Fourier Series and Orthogonal Functions
Title | Fourier Series and Orthogonal Functions PDF eBook |
Author | Harry F. Davis |
Publisher | Courier Corporation |
Pages | 436 |
Release | 2012-09-05 |
Genre | Mathematics |
ISBN | 0486140733 |
This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.
Fourier Series and Orthogonal Functions
Title | Fourier Series and Orthogonal Functions PDF eBook |
Author | Harry Floyd Davis |
Publisher | |
Pages | 415 |
Release | 1966 |
Genre | |
ISBN |
Fourier Series and Orthogonal Polynomials
Title | Fourier Series and Orthogonal Polynomials PDF eBook |
Author | Dunham Jackson |
Publisher | American Mathematical Soc. |
Pages | 234 |
Release | 1941-12-31 |
Genre | Fourier series |
ISBN | 1614440069 |
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.
Summationof the Fourier Series of Orthogonal Functions
Title | Summationof the Fourier Series of Orthogonal Functions PDF eBook |
Author | Kien-Kwong Chen |
Publisher | |
Pages | |
Release | 1957 |
Genre | |
ISBN |
Orthogonal Functions
Title | Orthogonal Functions PDF eBook |
Author | Giovanni Sansone |
Publisher | |
Pages | 440 |
Release | 1959 |
Genre | Functions, Orthogonal |
ISBN |
Highly regarded treatise contains a rich compilation of general results and convenient criteria concerning Fourier series, Legendre series, Laguerre and Hermite polynomials. Until publication of this book, much of the material had not been available in English. First paperback edition. Translated by Ainsley H. Diamond. Foreword. Bibliography. 14 black-and-white illustrations.
Summation of the Fourier Series of Orthogonal Functions
Title | Summation of the Fourier Series of Orthogonal Functions PDF eBook |
Author | Jian'gong Chen |
Publisher | |
Pages | 186 |
Release | 1957 |
Genre | Fourier series |
ISBN |
Wavelets and Other Orthogonal Systems with Applications
Title | Wavelets and Other Orthogonal Systems with Applications PDF eBook |
Author | Gilbert G. Walter |
Publisher | CRC Press |
Pages | 264 |
Release | 1994-07-13 |
Genre | Mathematics |
ISBN | 9780849378782 |
This book makes accessible to both mathematicians and engineers important elements of the theory, construction, and application of orthogonal wavelets. It is integrated with more traditional orthogonal series, such as Fourier series and orthogonal polynomials. It treats the interaction of both with generalized functions (delta functions), which have played an important part in engineering theory but whose rules are often vaguely presented. Unlike most other books that are excessively technical, this text/reference presents the basic concepts and examples in a readable form. Much of the material on wavelets has not appeared previously in book form. Applications to statistics, sampling theorems, and stochastic processes are given. In particular, the close affinity between wavelets and sampling theorems is explained and developed.