Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution.
| Foreword to the Classics Edition |
|
ix | |
| Preface |
|
xv | |
|
|
|
1 | (118) |
|
|
|
1 | (5) |
|
2 The concept of a function |
|
|
6 | (6) |
|
|
|
12 | (7) |
|
|
|
19 | (1) |
|
|
|
20 | (6) |
|
|
|
26 | (11) |
|
|
|
37 | (6) |
|
8 Bonnet's mean value theorem |
|
|
43 | (3) |
|
9 The Dirichlet conditions |
|
|
46 | (5) |
|
|
|
51 | (4) |
|
11 Fejer's arithmetic mean method |
|
|
55 | (6) |
|
12 Integration and differentiation of the Fourier series. The method of local smoothing |
|
|
61 | (14) |
|
13 Orthogonal functions systems |
|
|
75 | (13) |
|
14 The Fourier functions as solutions of an eigenvalue problem |
|
|
88 | (6) |
|
15 Fourier series and Taylor series |
|
|
94 | (4) |
|
16 The Bernoulli polynomials |
|
|
98 | (13) |
|
17 The method of trigonometric interpolation |
|
|
111 | (8) |
|
2 The Fourier Series in Approximation problems |
|
|
119 | (39) |
|
18 The problem of curve fitting |
|
|
119 | (1) |
|
19 Curve fitting by sine functions |
|
|
120 | (8) |
|
|
|
128 | (2) |
|
21 Global smoothing of noisy data |
|
|
130 | (7) |
|
22 Search for hidden periodicities |
|
|
137 | (3) |
|
23 Fourier series and power expansions |
|
|
140 | (8) |
|
24 Increased convergence by weighting |
|
|
148 | (10) |
|
|
|
158 | (92) |
|
|
|
158 | (1) |
|
26 Gradual enrichment of the Fourier spectrum |
|
|
159 | (9) |
|
27 Dirichlet's discontinuous factor |
|
|
168 | (4) |
|
|
|
172 | (8) |
|
29 Analytical approximation of the Fourier integral |
|
|
180 | (2) |
|
30 The Fourier series derived from the Fourier integral |
|
|
182 | (8) |
|
31 The infinite limits in Fourier's integral |
|
|
190 | (3) |
|
32 The method of residues |
|
|
193 | (15) |
|
|
|
208 | (9) |
|
|
|
217 | (3) |
|
35 Examples for the Laplace transform method |
|
|
220 | (17) |
|
36 Operations with the Laplace transform |
|
|
237 | (9) |
|
37 The convolution theorem |
|
|
246 | (4) |
| Bibliography |
|
250 | (1) |
| Index |
|
251 | |
Cornelius Lanczos (1893-1974) held positions at Purdue University, Indiana, the US National Bureau of Standards, University of Washington, Boeing, and the Dublin Institute for Advanced Studies. He wrote eight books and won the Chauvenet Prize for Excellence in Expository Mathematical Writing in 1960. The six-volume Collected Published Papers with Commentaries appeared in 1998.
