This monograph on generalised functions, Fourier integrals and Fourier series is intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical techniques is required; the book is suitable for advanced university students, and can be used as the basis of a short undergraduate lecture course. A valuable and original feature of the book is the use of generalised-function theory to derive a simple, widely applicable method of obtaining asymptotic expressions for Fourier transforms and Fourier coefficients.
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'An extremely lucid and well-written account ... a stimulating and valuable addition to the literature of applied mathematics, with a good deal of the charm of eighteenth-century mathematics. It may well become a minor classic before very long.' George Weiss, Science
'Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof ... the book should be well within the compass of an honours student in mathematics or theoretical physics, and they are most strongly urged to buy it and read it.' Science Progess
'Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof ... the book should be well within the compass of an honours student in mathematics or theoretical physics, and they are most strongly urged to buy it and read it.' Science Progess
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"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
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This review is from: An Introduction to Fourier Analysis and Generalised Functions (Cambridge Monographs on Mechanics) (Paperback)
Nice little book. Concise and clear. In the typical English style, many of the proofs are left to the reader. Lighhill will assume what he finds obvious is also obvious to the reader. This was not always the case for me. He does this alot in the proving theorems so have a pencil ready. It is alot fun to work through the proofs becuase he gives rough sketches and leaves you to fill in the details. He manages this without loss of clarity or rigor. It is good pedagogy for anyone familiar with basic analysis of real variables and some knowledge of complex variables.
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This book grew out of an undergraduate course in the University of Manchester, in which the author attempted to expound the most useful facts about Fourier series and integrals. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalised function, trigonometrical series, good function, inversion theorem, asymptotic expression, ordinary function New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This book grew out of an undergraduate course in the University of Manchester, in which the author attempted to expound the most useful facts about Fourier series and integrals. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
generalised function, trigonometrical series, good function, inversion theorem, asymptotic expression, ordinary function New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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100
books
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- Fourier Series by G. H. Hardy on page 1
- Signal Analysis: Time, Frequency, Scale, and Structure by Ronald L. Allen on 5 pages
- Wave Physics: Oscillations - Solitons - Chaos (Advanced Texts in Physics) by Stephen Nettel in Front Matter (1), Front Matter (2), and page 31
- Functions of a Complex Variable: Theory and Technique (Classics in Applied Mathematics) by George F. Carrier on page 244, and page 320
- Linear Elastic Waves (Cambridge Texts in Applied Mathematics) by John G. Harris on page 19, and page 36
- Data Analysis and Signal Processing in Chromatography, Volume 21 (Data Handling in Science and Technology) by A. Felinger on page 385, and Index
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