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Cover: 9780198501237 | Introduction to Integration | Hilary A. Priestley | Taschenbuch | 1997
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Introduction to Integration
Taschenbuch von Hilary A. Priestley
Sprache: Englisch

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Beschreibung
Introduction to Integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of examples and exercises. Intended as a first course in integration theory for students familiar with real analysis, the book begins with a simplified Lebesgue integral, which is then developed to provide an entry point for important results in the field. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measures. Designed as an undergraduate or graduate textbook, it is a companion volume to the author's Introduction to Complex Analysis and is aimed at both pure and applied mathematicians.
Introduction to Integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of examples and exercises. Intended as a first course in integration theory for students familiar with real analysis, the book begins with a simplified Lebesgue integral, which is then developed to provide an entry point for important results in the field. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measures. Designed as an undergraduate or graduate textbook, it is a companion volume to the author's Introduction to Complex Analysis and is aimed at both pure and applied mathematicians.
Inhaltsverzeichnis
  • 1: Setting the scene

  • 2: Preliminaries

  • 3: Intervals and step functions

  • 4: Integrals of step functions

  • 5: Continuous functions on compact intervals

  • 6: Techniques of Integration I

  • 7: Approximations

  • 8: Uniform convergence and power series

  • 9: Building foundations

  • 10: Null sets

  • 11: Linc functions

  • 12: The space L of integrable functions

  • 13: Non-integrable functions

  • 14: Convergence Theorems: MCT and DCT

  • 15: Recognizing integrable functions I

  • 16: Techniques of integration II

  • 17: Sums and integrals

  • 18: Recognizing integrable functions II

  • 19: The Continuous DCT

  • 20: Differentiation of integrals

  • 21: Measurable functions

  • 22: Measurable sets

  • 23: The character of integrable functions

  • 24: Integration VS. differentiation

  • 25: Integrable functions of Rk

  • 26: Fubini's Theorem and Tonelli's Theorem

  • 27: Transformations of Rk

  • 28: The spaces L1, L2 and Lp

  • 29: Fourier series: pointwise convergence

  • 30: Fourier series: convergence re-assessed

  • 31: L2-spaces: orthogonal sequences

  • 32: L2-spaces as Hilbert spaces

  • 33: The Fourier transform

  • 34: Integration in probability theory

  • Appendix I

  • Appendix II

  • Bibliography

  • Notation index

  • Subject index

Details
Empfohlen (bis): 8
Empfohlen (von): 4
Erscheinungsjahr: 1997
Produktart: Sachliteratur
Rubrik: Kinder & Jugend
Thema: Mathematik
Medium: Taschenbuch
Seiten: 320
ISBN-13: 9780198501237
ISBN-10: 0198501234
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Priestley, Hilary A.
Hersteller: OUP Oxford
Maße: 234 x 156 x 18 mm
Von/Mit: Hilary A. Priestley
Erscheinungsdatum: 28.09.1997
Gewicht: 0,488 kg
preigu-id: 108640588
Inhaltsverzeichnis
  • 1: Setting the scene

  • 2: Preliminaries

  • 3: Intervals and step functions

  • 4: Integrals of step functions

  • 5: Continuous functions on compact intervals

  • 6: Techniques of Integration I

  • 7: Approximations

  • 8: Uniform convergence and power series

  • 9: Building foundations

  • 10: Null sets

  • 11: Linc functions

  • 12: The space L of integrable functions

  • 13: Non-integrable functions

  • 14: Convergence Theorems: MCT and DCT

  • 15: Recognizing integrable functions I

  • 16: Techniques of integration II

  • 17: Sums and integrals

  • 18: Recognizing integrable functions II

  • 19: The Continuous DCT

  • 20: Differentiation of integrals

  • 21: Measurable functions

  • 22: Measurable sets

  • 23: The character of integrable functions

  • 24: Integration VS. differentiation

  • 25: Integrable functions of Rk

  • 26: Fubini's Theorem and Tonelli's Theorem

  • 27: Transformations of Rk

  • 28: The spaces L1, L2 and Lp

  • 29: Fourier series: pointwise convergence

  • 30: Fourier series: convergence re-assessed

  • 31: L2-spaces: orthogonal sequences

  • 32: L2-spaces as Hilbert spaces

  • 33: The Fourier transform

  • 34: Integration in probability theory

  • Appendix I

  • Appendix II

  • Bibliography

  • Notation index

  • Subject index

Details
Empfohlen (bis): 8
Empfohlen (von): 4
Erscheinungsjahr: 1997
Produktart: Sachliteratur
Rubrik: Kinder & Jugend
Thema: Mathematik
Medium: Taschenbuch
Seiten: 320
ISBN-13: 9780198501237
ISBN-10: 0198501234
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Priestley, Hilary A.
Hersteller: OUP Oxford
Maße: 234 x 156 x 18 mm
Von/Mit: Hilary A. Priestley
Erscheinungsdatum: 28.09.1997
Gewicht: 0,488 kg
preigu-id: 108640588
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