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| Davis H.T. — Introduction to nonlinear differential and integral equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel's equation 74—75
Abel, N.H. 74 145 545
Action, definition of 457
Adams — Bashfortli method 481
Adams, J.C. 481
Agnew, R.P. 545
Airey, J.R. 373
Airy, G.B. 368
Algebraic functions 7
Almost periodic functions 290—291
Ampere, A.M. 19
Analytic continuation 245 246 Chap.
Andrews, A.H. 61
Andronow, A. 545
Antosiewicz, H.A. 545
Appell, P. 545
Appleton, e.v. 545
Archibald, R.C. 114 545
Archimedes 439
Asymptotic series 5
Automorphic functions, definition of 222
Autonne, L. 545
Ayre, R.S. 551
Baggott, E.A. 31 553
Baker, E.D. 406—407
Balze, O. 443
Barocio, S. 545
Bashforth, F. 481
Bass, R.W. 545
Bateman, H. 20 21 455 545
Bautin, N.N. 344 346 545
Bellman, R. 545
Bendixson's theorem 354—355
Bendixson, I. 186 309 351—352 354—355 545
Bernhart, A. 545
Bernoulli numbers 473
Bernoulli's equation 49
Bernoulli, Daniel 58 546
Bernoulli, James 49 57 473
Bernoulli, John 57 546
Berry, A. 546
Besicovitch, A.S. 290
Bessel functions 4 5 68—70
Bieberbach, L. 21 546
Birkhoff, G.D. 285 546
Blasius equation 16 400—405
Blasius, H. 16 400—404 546
Block, H. 546
Blodgett, Katherine B. 552
Bocher, M. 83
Bochner, S. 546
Bogoliuboff, N. 365 367 552
Bohr, H. 290
Boltzmann, L. 284
Bompiani, E. 546
Boole, G. 115 546
Bouguer, P. 114—115
Bouquet, j.c. 79
Boutroux, M.P. 232 242 244 54
Branch points 14 185 225
Brassinne, E. 546
Bratu's equation 432—434
Bratu, G. 415 432—434 546
Briot, C. 79
Brocard, H. 114
Brodetsky, S. 26
Brown, E, W. 285
Brownell, F.H. 546
Brucht, G. 546
Burkhardt 161
Bush, V. 407 547
Bushaw, D. 547
C-discriminant 50 54
Cajori, F. 172
Calculus of limits 79—83 190—191
Calculus of variations Chap. 14
Calculus of variations, Fundamental Lemma of 443
Calculus of variations, necessary conditions for extremals in 449—450
Caldwell, S.H. 407 547
Capture point 117 123—124
Caque, J. 83
Carleman, T. 454 547
Carlson, A.J. 61
Cartan, E. 20
Cartwright, Mary L. 368 547
Cauchy — Lipschitz, method of 88—93
Cauchy, A.L. 19 79 88 468
Cavalieri, F.B. 478
Cayley, A. 53 58 547
Center 322
Center, conditions for 350
Cepheid variable stars 368—371
Ceskro, E. 299
Chaikin, S. 545
Challis, H.W. 547
Chandrasekhar, S. 377 408 547
Characteristic equation 311 317
Chiellini, A. 547
Chrystal's equation 51—53
Chrystal, G. 51 55 547
Clairaut's equation 49—51
Clairaut, A.C. 49
Clebsch, R.F.A. 19
Coddington, E.A. 547
Coefficient of heredity 113
Collet, A. 547
Complementary elliptic integral 131
Complete elliptic integrals, definition of 131
Complete elliptic integrals, definition of, differential equations of 137
Complete elliptic integrals, definition of, expansions of 133—135
Continued fractions 70—72
Continuous analytic continuation Chap. 9
Continuous analytic continuation, application around a singular point 263—266
Continuous analytic continuation, method of 251—256
Convolution, nonlinear 434—437
Copson, E.T. 547
Corbeiller, Ph.Le 547
Cotton, E. 414 547
Critical points 14 185 225
Curvature, method of 29—32 248—249
Curves of pursuit see "Pursuit"
Cusp-locus 54—56
d'Adhemar, R. 545
D'Alembert 53
D'Alembert's equation 53
da Vinci, Leonado 95
Darboux, J.G. 19 53 547
Davis, H.T. 295 302 548
De Baggio, H.F. 548
de Maupertuis, P.L.M. 114 440 457
De Vogelaere, R. 548
Delaunay, C. 285
Dido's problem 439 445—447
Differential equation of third order, Blasius 16 400—405
Differential equations of first order Chap. 2
Differential equations of first order, Abel's 74—75
Differential equations of first order, Bernoulli's 49
Differential equations of first order, Chrystal's 51—53
Differential equations of first order, Clairaut's 49—51
Differential equations of first order, d'Alembert's 53
Differential equations of first order, graphical method of solution 26—29
Differential equations of first order, homogeneous case of 36—45
Differential equations of first order, Riccati's Chap. 3
Differential equations of first order, solution by isoclines and curvature 29—32
Differential equations of second order Chap. 7 Chap.
Differential equations of second order of polynomial class Chap. 8
Differential equations of second order with fixed critical points 184—185 225—228
Differential equations of second order with periodic solutions 186 297—308 339—351
Differential equations of second order, classification of 182—189
Differential equations of second order, Duffing's 15 180 271 386—400
| Differential equations of second order, elliptic 14 179 183—184 194—211 270
Differential equations of second order, Emden type 381—386 408
Differential equations of second order, Emden's 15 181 371—377
Differential equations of second order, existence theorems for 189—192
Differential equations of second order, generalized Riccati 76—79 186 218—221
Differential equations of second order, Kidder's 16 410—411
Differential equations of second order, Langmuir's 16 181
Differential equations of second order, Painleve's 14 185 229—244 233—234 239—244 258—261 263—266 501—504
Differential equations of second order, Painleve's, values of 507—530
Differential equations of second order, Rayleigh's 15 181 186—187
Differential equations of second order, Thomas — Fermi's 16 405—407
Differential equations of second order, Van der Pol's 15 17 181 186—187 270 358—368
Differential equations of second order, Van der Pol's, values of 531—536
Differential equations of second order, Volterra's 102 180 270 324—327 355
Differential equations of second order, Volterra's, values of 537—542
Differential equations of second order, Volterra's, white dwarf 16 408
Diliberto, S.P. 548
Dirichlet, P.G.L. 291 455
Doetsch, G. 548
Dorodnicyn, A.A. 368 548
Douglas, J. 454
Duff, G.F. 548
Duffin, R.J. 548
Duffing's equation 15 180 271 386—400
Duffing, G. 15 180 271 386 395 548
Dulac, H. 343 548
Duncan, J.C. 368
Dunoyer, L. 114 548
Eckweiler, H.J. 548
Eddington, A.S. 376 548
Einstein, A. 180
Elliptic equations 14 179 183—184 194—211 270
Elliptic functions Chap. 6 see elliptic "Weier-strass elliptic
Elliptic integrals Chap. 6
Elliptic integrals, computation of 137—141
Elliptic integrals, expansions of 135—137
Elliptic integrals, first kind 131
Elliptic integrals, second kind 131
Elliptic integrals, tables of 142—143
Elliptic integrals, third kind 132
Elliptic modular functions 169—171
Elliptic modular functions, use in solving quintic 172—175
Emde, F. 203 551
Emden type equations 381—386 408
Emden's equation 15 181 371—377
Emden, R. 15 181 371 376—378 381 548
Equation, differential see "Differential equations"
Equation, differential of continuity 21
Equation, differential, Euler's 15 443
Equation, differential, Liouville's 20 377
Equation, differential, Navier — Stokes 21
Equation, differential, Poisson's 19
Equations, integral Chap. 13 see
Equations, numerical integration of Chap. 15
Equations, numerical integration of by Adams — Bashforth method 481
Equations, numerical integration of by continuous analytic continuation Chap. 9
Equations, numerical integration of by Milne method 486—488 491
Equations, numerical integration of by Runge — Kutta method 482—486
Equations, with fixed critical points 495—498
Equiharmonic case of elliptic functions 161
Equivalent linearization 367
Ergchorad 285
Ergodic theorem 285
Euler cordition 441—445
Euler cordition for double integrals 450—452
Euler cordition in isoperimetric case 445—447
Euler equation 15 443
Euler — Maclaurin formula 473
Euler's theorem on homogeneous functions 36
Euler, L. 1 15 36 58 162 440 441—447 473 548
Evans, G.C. 414 548
Excess function 441
Existence theorems Chap. 4 189—192 415—416 424—425
Exponents, preservation of 215
Exponents, preservation of, theorems concerning 215—218
Extremal, definition of 443
Extremal, definition of, necessary conditions for 449—450
Falkenhagen, J.H.M. 548
Falkner, V.M. 400 548
Falling body, velocity of 60—62
Farnell, A.B. 552
Faulkner, J.E. 344 346
Fejer, L. 299
Fermat, P. 440 456—457
Fermi, E. 405 548
Finite differences, calculus of 468—472
Fisher, R.A. 61
Flanders, D. 549
Fletcher, A. 140
Floquet's theory 300—303
Floquet, O. 300—303
Focus 268 314 322
Forcing functions and phase curves 273—283
Ford, L.R. 214 222 549
Forsyth, A.R. 20 54 444 549
Fourier series, in pendulum problem 291—297
Fourier series, in pendulum problem in expansion of Jacobi's elliptic functions 167—169
Fourier series, in pendulum problem in problem of periodicity 298—300
Fourier series, in pendulum problem in solution of Duffing's equation 388—396
Fourier, J. 162 291 434
Fredholm's nonlinear integral equation 424—433
Fredholm's nonlinear integral equation, existence theorem for 424—425
Fredholm, I. 414 424—425
Friedricks, K.O. 549
Frommer's curve 341—342
Frommer's theorem 341
Frommer, M. 340—341 343 350 549
Fuchs, L. 83
Functions, automorphic 222
Functions, Bessel's 4 5 68—70
Functions, classification of 7
Functions, elliptic modular 169—171
Functions, homogeneous 36
Functions, Jacobi's elliptic 145—156
Functions, Mathieu's 303
Functions, theta 162—167
Functions, Weierstrass elliptic 156—161
Gambier, B. 183—185 223 225 493 549
Garnier, R. 549
Gas spheres, isothermal 377—378
Gas spheres, theory of 371—377
Gause, G.F. 102
Gauss's limit 144
Gauss, C.F. 19 144 145
Generalized coordinates 458
Generalized Riccati equation 76—79 186 218—221
Geppert, H. 144
Gerber, P. 180 549
Glaisher, J.W.L. 58 549
Goldstein, S. 400 549
Golomb, M. 549
Gomory, R.E. 549
Gompertz curve 98
Gompertz, B. 98
Goursat, E.J.B. 20 54 89—90 443 550
Graffi, D. 550
Green, G. 451
Greenhill, A.G. 58 160 168 203 550
Gregory formula 474
Gregory — Newton formula 469
Gregory, J. 469 474 478
Greig, J. 547
Gronwall, T.H. 550
Groups, associated with linear fractional transformation 222
Growth, hereditary factor in 112—113 413 417—423
Growth, problem of 99—112
Gudermann, C. 152 550
Guigue, R. 550
Haag, J. 368 550
Haar, A. 454
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