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Jeffreys H. — Methods Of Mathematical Physics
Jeffreys H. — Methods Of Mathematical Physics

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Название: Methods Of Mathematical Physics

Автор: Jeffreys H.

Аннотация:

METHODS OF MATHEMATICAL PHYSICS by HAROLD JEFFREYS, M. A., D. Sc., F. R. S. Plumian Professor of Astronomy, University of Cambridge, and Fellow of St Johns College and BERTHA SWIRLES JEFFREYS, M. A., Ph. D. Felloiv and Lecturer of Girton College SECOND EDITION CAMBRIDGE At the University Press 1950 PUBLISHED BY THE SYNDICS OF THE CAMBRIDGE UNIVERSITY PRESS London Office Bontley House, N. W. I American Branch New York Agents for Canada, India, and Pakistan Macmillan First Edition 1946 Second Edition 1950 Printed in Oreat Britain at the University Press, Cambridge Brooke CrutcMey, University Printer Preface This book is intended to provide an account of those parts of pure mathematics that are most frequently needed in physics. The choice of subject-matter has been rather difficult. A book containing all methods used in different branches of physios would be impossibly long. We have generally included a method if it has applications in at least two branches, though we do not claim to have followed the rule invariably. Abundant applications to special problems are given as illustrations. We think that many students whose interests are mainly in applications have difficulty in following abstract arguments, not on account of incapacity, but because they need to see the point before theit Interest can be aroused. . v A knowledge of calculus is assumed. Some explanation of the standard of rigour and generality aimed at is desirable. We do not accept the common view t at any argument is good enough if it is intended to be used by scientists. We hold that it is as necessary to science as to pure mathematics that the fundamental principles should be clearjy stated and that the conclusions shall follow from them. But in science it is also necessary that the principles taken as fundamental should be as closely related to observation as possible it matters little to pure mathematics what is taken as fundamental, but it is of primary importance to science. We maintain therefore that careful analysis is more important in science than in pure mathematics, not less. We have also found repeatedly that the easiest way to make a statement reasonably plausible is to give a rigorous proof. Some of the most important results e. g. Cauchys theorem are so surprising at first sight that nothing short of a proof can make them credible. On the other hand, a pure mathematician is usually dissatisfied with a theorem until it has been stated in its most general form. The scientific applications are often limited to a few special types. We have therefore often given proofs under what a pure mathematician will consider unneces sarily restrictive conditions, but these are satisfied in most applications. Generality is a good thing, but it can be purchased at too high a price. Sometimes, if the conditions we adopt are not satisfied in a particular problem, the method of extending the theorem will be obvious but it is sometimes very difficult, and we have not thought it worth while to make elaborate provision against cases that are seldom met. For some exten sive subjects, which are important but need long discussion and are well treated in some standard book, we have thought it sufficient to give references. We consider it especially important that scientists should have reasonably accessible statements of conditions for the truth of the theorems that they use. One often sees a statement that some result has been rigorously proved, unaccompanied by any verifica tion that the conditions postulated in the proof are satisfied in the actual problem and very often they are not. This misuse of mathematics is to be found in most branches of science. On the other hand, many results are usually proved under conditions that are sufficient but not necessary, and scientists often hesitate to use them, under the mistaken belief that they are necessary...


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 716

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$D_{n}(x)$      623
$Hh_{n}(x)$      62
$Hi_{n}(x)$      575
$Hs_{n}(x)$      575
$I_{n}(x)$      574
$J_{n}(x)$      574
$Khei_{n}(x)$, $Kher_{n}(x)$      588
$Kh_{n}(x)$      579
$\delta_{ik}$      59
$\epsilon$      8
$\epsilon_{ikm}$      69 73 75
Abel summation      370 436 456
Abel's test (integrals)      45
Abel's test (series)      42 370
Abel, N.H.      405 473 669 688
Abelian functions      673
Abraham, M. and Becker, R.      106
Absolute convergence      see "Convergence"
Adams — Bashforth formula      see "Differential equations"
Adams, J.C.      284 293 640 641
Ai(x)      476 695
Airey, J.R.      291 502 616 626
Airy integral      476 508 518 525 695
Algebra, complex numbers      333
Algebra, infinity      12
Algebra, matrices      114
Algebra, operators      228
Algebra, rules of      1
Algebraic equations, linear      118
Algebraic equations, numerical solution      304
Algebraic equations, numerical solution, higher degrees      274 378 692
Allied Fourier integral      453 456
Allied Fourier series      431
Almost everywhere      30
Amplitude (complex number)      see "Argument"
Analitic function, integral of      343 348
Analytic continuation      362
Analytic function      333 337
Andress, W.R.      408
Angular velocity      79 81 97
Appell, P.      323
Area of surface      188 691
Argand diagram      245 341
Argument of complex number      341
Arithmetic, rules of      1
Associative law      1 66 115 116 334
Astronomy      111
Asymptotic expansions      498 624
Asymptotic formulae      282 466 649
Asymptotic solutions of differential equations      520
Asymptotic solutions of differential equations, Green's type      523 586
Asymptotic solutions of differential equations, Stokes's type      520 582 609
Baber, W.G.      488
Baker, H.F.      228 691
Barnes, E.W.      612
Bashforth, F.      293
Bateman, H.      652
Bayes, T.      467
Bell, E.T.      341
Berestetsky, V.      662
Bernoulli, Daniel      436
Bernoulli, James, numbers and polynomials      280 387 431 439
Bernoulli, John      317
Besicovitch, A.S.      54 192
Bessel functions      574
Bessel functions of operators      585 612
Bessel functions, $I_{n}$, $Kh_{n}$      579
Bessel functions, $J_{n+\frac{1}{2}}$      539 589 659
Bessel functions, $Y_{n}$      576
Bessel functions, applications      597
Bessel functions, ber, bei, ker, kei      588
Bessel functions, complex integrals      491 574 580
Bessel functions, definite integrals containing      589
Bessel functions, expansions containing      591 593
Bessel functions, Hankel functions      575 591 660
Bessel functions, large order$      586
Bessel functions, operational forms      574
Bessel functions, recurrence formulae      581
Bessel's equation      489 521 526 536
Bessel's interpolation formula      see "Interpolation"
beta function      463
Bethe, H.A.      619
Bi(x)      695
Biaxial harmonics      647
Bickley, W.G.      135 383 425 495 527 696
Bicycle      323
Bleieck, W.E.      383
Block matrices      129
Bocher, M.      136
Bolzano, N.      10 20 172
Bonnet, O.      52
Boole, G.      229
Born, M.      202
Bounded      11
Bounded variation      24
bounds      13 21
Bourguet, L.      467
Brachistochrone      317
Branch points      355
Briggs, L.J.      273
Brinkman, H.C.      662
Bromwich integral      392 394
Bromwich, T.J.I'A.      48 142 247 392 491 557 561 571
Brown, E.W.      488
Cable, submarine      602
Calculus of restricted variation      319
Calculus of variation of limits      317
Calculus of variations      314
Campbell, N.R.      3
Cantor, G.      6 12
Capacity      310 418
Caque, J.      229 476
Caratheodory, C.      192
Carlini, G.      524
Carnap, R.      2
Carter, G.W.      260
Cartesian coordinates      57
Cauchy — Riemann relations      333 337 338 346 361
Cauchy's inequality      54 336
Cauchy's inequality (power series)      361
Cauchy's integral      360
Cauchy's theorem      344 347
Cauchy, A.L.      362 476
Cavalieri, B.      286
Centre of mass      83 543
Cesaro, E.      436
Change of variable in multiple integral      182
Change of variable in single integral      33
Chappell, E.      273
Characteristic values      127
Charge function      412
checking      275
Ci(x), ci(x)      471
Circle of convergence      350
Circulation      195
Clairaut's formula      646
Closed interval      19
Closed region      174
Coaxal circles      415
Collineatory transformation      128
Commutative laws      1 62 66 106 115 334
Commuting matrices      115
Comparability      2
Comparison series      43
complex numbers      333
Complex potential      412
Comrie, L.J.      271 273 274 692
Condenser, charging of      244
Condenser, discharge of      245
Condon, E.J., and Shortley, G.H.      133 633
Conduction of heat      529 563 600
Confluent hypergeometric function      607
Confluent hypergeometric function, integrals for      608
Confluent hypergeometric function, Whittaker's form      616
Confocal conics      419 see
Conformal mapping      409
Consistent units      4
Contact transformation      328
Continuation, analytic      362
Continuity      17 176 342
Continuity, sectional      19
Continuity, uniform      23 342
Continuous distributions (mass or charge)      202
contour      172 344
Contour integration      375
Contraction of tensor      87
Contravariant components      158
Convergence      11 53
Convergence factors      502
convergence of integrals      33
Convergence, absolute      16 37 185
Convergence, conditional      16
Convergence, radius of      350
Convergence, uniform      38 44 48 351 371
Cooling of bars      563
Cooling of earth      569
Cooling of Earth, thermometer bulb      571
Cosine transform      457
Courant, R. and Hilbert, D.      127 495 619 638 694
Courant, R. and Robbins, H.      189 316
Covariant components      158
Covering theorems      19 175
Cowell, P.H.      300
Crommelin, A.C.D.      300
Crossley, A.F.      259
Crystals      155
Curl      90
CURVES      72
Curves, length of      173
Curvilinear coordinates      157 532 694
Cuts (complex)      341 355
Cylinder, lift on      414
Cylindrical coordinates      534 695
Cylindrical pulse      595
D'Alembert's principle      83 322
D'Alembert, J.le R.      436 547
Dalzell, D.P.      395 396
Darwin, C.G.      633
Darwin, G.H.      450
Debye, P.      501 503
Decreasing functions      23
Dedekind section      6 13
Dedekind, R.      1
Definite integration, as linear operator      229
Derived magnitudes      4
Determinantal equations      127
Determinantal equations, root-separation theorem      140 146 254
Determinants, infinite      488
Determinants, multiplication of      119
Diagonal block matrices      130
Diagonal matrices      94 117 128
Diameter of region      175
Differentiability      665
Differentiability of function of several variables      178 180 337
Differentiability on one side      691
Differential equations, asymptotic solutions      520
Differential equations, existence of solution      474
Differential equations, indicial equation      478
Differential equations, numerical solution      290
Differential equations, numerical solution, Adams — Bashforth      292 693
Differential equations, numerical solution, central differences      293
Differential equations, numerical solution, Gauss — Jackson      300 694
Differential equations, numerical solution, jury problems      306
Differential equations, numerical solution, Taylor's series      290
Differential equations, operational method, first order      232
Differential equations, operational method, higher orders      239
Differential equations, regular singularities      478
Differential equations, singular points      474 477
Differential equations, singularities at infinity      480
Differential equations, solution by complex integrals      489
Differential equations, three-term recurrence relations      485
Differentiation of integral      31
differentiation of power series      352
Differentiation under integral sign      45
Differentiation, as linear operator      229 398
Differentiation, non-commutative property      230
Differentiation, Numerical      277
Diffraction      621
Diffusion      600
Digamma function      465
dimensions      4
Dipole      206
Dirac, P.A.M.      153
Direction vector      64
Dirichlet integrals      468
Dirichlet — Hardy test (series)      42
Dirichlet — Hardy test, integrals      46
Dirichlet, P.G.L.      436
Discontinuity      18 26
Discontinuity and non-uniform convergence      40 43 47 49
Discontinuity of arbitrary constants      511
Discontinuity, removable      26 367
Discontinuity, simple      18 26
dispersion      511 600
Dispersion of water waves      515
Dissipative systems      254
Distance      57 171
Distance from set      177
Distributive law      1 66 116 334
Divergence (sequences)      12
Divergence of vector      90
Divergence theorem      193 345
Divided differences      262
Division of vectors      73
Doodson, A.T.      450
Double integrals      180
Doublet      207
Doublet shell      207 215
Doubly-periodic functions      see "Elliptic functions"
Durell, C.V., and Robson, A.      73
Dyadics      89
Earth, cooling of      569
Earth, figure of      222 643
Earthquakes      253
Eddington, A.S.      108 151 153
Edser, E.      568
ei(x)      470
Eigenvalues      127
Einstein, A.      332
Elasticity      99
Electromagnetic radiation      660
Electromagnetic stress tensor      105
Electromagnetic theory      160
Ellipsoidal coordinates      541
Elliptic coordinates      419 536
Elliptic equations      531
Elliptic functions      667
Elliptic functions, addition formulae      678
Elliptic functions, infinite products      679
Elliptic functions, residues      675
Elliptic functions, trigonometric expansions      676
Elliptic functions, ubiquity      696
Elliptic integral, complete      687
Elliptic integral, first      669
Elliptic integral, second      686
Elliptic integral, standard form      685
Elliptic integral, third      687
Empirical periodicities      450
Enneper, A.      667
Enumerable sets      10
1 2
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