Fourier analysis and its applications/ (Record no. 177080)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 00379nam a2200133Ia 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0387008365 (acid-free paper) |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.2433 |
| Item number | VRE/F |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Vretblad.,Anders |
| 245 #0 - TITLE STATEMENT | |
| Title | Fourier analysis and its applications/ |
| Statement of responsibility, etc. | Anders Vretblad. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New York :: |
| Name of publisher, distributor, etc. | Springer, |
| Date of publication, distribution, etc. | c2003. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xi, 269 p. : |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | <br/><br/>1 Introduction 1<br/>1.1 The classical partial differential equations 1<br/>1.2 Well-posed problems 3<br/>1.3 The one-dimensional wave equation 5<br/>1.4 Fourier's method 9<br/>2 Preparations 15<br/>2.1 Complex exponentials 15<br/>2.2 Complex-valued functions of a real variable 17<br/>2.3 Cesaro summation of series 20<br/>2.4 Positive summation kernels 22<br/>2.5 The Riemann-Lebesgue lemma 25<br/>2.6 *Some simple distributions 27<br/>2.7 ^Computing with S 32<br/>3 Laplace and Z transforms 39<br/>3.1 The Laplace transform 39<br/>3.2 Operations 42<br/>3.3 Applications to differential equations 47<br/>3.4 Convolution , 53<br/>3.5 *Laplace transforms of distributions 57<br/>3.6 The Z transform 60<br/>X Contents<br/>3.7 Applications in control theory 57<br/>Summary of Chapter 3 70<br/>4 Fourier series 73<br/>4.1 Definitions 73<br/>4.2 Dirichlet's and Fejer's kernels; uniqueness 80<br/>4.3 Differentiable functions 34<br/>4.4 Point wise convergence 35<br/>4.5 Formulae for other periods qq<br/>4.6 Some worked examples 91<br/>4.7 The Gibbs phenomenon 93<br/>4.8 *Fourier series for distributions 96<br/>Summary of Chapter 4<br/>5 Theory 105<br/>5.1 Linear spaces over the complex numbers 105<br/>5.2 Orthogonal projections HO<br/>5.3 Some examples H4<br/>5.4 The Fourier system is complete II9<br/>5.5 Legendre polynomials I23<br/>5.6 Other classical orthogonal polynomials 127<br/>Summary of Chapter 5 130<br/>6 Separation of variables 137<br/>6.1 The solution of Fourier's problem I37<br/>6.2 Variations on Fourier's theme I39<br/>6.3 The Dirichlet problem in the unit disk I43<br/>6.4 Sturm—Liouville problems 133<br/>6.5 Some singular Sturm—Liouville problems I59<br/>Summary of Chapter 6 IgO<br/>7 Fourier transforms 13^<br/>7.1 Introduction Igg<br/>7.2 Definition of the Fourier transform 166<br/>7.3 Properties Igg<br/>7.4 The inversion theorem 171<br/>7.5 The convolution theorem 17g<br/>7.6 Plancherel's formula IgQ<br/>7.7 Application 1 Ig2<br/>7.8 Application ^ 185<br/>7.9 Application 3: The sampling theorem I37<br/>7.10 Connection with the Laplace transform I33<br/>7.11 *Distributions and Fourier transforms 19q<br/>Summary of Chapter 7 ! . . . ! 192<br/>' Contents xi<br/>8 Distributions 197<br/>8.1 History 197<br/>8.2 Fuzzy points - test functions 200<br/>8.3 Distributions 203<br/>8.4 Properties 206<br/>8.5 Fourier transformation 213<br/>8.6 Convolution 218<br/>8.7 Periodic distributions and Fourier series 220<br/>8.8 Fundamental solutions 221<br/>8.9 Back to the starting point 223<br/>Summary of Chapter 8 224<br/>9 Multi-dimensional Fourier analysis 227<br/>9.1 Rearranging series 227<br/>9.2 Double series 230<br/>9.3 Multi-dimensional Fourier series 233<br/>9.4 Multi-dimensional Fourier transforms 236<br/>Appendices<br/>A The ubiquitous convolution 239<br/>B The discrete Fourier transform 243<br/>C Formulae 247<br/>C.l Laplace transforms 247<br/>C.2 Z transforms 250<br/>C.3 Fourier series 251<br/>C.4 Fourier transforms 252<br/>C.5 Orthogonal polynomials 254<br/>D Answers to selected exercises 257<br/>E Literature 265<br/>Index 267 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 515.2433 VRE/F | P32082 | 29/08/2016 | General Books |