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Produktbild: Real Analysis and Foundations
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Real Analysis and Foundations

Aus der Reihe Textbooks in Mathematics
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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

27.05.2022

Abbildungen

74 SW-Abb., 74 SW-Zeichn., 1 Tabellen

Verlag

Taylor & Francis

Seitenzahl

502

Maße (L/B/H)

24/16,1/3,1 cm

Gewicht

913 g

Auflage

5. Auflage

Sprache

Englisch

ISBN

978-1-03-210272-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

27.05.2022

Abbildungen

74 SW-Abb., 74 SW-Zeichn., 1 Tabellen

Verlag

Taylor & Francis

Seitenzahl

502

Maße (L/B/H)

24/16,1/3,1 cm

Gewicht

913 g

Auflage

5. Auflage

Sprache

Englisch

ISBN

978-1-03-210272-6

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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Die Leseprobe wird geladen.
  • Produktbild: Real Analysis and Foundations

  • Preface

    0 Background Material
    0.1 Number Systems
    0.1.1 The Natural Numbers
    0.1.2 The Integers
    0.1.3 The Rational Numbers

    02 Logic and Set
    0.2.1 And" and "Or"
    0.2.2 "not" and "if then"
    0.2.3 Contrapositive, Converse, and "Iff"
    0.2.4 Quantifiers
    0.2.5 Set Theory and Venn Diagrams
    0.2.6 Relations and Functions
    0.2.7 Countable and Uncountable Sets

    1 Real and Complex Numbers
    1.1 The Real Numbers
    Appendix: Construction of the Real Numbers
    1.2 The Complex Numbers
    2 Sequences 71
    2.1 Convergence of Sequences
    2.2 Subsequences
    2.3 Limsup and Liminf
    2.4 Some Special Sequences

    3 Series of Numbers
    3.1 Convergence of Series
    3.2 Elementary Convergence Tests
    3.3 Advanced Convergence Tests
    3.4 Some Special Series
    3.5 Operations on Series

    4 Basic Topology
    4.1 Open and Closed Sets
    4.2 Further Properties of Open and Closed Sets
    4.3 Compact Sets
    4.4 The Cantor Set
    4.5 Connected and Disconnected Sets
    4.6 Perfect Sets

    5 Limits and Continuity of Functions
    5.1 Basic Properties of the Limit of a Function
    5.2 Continuous Functions
    5.3 Topological Properties and Continuity
    5.4 Classifying Discontinuities and Monotonicity

    6 Differentiation of Functions
    6.1 The Concept of Derivative
    6.2 The Mean Value Theorem and Applications
    6.3 More on the Theory of Differentiation

    7 The Integral
    7.1 Partitions and the Concept of Integral
    7.2 Properties of the Riemann Integral
    7.3 Change of Variable and Related Ideas
    7.4 Another Look at the Integral
    7.5 Advanced Results on Integration Theory

    8 Sequences and Series of Functions
    8.1 Partial Sums and Pointwise Convergence
    8.2 More on Uniform Convergence
    8.3 Series of Functions
    8.4 The Weierstrass Approximation Theorem

    9 Elementary Transcendental Functions
    9.1 Power Series
    9.2 More on Power Series: Convergence Issues
    9.3 The Exponential and Trigonometric Functions
    9.4 Logarithms and Powers of Real Numbers

    10 Functions of Several Variables
    10.1 A New Look at the Basic Concepts of Analysis
    10.2 Properties of the Derivative
    10.3 The Inverse and Implicit Function Theorems

    11 Advanced Topics
    11.1 Metric Spaces
    11.2 Topology in a Metric Space
    11.3 The Baire Category Theorem
    11.4 The Ascoli-Arzela Theorem

    12 Differential Equations
    12.1 Picard's Existence and Uniqueness Theorem
    12.1.1 The Form of a Differential Equation
    12.1.2 Picard's Iteration Technique
    12.1.3 Some Illustrative Examples
    12.1.4 Estimation of the Picard Iterates
    12.2 Power Series Methods

    13 Introduction to Harmonic Analysis
    13.1 The Idea of Harmonic Analysis
    13.2 The Elements of Fourier Series
    13.3 An Introduction to the Fourier Transform
    Appendix: Approximation by Smooth Functions
    13.4 Fourier Methods and Differential Equations
    13.4.1 Remarks on Different Fourier Notations
    13.4.2 The Dirichlet Problem on the Disc
    13.4.3 Introduction to the Heat and Wave Equations
    13.4.4 Boundary Value Problems
    13.4.5 Derivation of the Wave Equation
    13.4.6 Solution of the Wave Equation
    13.5 The Heat Equation

    Appendix: Review of Linear Algebra
    Table of Notation
    Glossary
    Bibliography
    Index