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| Ïîèñê ïî óêàçàòåëÿì |
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| Korner T.W. — Fourier Analysis |
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| Ïðåäìåòíûé óêàçàòåëü |
Labeyrie, diameters of stars 484—485
Lagrange, links with Fourier 170—171 476 478—479
Laplace doubts about Fourier's work 478—479
Laplace states central limit theorem 347
Laplace transform analyticity 379—382
Laplace transform analyticity (and analytic extension) 382—384
Laplace transform and stability 368 388—406
Laplace transform elementary properties 374—377
Laplace transform importance in number theory 546—551
Laplace transform in solution of linear differential equations 377—378
Laplace transform is analytic 379—382
Laplace transform need for care 386 4036
Laplace transform uniqueness 373—374 384—385
Laplace transform, connection with Fourier transform 372—373
Laplace transform, defined 372—373
Laplace transform, inversion (numerical) 386
Laplace transform,inversion 373—374 386—388
Laplace work on heat equation 274 478—479
Laplace's equation see also “Dirichlet problem”
Laplace's equation connection with analytic functions 122—124 126—129
Laplace's equation connection with Brownian motion 55 451—453
Laplace's equation Gauss mean value theorem 129
Laplace's equation maximum principle 129—130 135—136
Law of errors 347 583;
Lebesgue mathematically infra dig 42—43
Lebesgue measure essential for later work 572
Lebesgue measure strikes panic into engineers 406
Lebesgue on generalisation 572
Lenstra, work on factorisation 512
Lerch's theorem, uniqueness of Laplace transform 384
Levy analytic maps of Brownian motion 458
Levy early interest in non differentiability 43
Levy interest in Brownian motion 45
Levy uniqueness of Brownian motion 583
Liapounov and central limit theorem 347
Liapounov method for proving stability 79—98
Linear programming, Fourier's interest in 480 499
Liouville and Kelvin 178 271
Liouville life 175—178
Littlewood long paper with Cartwright 114
Littlewood on Euler's formula 525
Logarithm of complex number elementary facts 535—536
Logarithm of complex number elementary problems 536
Logarithm of complex number elementary problems (resolved) 541—542
Long time averages 29—30 392
Lyell, Principles of Geology 282—283
Mathematical Brownian motion see also “Brownian path”
Mathematical Brownian motion connection with analytic functions 454—460
Mathematical Brownian motion connection with Laplace's equation 55 451—453
Mathematical Brownian motion dimensional differences 451—454
Mathematical Brownian motion heuristic construction 50—55
Mathematical Brownian motion nowhere differentiable 55
Mathematical Brownian motion probability of return 451—454
Mathematical Brownian motion rigorous construction given by Wiener 45
Mathematical Brownian motion studied by Bachelier, Kolmogorov, Levy and Wiener 45 583—584
Mathematical Brownian motion, will it tangle? 461—466
Mathematicians see also “Cambridge”
Mathematicians condescend to help scientific brother 290
Mathematicians good thing 43
Mathematicians, how recognised 178
Maximum methods for uniqueness, Dirichlet problem 134—135
Maximum methods for uniqueness, heat equation 344—346
Maxwell admires mirror galvanometer 334 575—576
Maxwell on stability 365—366
Maxwell relations with Kelvin 272—273 575
Mean square approximation 145—150 183
Mean square convergence 155—158 184
Measure theory, essential for later work 469 572
Meyer, wavelets 23
Michelson, interferometer 62 487
Mirror galvanometer 334 575—576
Moewus, amazing luck 427—428
Moment problem 21—23 385
Monte Carlo method 46
Monte Carlo method for integration 46—47
Monte Carlo method for Laplace's equation 47—49
Newton, and double tides 24
Non-linear differential equations general remarks 99 112 114—115
Non-linear differential equations stability 79—98
Non-linear differential equations, Duffing's equation 101—115
Nowhere differentiable functions and mathematical Brownian motion 51—55
Nowhere differentiable functions construction 38—41
Nowhere differentiable functions exist in real world 43—45
Numerical computation differential equations 115
Numerical computation Fast Fourier Transform 497—499
Numerical computation Fourier transform 481—490
Numerical computation integrals 46—47 191—196
Numerical computation tides 29—30
Numerical computation uniform approximation 215—217
Numerical computation, central to mathematics 558
Numerical computation, Dirichlet's problem 47—49
Numerical computation, easy to make mistakes in 436
Numerical computation, futile overelaboration 37
Numerical computation, Gibbs phenomenon 65—66
Numerical computation, inverse Laplace transform 368
Numerical computation, Parkinson's law for 497
Organs, electronic 35
Orthonormality of eigen functions 181
Orthonormality, defined 147
Orthonormality, for polynomials 185—190
Oxford breakaway technical college somewhere in the fens see “Cambridge”
Oxford stories 481
| Oxford, professorial appointments 505
Parseval's formula 156—157 184 187
Pathologies, not always as black as painted 23 45
Pearson, inventor of chi squared test 419
Peaucellier's linkage 198—200
Perrin description of Brownian motion 43 52—54
Perrin nature need not be smooth 43 98
Perrin says nice things about mathematicians 43
Picard's little theorem discussed 467
Picard's little theorem proof via Brownian motion 467—469
Poincare 42 347 582
Poisson annoys Jacobi 532
Poisson reality of eigen values 182
Polya's theorem, on return for random walks 443—449
Polynomials see also “Tchebychev polynomials” “Trigonometric “Weierstrass
Polynomials, best uniform approximation by 202—217
Polynomials, Legendre 188—190 192—196
Polynomials, orthogonal 185—190
Principal character 533
Principle of the argument, proved 577—579
Principle of the argument, used 397—399
Random variables see “Sums of independent random variables”
Random walk 443—450
Regression to mean 430
Resonance 95—98
Revest, secret codes 505 509
Riemann Lebesgue lemma 260—261 489 573—574
Rutherford, age of earth 290—291
Schonage, fast multiplication 502
Second order differential equations see “Damped oscillator” “Sturm
Shamir, secret codes 505 509
Simple singularities, treatment of discontinuities and Fourier series 59—66
Simple singularities, treatment of discontinuities and Fourier transforms 300—307
Simple singularities, treatment of key idea 61
Simple singularities, treatment of poles and Laplace transforms 388—391
Stability for damped oscillator 79—97
Stability general remarks 97—98 365—367
Stability via Laplace transform 368 388—406
Stability, types of instability 365—366 368—369
Stars, diameter of 62 484—487 559
Stieltjes, convergence of Gaussian quadrature 195—196
Strassen, fast multiplication 502
Sturm Liouville theory, Fourier's investigation 170—174
Sturm Liouville theory, general 179—184
Sturm, “Voila mon affaire!” 211
Subsoil temperature 25—27
Summation methods see “Sums”
Sums see also “Fourier sums”
Sums of independent random variables see also “Central limit theorem”
Sums of independent random variables and convolution 253
Sums of independent random variables, Cauchy 246—252
Sums of independent random variables, general 245—246
Sums of independent random variables, normal 246—250
Sums, Cesaro 4
Sums, de la Vallee Poussin 56—57
Sums, Fejer 4—10 56 407
Sums, general remarks 4 120
Sums, Poisson 116—120
Tait superiority of mathematical argument 290
Tait, Thomson and Tait 273
Taylor's theorem primitive version 352
Taylor's theorem, discussed 15—17
Tchebychev and uniform approximation 202—206 212—215
Tchebychev equiripple criterion 202—206 212 215
Tchebychev interest in mechanisms 197 201
Tchebychev polynomial and best uniform approximation 212—217
Tchebychev polynomial orthogonality 187
Tchebychev polynomial, defined 19—20
Tchebychev proves central limit theorem 347
Thomson see “Kelvin Lord”
Time delay equation 395—402
Titchmarsh, and Hardy 481
Transatlantic cable 332—337
Transcendental numbers, Liouville's construction 176
Transients 91—92
Trigonometric polynomials, definition 10
Trigonometric polynomials, uniformly dense 10
Trigonometric polynomials, uniformly dense (result used) 12 19 97
Tukey, Fast Fourier Transform 499
Tychonov, non-unique solution of heat equation 338—343
Ulam, Monte Carlo method 46
Uniqueness of factorisation and Euler's formula 526
Uniqueness of factorisation and group of units modulo n 506—507
Vladivostok, telephone directory 591
Von Neumann on mathematics v
Wallis, codebreaker and mathematician 505
Watt governor 365
Watt parallelogram 197 201
Watt redesigns steam engine 197
Wave equation 324—331
Wavelets 23
Weierstrass and existence of minima 126 208
Weierstrass nowhere differentiable function 38—41
Weierstrass polynomial approximation theorem, context 15—17
Weierstrass polynomial approximation theorem, proofs 17—18 19—20 292—294
Weierstrass polynomial approximation theorem, used 186 196
Weierstrass, proof of Weierstrass's theorem 292—294
Weyl's theorem, on equidistribution 11—13
Wiener, constructs Brownian motion 45
Wilbraham, Gibbs phenomenon 66 499
Zaremba, non existence of solution to Dirichlet's problem 140 163—164
Zeta function, brief appearance 551
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