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| Ïîèñê ïî óêàçàòåëÿì |
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| Korner T.W. — Fourier Analysis |
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| Ïðåäìåòíûé óêàçàòåëü |
Laplace transform, analyticity (and analytic extension) 382—384
Laplace transform, connection with Fourier transform 372—373
Laplace transform, defined 372—373
Laplace transform, elementary properties 374—377
Laplace transform, importance in number theory 546—551
Laplace transform, inversion 373—374 386—388
Laplace transform, inversion, (numerical) 386
Laplace transform, need for care 386 403—406
Laplace transform, uniqueness 373—374 384—385
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 see
Laplace's equation, maximum principle 129—130 135—136
Laplace, doubts about Fourier's work 478—479
Laplace, states central limit theorem 347
Laplace, work on heat equation 274 478—479
Law of errors 347 583 see
Lebesgue measure, essential for later work 572
Lebesgue measure, strikes panic into engineers 406
Lebesgue on generalisation 572
Lebesgue, mathematically infra dig 42—43
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 on Euler's formula 525
Littlewood, long paper with Cartwright 114
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, 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 see
Mathematicians, condescend to help scientific brother 290
Mathematicians, good thing 43
Mathematicians, how recognised 178 see
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 for integration 46—47
Monte Carlo method for Laplace's equation 47—49
Newton, and double tides 24
Non-linear differential equations, Duffing's equation 101—115
Non-linear differential equations, general remarks 99 112 114—115
Non-linear differential equations, stability 79—98
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, central to mathematics 558
Numerical computation, differential equations 115
Numerical computation, Dirichlet's problem 47—49
Numerical computation, easy to make mistakes in 436
Numerical computation, Fast Fourier Transform 497—499
Numerical computation, Fourier transform 481—490
Numerical computation, futile overelaboration 37
Numerical computation, Gibbs phenomenon 65—66
Numerical computation, integrals 46—47 191—196
Numerical computation, inverse Laplace transform 368
Numerical computation, Parkinson's law for 497
Numerical computation, tides 29—30
Numerical computation, uniform approximation 215—217
Organs, electronic 35
Orthonormality for polynomials 185—190
Orthonormality of eigen functions 181
Orthonormality, defined 147
Oxford breakaway technical college somewhere in the fens see "Cambridge"
Oxford professorial appointments 505
Oxford stories 481
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 says nice things about mathematicians 43
Perrin, description of Brownian motion 43 52—54
Perrin, nature need not be smooth 43 98
Picard's little theorem proof via Brownian motion 467—469
Picard's little theorem, discussed 467
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, best uniform approximation by 202—217
Polynomials, Legendre 188—190 192—196
Polynomials, orthogonal 185—190 see "Trigonometric "Weierstrass
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 and Sturm Liouville theory"
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, types of instability 365—366 368—369
Stability, via Laplace transform 368 388—406
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!' 111
Subsoil temperature 25—27
Summation methods see "Sums"
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 see
Sums, Cesaro 4
Sums, de la Vallee Poussin 56—57
Sums, Fejer 4—10 56 407
Sums, general remarks 4 120 see
Sums, Poisson 116—120
Tait, superiority of mathematical argument 290
Tait, Thomson and Tait 273
Taylor's theorem, discussed 15—17
Taylor's theorem, primitive version 352
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, defined 19—20
Tchebychev polynomial, orthogonality 187
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
Von Neumann, Monte Carlo method 46
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 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
Weierstrass, nowhere differentiable function 38—41
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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