| eBook ISBN: | 978-1-61444-006-2 |
| Product Code: | CAR/6.E |
| List Price: | $45.00 |
| MAA Member Price: | $33.75 |
| AMS Member Price: | $33.75 |
| eBook ISBN: | 978-1-61444-006-2 |
| Product Code: | CAR/6.E |
| List Price: | $45.00 |
| MAA Member Price: | $33.75 |
| AMS Member Price: | $33.75 |
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Book DetailsThe Carus Mathematical MonographsVolume: 6; 1941; 234 pp
The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics.
The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence.
There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.
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Table of Contents
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Chapters
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Chapter I. Fourier series
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Chapter II. Legendre polynomials
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Chapter III. Bessel functions
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Chapter IV. Boundary value problems
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Chapter V. Double series; Laplace series
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Chapter VI. The Pearson frequency functions
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Chapter VII. Orthogonal polynomials
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Chapter VIII. Jacobi polynomials
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Chapter IX. Hermite polynomials
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Chapter X. Laguerre polynomials
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Chapter XI. Convergence
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Additional Material
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Reviews
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The author has been able, by not proving everything, to include a great deal of interesting material; by proving typical results in detail, he has shown how the formal results may be justified and safely used. Considerable attention is paid to physical applications of orthogonal functions. This rather unusual synthesis of two different attitudes should be good for students beginning advanced work in either pure or applied analysis.
R. P. Boas, Jr., Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics.
The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence.
There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.
-
Chapters
-
Chapter I. Fourier series
-
Chapter II. Legendre polynomials
-
Chapter III. Bessel functions
-
Chapter IV. Boundary value problems
-
Chapter V. Double series; Laplace series
-
Chapter VI. The Pearson frequency functions
-
Chapter VII. Orthogonal polynomials
-
Chapter VIII. Jacobi polynomials
-
Chapter IX. Hermite polynomials
-
Chapter X. Laguerre polynomials
-
Chapter XI. Convergence
-
The author has been able, by not proving everything, to include a great deal of interesting material; by proving typical results in detail, he has shown how the formal results may be justified and safely used. Considerable attention is paid to physical applications of orthogonal functions. This rather unusual synthesis of two different attitudes should be good for students beginning advanced work in either pure or applied analysis.
R. P. Boas, Jr., Mathematical Reviews
