H. A. Priestley, Hilary A. Priestley

Introduction to Integration

• Broschiertes Buch

Produktbeschreibung

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 illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditional Riemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians. Prerequisites are the rudiments of integral calculus and a first course in real analysis.

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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.

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Produktdetails

• Verlag: OUP Oxford
• Seitenzahl: 320
• Altersempfehlung: 4 bis 8 Jahre
• Erscheinungstermin: 28. September 1997
• Englisch
• Abmessung: 234mm x 156mm x 18mm
• Gewicht: 488g
• ISBN-13: 9780198501237
• ISBN-10: 0198501234
• Artikelnr.: 22028652

Inhaltsangabe

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