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| Davis H.T. — Introduction to nonlinear differential and integral equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Haas, F. 550
Haas, Violet 550
Hadcock, A.G. 203 550
Hamel, G. 550
Hamilton's equations 461—465
Hamilton's principle 15 456—465
Hamilton, W.R. 1 440 441 456—459 461—463
Hammerstein, A. 550
Hargreave, C.J. 58 550
Harmonic Law 461
Hartog, J.P.Den 550
Hartree, D.R. 400 403—404 550
Hathaway, A.S. 115 123 550
Hereditary factor in problem of growth 112—113 413 417—423
Hermite, C. 171—172
Hetherington, N. 393
Hilb, E. 550
Hilbert, D. 284
Hill, G.W. 283 285 302—303 551
Hill, M.J.M. 53 551
Hirschman, I.I. 551
homogeneous functions 36
Horn, J. 20 551
Howarth, L. 400 403—404 551
Hudson, R.W.H.T. 551
Hufford, G. 548 551
Hynek, J.A. 377
Hysteresis 99
Iglisch, R. 551
Ince, E.L. 54 90 225 301 495 551
Independent variable, transformation of 221—224
Integral equations, nonlinear Chap. 13
Integral equations, nonlinear for Fredholm type 424—425
Integral equations, nonlinear, existence theorem for Volterra type 415—417
Integrating factor 32—36
Integrating factor, definition of 35
Integrating factor, special cases of 45—48
Integro-differential equations 112 417—423
Integro-differential equations, one variable problem 417—419
Integro-differential equations, two variable problem 419—423
Iseli, P. 561
Isoclines 29—32
Isoperimetric problem 445—447
Isothermal gas spheres 377—378
Ivy, A.C. 61
Jacobi's equation 449—450
Jacobi, C.G.J. 19 130 145 155 162 440 449—450
Jacobi, elliptic functions of 145—156
Jacobi, elliptic functions of as Fourier series 167—169
Jacobi, elliptic functions of, addition theorems for 148—150
Jacobi, elliptic functions of, derivatives of 147—148
Jacobi, elliptic functions of, double and half-angle formulas 150—152
Jacobi, elliptic functions of, expansions of 152—153
Jacobi, elliptic functions of, integrals of 148
Jacobi, elliptic functions of, pole s and zeros of 153—154
Jacobi, elliptic functions of, properties of 145—147
Jacobi, elliptic functions of, tables of 175—178
Jacobi, elliptic functions of, theta functions and 166
Jacobsen, L.S. 551
Jahnke, E. 203 551
Janet, I.M. 20
Jordan, C. 284
Jump phenomenon 395 398—400
Kakutani, S. 551
Kamke, E. 20 182 551
Kapteyn, W. 343 551
Keelhoff 114
Kepler, J. 461
Kidder's equation 16 410—411
Kidder, R.E. 16 410—411 552
Killeen, J. 231
Koenig, H. 483
Koosis, P. 552
Kourensky, M. 552
Kovalevslci, Sophia 20
Krasno, L.R. 61
Krogdahl, W.S. 368
Kryloff, N. 365 367 552
Ku, Y.H. 552
Kummer, E.E. 552
Kutta, W. 482
Kyner, W.T. 552
Lagrange, J. 19 20 295 440 457—459 463
Lagrange, R. 552
Lagrangian, definition of 457
Lalesco, T. 414—415 552
Lamb, H. 20 21 401
Landen's transformations 137—139
Landen, J. 137
Landis, E.M. 344 346 555
Langenhop, C.E. 552
Langmuir's equation 16 181 409
Langmuir, I. 16 181 409 552
Laplace's equation 48 453
Laplace, P.S. 19 48 453 455
LaSalle, J. 552
Laurent, H. 197
Least action, principle of see "Hamilton's principle"
Lefschetz, S. 352 552
Legendre, A.M. 140 440 449
Legeudre's condition 449
Leibniz, G.W. 57 58
Leibniz, rule of 82
Lempke, H. 552
Leray, J. 553
Levenson, M.L. 553
Levinson, N. 304 307 547 553
Levy, H. 31 553
Levy, P. 553
Liapounoff, A. 186 309 318 553
Lichtenstein, L. 21 553
Lienard, A. 304—305 358 553
Lienard-plane 305
Limit cycles, definition of 269 331—339
Limit cycles, definition of, number of 346
Limit in the mean, definition of 279
Limits, calculus of 79—83 190—191
Linear deficiency 2
Linear fractional transformation, application of 218—221
Linear fractional transformation, elements of 499—500
Linear fractional transformation, groups associated with 222
Linear fractional transformation, properties of 213—218
Linear operator, definition 2
Liouville's equation 20 377
Liouville, J. 20—21 58 83 377 553
Liouville, R. 553
Lipschitz, R. 85 88—89
Littlewood, J.E. 547
Lobatto, R. 553
Logistic curve 96—98
Lotka, A.J. 101—102
Lowan, A.N. 553
Lunar perigee, problem of 302
Maclaurin, C. 473
Majorante, definition of 80
Malkin, I.G. 554
Manning, H.P. 114 545
Marcus, M.D. 548 554
Markus, L. 551 554
Martin, W.T. 546
Massera, J.L. 554
Mathieu's functions 303
Mathieu, E.L. 302—303
Maxwell, J.C. 284
McCarthy, J. 553
McLachlan, N.W. 554
Mean curvature 453
Mendelson, P. 554
Method of Cauchy — Lipschitz 88—93
Method of successive approximations 83—88
| Miller, J.C.P. 140
Milne's method 486—488 491
Milne, W.E. 486 491
Milne-Thompson, L.M. 175
Minding, F. 554
Minetti, S. 554
Minimal surface, problem of 452—456
Minimum surface of revolution 444
Minorslcy, N. 301 554
Mitrenovitch, D. 554
Modulus of elliptic integrals 131
Moigno, F. 89
Monge, G. 19
Moore, E.H. 284
Morley, F.V. 115 554
Morton, W.B. 554
Movable singular points 8 185
Murphy, R. 554
Natural boundary 7
Navier — Stokes equations 21
Navier, L.M.H. 21
Necessary conditions for extremals 449—450
Newton's problem 448
Newton, Isaac 448 450 457 469
Nodal Locus 54—56
Nodal point 312—314
Nonlinear equations, origin of 9—12
Nonlinear equations, partial differential 18—24
Nonlinear equations, problem of 12—16
Nonlinear equations, solution of 3—9
Nonlinear equations, systems of 16—18
Nonlinear integral equations see "Integral equations"
Nonlinear mechanics Chap. 11 17
Nonlinear operator, definition of 1—2
Nonlinear resonanoe 395—400
Norriss heart 393—394
Numerical integration Chap. 15
Obi, C. 554
Operator, linear 2
Operator, nonlinear 1—2
Orlando, L. 554
p-discriminant 54
Painleve's transcendents 14 185
Painleve's transcendents, first 229—239
Painleve's transcendents, first, analytical continuation of 263—266
Painleve's transcendents, first, coefficients in expansion of 501—502
Painleve's transcendents, first, numerical solution of 258—260
Painleve's transcendents, first, transformation of 232—234
Painleve's transcendents, second 239—244
Painleve's transcendents, second, coefficients in expansion of 503—504
Painleve's transcendents, second, numerical solution of 260—261
Painleve's transcendents, second, transformation of 242—244
Painleve, P. 14 184—185 225 229 232 236 238—239 260 501 503 554
Partial differential equations, nonlinear 18—24
Pascal, E. 555
Peano's curve 284
Peano, G. 83 284
Pearl, R. 96
Peixoto, M.M. 555
Pendulum as Fourier series 291—297
Pendulum, problem of 192—194
Pendulum, spherical 465
Period parallelogram 159
Periodic solutions 297—299
Periodic solutions in homogeneous polynomial case 339—343
Periodic solutions in quadratic polynomial case 343—351
Periodicity as phenomenon of the phase-plane 303—308
Periodicity, Floquet's theory of 300—303
Perron, O. 555
Petrovitch, M. 555
Petrovskii, I.G. 344 346 555
Pfaff's problem 19
Pfaff, J.F. 19
Phase curves and forcing functions 273—283
Phase trajectories 101 268
Phase-plane Chap. 10
Phase-plane, definition of 268
Picard, E. 17 21 54 79 83 112 184 225 354 414 468 555
Picone, M. 414 556
Pinney, E. 556
Plateau's problem 20 454
Plateau, J. 20 454
Poincare's index 352—354
Poincare, H. 17 21 115 186 267 284 309 334 339 351—352 357 556
Poisson's equation 19
Poisson, S.D. 21 339 377
Pole-vaulting, method of 245
Pompeiu, D. 556
Poole, E.G.C. 556
Pursuit, circular 119—125 332—334
Pursuit, curves of 113—127
Pursuit, general 115—116 125—127
Pursuit, linear 115—119
Quetelet, L.A.J. 96
Quintic equation, solution of 172—175
Rado, T. 455
Raffy, L. 556
Rainville, E.D. 556
Rauch, L.L. 556
Rauscher, M. 556
Rawson, R. 556
Rayleigh's equation 15 181 186—187
Rayleigh, Lord (J.W. Strutt) 15 180—181 186—187 270 284 367 556
Reed, L.J. 96
Reid, W.T. 449 454 456 556
Relaxation oscillations 273
Resonance, definition of 275
Resonance, nonlinear 395—400
Reuter, G.E.H. 556
Ricatti's equation Chap. 3 11 12—13 188 368
Ricatti's equation, cross-ratio theorem of 62—63
Ricatti's equation, generalized 76—79 186 218—221
Ricatti's equation, integration of 63—65
Ricatti's equation, singularities of 73—74
Ricatti's equation, solution by continued fractions 70—72
Riccati, Count (Jacoko Francisco) 57 186 213 220 368 449
Richardson, O.W. 378—380 557
Riemann, G.F.B. 19 89
Ritt, J.F. 557
Rosenhead, L, 140
Routh, E.J. 557
Rule of Leibniz 82
Runge — Kutta method 482—486
Runge, C. 482—483
Saddle point 270 314
Saddle point, definition of 321
Sansone, G. 557
Schaefii, L. 557
Schmidt, E. 414 557
Schoncke, L.A. 170
Schouten, J.A. 20
Schwarzian derivative 224
Secular terms 300—301
Seifert, G. 557
Separatrix, definition of 270
Series, asymptotic 5
Series, Fourier 167—169 291—300 388—396
Series, semiconvergent 5
Serret, M. 172
Shimizu, T. 557
Shohat, J.A. 557
Siacci, F. 557
Sigma function 161
Simpson's one-third rule 478
Simpson, T. 478
Singular points 14 111 185 225
Singular solutions 49 53—56
Skan, S.W. 400 548
Slotnick, D.L. 557
Smith, O.K. 304 307 553
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