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Fourier Analysis Revised edition [Pehme köide]

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(University of Cambridge), Foreword by (University of California, Los Angeles)
  • Formaat: Paperback / softback, 610 pages, kõrgus x laius x paksus: 245x170x30 mm, kaal: 1060 g, Worked examples or Exercises
  • Sari: Cambridge Mathematical Library
  • Ilmumisaeg: 09-Jun-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009230050
  • ISBN-13: 9781009230056
Teised raamatud teemal:
Fourier Analysis Revised editionSuurem pilt
  • Formaat: Paperback / softback, 610 pages, kõrgus x laius x paksus: 245x170x30 mm, kaal: 1060 g, Worked examples or Exercises
  • Sari: Cambridge Mathematical Library
  • Ilmumisaeg: 09-Jun-2022
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009230050
  • ISBN-13: 9781009230056
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781009230056.html
Märksõnad:
Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.

Arvustused

'This is an extraordinary and very attractive book I would like to see the book on the desk of every pure mathematician with an interest in classical analysis, and of every teacher of applied mathematics whose work involves analysis This is how mathematics ideally should be presented, but too seldom is.' R. P. Boas, SIAM Review 'This is a wonderful book More than anything, this is just fun to read, to browse, to study. Fourier Analysis is literate, lively and a true classic. I highly recommend it.' William J. Satzer, MAA Reviews 'I cannot imagine a mathematically prepared reader failing to enjoy this book.' P. G. MacGregor, The Mathematical Gazette

Muu info

A lively and engaging look at some of the ideas, techniques and elegant results of Fourier analysis, and their applications.
Foreword xi
Terence Tao
Preface xiii
Part I Fourier Series
1(76)
1 Introduction
3(3)
2 Proof of Fejer's theorem
6(5)
3 Weyl's equidistribution theorem
11(4)
4 The Weierstrass polynomial approximation theorem
15(4)
5 A second proof of Weierstrass's theorem
19(2)
6 Hausdorff's moment problem
21(3)
7 The importance of linearity
24(4)
8 Compass and tides
28(4)
9 The simplest convergence theorem
32(3)
10 The rate of convergence
35(3)
11 A nowhere differentiable function
38(4)
12 Reactions
42(4)
13 Monte Carlo methods
46(4)
14 Mathematical Brownian motion
50(6)
15 Pointwise convergence
56(3)
16 Behaviour at points of discontinuity I
59(3)
17 Behaviour at points of discontinuity II
62(5)
18 A Fourier series divergent at a point
67(7)
19 Pointwise convergence, the answer
74(3)
Part II Some Differential Equations
77(66)
20 The undisturbed damped oscillator does not explode
79(4)
21 The disturbed damped linear oscillator does not explode
83(5)
22 Transients
88(5)
23 The linear damped oscillator with periodic input
93(6)
24 A non-linear oscillator I
99(5)
25 A non-linear oscillator II
104(9)
26 A non-linear oscillator III
113(3)
27 Poisson summation
116(5)
28 Dirichlet's problem for the disc
121(3)
29 Potential theory with smoothness assumptions
124(7)
30 An example of Hadamard
131(3)
31 Potential theory without smoothness assumptions
134(9)
Part III Orthogonal Series
143(76)
32 Mean square approximation I
145(5)
33 Mean square approximation II
150(5)
34 Mean square convergence
155(4)
35 The isoperimetric problem I
159(7)
36 The isoperimetric problem II
166(4)
37 The Sturm-Liouville equation I
170(5)
38 Liouville
175(4)
39 The Sturm-Liouville equation II
179(6)
40 Orthogonal polynomials
185(6)
41 Gaussian quadrature
191(6)
42 Linkages
197(4)
43 Tchebychev and uniform approximation I
201(6)
44 The existence of the best approximation
207(5)
45 Tchebychev and uniform approximation II
212(7)
Part IV Fourier Transforms
219(144)
46 Introduction
221(5)
47 Change in the order of integration I
226(4)
48 Change in the order of integration II
230(10)
49 Fejer's theorem for Fourier transforms
240(5)
50 Sums of independent random variables
245(8)
51 Convolution
253(6)
52 Convolution on T
259(6)
53 Differentiation under the integral
265(5)
54 Lord Kelvin
270(4)
55 The heat equation
274(8)
56 The age of the earth I
282(3)
57 The age of the earth II
285(4)
58 The age of the earth III
289(3)
59 Weierstrass's proof of Weierstrass's theorem
292(3)
60 The inversion formula
295(5)
61 Simple discontinuities
300(8)
62 Heat flow in a semi-infinite rod
308(7)
63 A second approach
315(9)
64 The wave equation
324(8)
65 The transatlantic cable I
332(3)
66 The transatlantic cable II
335(3)
67 Uniqueness for the heat equation I
338(6)
68 Uniqueness for the heat equation II
344(3)
69 The law of errors
347(2)
70 The central limit theorem I
349(8)
71 The central limit theorem II
357(6)
Part V Further Developments
363(108)
72 Stability and control
365(3)
73 Instability
368(4)
74 The Laplace transform
372(7)
75 Deeper properties
379(7)
76 Poles and stability
386(9)
77 A simple time delay equation
395(8)
78 An exception to a rule
403(4)
79 Many dimensions
407(6)
80 Sums of random vectors
413(5)
81 A chi squared test
418(7)
82 Haldane on fraud
425(4)
83 An example of outstanding statistical treatment I
429(5)
84 An example of outstanding statistical treatment II
434(2)
85 An example of outstanding statistical treatment III
436(7)
86 Will a random walk return?
443(8)
87 Will a Brownian motion return?
451(4)
88 Analytic maps of Brownian motion
455(6)
89 Will a Brownian motion tangle?
461(6)
90 La Famille Picard va a Monte Carlo
467(4)
Part VI Other Directions
471(92)
91 The future of mathematics viewed from 1800
473(2)
92 Who was Fourier? I
475(3)
93 Who was Fourier? II
478(3)
94 Why do we compute?
481(3)
95 The diameter of stars
484(4)
96 What do we compute?
488(3)
97 Fourier analysis on the roots of unity
491(6)
98 How do we compute?
497(3)
99 How fast can we multiply?
500(3)
100 What makes a good code?
503(3)
101 A little group theory
506(3)
102 A good code?
509(4)
103 A little more group theory
513(6)
104 Fourier analysis on finite Abelian groups
519(6)
105 A formula of Euler
525(7)
106 An idea of Dirichlet
532(7)
107 Primes in some arithmetical progressions
539(7)
108 Extension from real to complex variable
546(6)
109 Primes in general arithmetical progressions
552(8)
110 A word from our founder 558 Appendix A: The circle T
560(3)
Appendix B Continuous function on closed bounded sets 563(2)
Appendix C Weakening hypotheses 565(10)
Appendix D Ode to a galvanometer 575(2)
Appendix E The principle of the argument 577(3)
Appendix F Chase the constant 580(1)
Appendix G Are share prices in Brownian motion? 581(4)
Index 585
T. W. Körner is Emeritus Professor of Fourier Analysis at the University of Cambridge. His other books include The Pleasures of Counting (Cambridge, 1996) and Where Do Numbers Come From? (Cambridge, 2019).