Introduction to Integration
“Introduction to Integration” by Hilary A. Priestley, published by Clarendon Press in 1997, offers a comprehensive overview of integration theory, spanning 306 pages in English. This book presents a practical guide to the Lebesgue integral, featuring numerous illustrative examples and exercises. It begins with a simplified version of the Lebesgue-style integral, making it suitable for a first course in integration, and progresses to selected applications primarily related to Fourier analysis.
Readers will find that the book emphasizes integrable functions rather than measure, catering to both pure and applied mathematicians. It is designed as an undergraduate or introductory graduate textbook, requiring only a basic understanding of integral calculus and a first course in real analysis. The structure and style of this work align closely with Priestley’s “Introduction to Complex Analysis,” serving as a companion volume for those looking to deepen their understanding of mathematical concepts in calculus and numerical analysis.
Official synopsis Publisher
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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