upper Bounds

        Cauchy Sequences

        Cluster Points: lim inf and lim sup

        Euclidean Space

        Norms, Inner Products, and Metrics

        The Complex Numbers

        

      
    3. Topology of Euclidean Space
        Open Sets

        Interior of a Set

        Closed Sets

        Accumulation Points

        Closure of a Set

        Boundary of a Set

        Sequences

        Completeness

        Series of Real Numbers and Vectors

        

      
    4. Compact and Connected Sets
        Compacted-ness

        The Heine-Borel Theorem

        Nested Set Property

        Path-Connected Sets

        Connected Sets

        

      
    5. Continuous Mappings
        Continuity

        Images of Compact and Connected Sets

        Operations on Continuous Mappings

        The Boundedness of Continuous Functions of Compact Sets

        The Intermediate Value Theorem

        Uniform Continuity

        Differentiation of Functions of One Variable

        Integration of Functions of One Variable

        

      
    6. Uniform Convergence
        Pointwise and Uniform Convergence

        The Weierstrass M Test

        Integration and Differentiation of Series

        The Elementary Functions

        The Space of Continuous Functions

        The Arzela-Ascoli Theorem

        The Contraction Mapping Principle and Its Applications

        The Stone-Weierstrass Theorem

        The Dirichlet and Abel Tests

        Power Series and Cesaro and Abel Summability

        

      
    7. Differentiable Mappings
        Definition of the Derivative

        Matrix Representation

        Continuity of Differentiable Mappings; Differentiable Paths

        Conditions for Differentiability

        The Chain Rule

        Product Rule and Gradients

        The Mean Value Theorem

        Taylors Theorem and Higher Derivatives

        Maxima and Minima

        

      
    8. The Inverse and Implicit Function Theorems and Related Topics
        Inverse Function Theorem

        Implicit Function Theorem

        The Domain-Straightening Theorem

        Further Consequences of the

        Implicit Function Theorem

        An Existence Theorem for Ordinary Differential Equations

        The Morse Lemma

        Constrained Extrema and Lagrange Multipliers

        

      
    9. Integration
        Integrable Functions

        Volume and Sets of Measure Zero

        Lebesgues Theorem

        Properties of the Integral

        Improper Integrals

        Some Convergence Theorems

        Introduction to Distributions

        

      
    10. Fubinis Theorem and the Change of Variables Formula
        Introduction

        Fubinis Theorem

        Change of Variables Theorem

        Polar Coordinates

        Spherical Coordinates and Cylindrical Coordinates

        A Note on the Lebesgue Integral

        Interchange of Limiting Operations

        

      
    11. Fourier Analysis
        Inner Product Spaces

        Orthogonal Families of Functions

        Completeness and Convergence Theorems

        Functions of Bounded Variation and Fejér Theory (Optional)

        Computation of Fourier Series

        Further Convergence Theorems

        Applications

        Fourier Integrals

        Quantum Mechanical Formalism

        

      
    Miscellaneous Exercises
      
    References
      
    Answers to Selected Odd-Numbered Exercises
      
    Index