|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Simmons G.F. — Differential Equations with Applications and Historical Notes |
|
|
|
| Предметный указатель |
Gelfond, A. O. 139
General solution 7 271
Generalized coordinates 381
Generalized hypergeometric equation 214
Generating function, Bessel functions 261
Generating function, Hermite polynomials 189
Generating function, Legendre polynomials 224
Geodesics 361 367 373
Geodesics, in physics 380
Geodesics, on cone 365
Geodesics, on cylinder 366 376
Geodesics, on sphere 365 374
Gibbs, W. 387
Grassmann, H. 387
Gravitation, Newton’s law of 24 103 267 413
Gravitational force 103
Gravitational potential 250
Gray, A. 260n 263n
Green, G. 202n
Hadamard, J. 218
Hailey, E. 113 376
Half-life 16
Halperin, I. 397n
Hamilton, W. R. 376 387
Hamilton’s principle 354 378
Hardy, G. H. 5n 139n
harmonic oscillator 194
Heat equation 3 250
Hegel, G. W 199
Hermite functions 192 194
Hermite functions, orthogonality 192
Hermite polynomials 159 187—196
Hermite polynomials, generating function 189
Hermite polynomials, Rodrigues’ formula 191
Hermite series 193
Hermite, C. 139 196 416
Hermite’s equation 138 158 187
Higher transcendental functions 140
Hilbert, D. 69n 138 202 239n 254 285n
Homogeneous equation 36 74
Homogeneous function 36
Homogeneous function, Euler’s theorem 382
Homogeneous linear system 269
Hooke, R. 113
Hurewicz, W. 325n 326n 341n
Hypergeometric equation, confluent 181 183
Hypergeometric equation, Gauss’s 174 181 211
Hypergeometric equation, generalized 214
Hypergeometric function 176
Hypergeometric function, confluent 183
Hypergeometric series 175
Improper integral, absolute convergence 393
Improper integral, comparison test 393
Improper integral, convergence 392
Improved Euler method 68
Ince, E. L. 109n
Indicial equation 164 165 170
Initial condition 7
Initial value problems 124
Integral curves 6
Integral equation 409 419
Integral equation, Abel’s 411
Integral transformation 389
Integrating factor 42
Interval of convergence 143
Interval, closed 73n
Interval, open 73n
Inverse Laplace transform 399
Inverse Laplace transformation 399
Irregular singular point 160
Isolated critical point 293
Isoperimetric inequality 372
Isoperimetric problem 366 370 371 375
Jacobi, and Gauss 204
Jacobi, C. G. I. 214 220n
Jacobi, on Abel 347 416
Jeans, J. 268n
Jennings, W. 66n 70n
Jump discontinuities 130
Kant, I. 204
Kellogg, O. D. 254n
Kepler, J. 103n 113
Kepler’s law, first 104
Kepler’s law, second 103
Kepler’s law, third 107
Kernel, integral transformation 389
kinetic energy 20 105 320 378
Kirchhoff, G. R. 60n
Kirchhoff’s law 60
Klein, F. 199n
Kolmogorov, A. N. 429n
Kutta, M. W. 69n
Lagrange multiplier 368
Lagrange, J. L. 376 377 385 414
Lagrange’s equations 382
Lagrangian 378
Laguerre polynomials 183
Laguerre, E. 183n
Laguerre’s equation 138 183
Lambert, J. H. 19n 139 219 264
Lambert’s law of absorption 19
Lanczos, C. 201n
Laplace transform 390
Laplace transform, inverse 399
Laplace transformation 389
Laplace transformation, inverse 399
Laplace, P. S. 387 413 415
Laplace’s equation 3 249
Law of conservation of energy 20 382
Law of gravitation, Newton’s 24 103 267 413
Law of mass action 18
Lawyers 33 198
Least action, principle of 379
Least squares approximation 229
Least time, Fermat’s principle of 27 387
Lebedev, N. N 229n 251n 260n
Legendre expansion theorem 229n
Legendre functions 155
Legendre polynomials 155 221
Legendre polynomials, applications 253 255
Legendre polynomials, generating function 224 254
Legendre polynomials, orthogonality 226 230 23 1
Legendre polynomials, Rodrigues’ formula 223
Legendre series 228
Legendre, A. M. 198 220n 264 416
Legendre’s equation 3 83 138 153 160 182 220 253
Leibniz, G. W. 31 112
Leigh, E. R. 285n
Li iard’s equation 343 349
Linard, A. 343n
Linard’s theorem 343 349
Liapunov function 318
Liapunov, A. M 317 318 327
Libby, W. 17 18n
Lindemann, F. 139
linear combination 75
Linear differential equation 47 72
Linear system, homogeneous 269
Linear system, nonhomogeneous 269
Linear system, uncoupled 280n
Linear transformation 389
Linearization 288 323
Linearly dependent 77 272
Linearly independent 77 212
Liouville, J. 138 139 243
Lipschitz condition 428
Lipschitz, R. 428n
Littlewood, J. E. 113n
Lobachevsky,N.I. 55 203
Lorentz, G, G 209n
| Lotka, A. J. 285n
Mass action, law of 18
Mathews, G. B. 260n 263n
Maxwell, J. C. 111 202
Mead, D. G. 5n 139n
Mechanistic determinism 268
Method of Frobenius 163
Method of separation of variables 127 252 258
Minimal surfaces 385
Minimax property 209
Motion, Newton’s second law of 1 63 93 102 126 256 378
Negative definite function 317
Negative semidefinite function 317
Newton, Isaac 19n 30 31 110 111 114 414
Newton’s Law of Cooling 19
Newton’s law of gravitation 24 103 267 413
Newton’s second law of motion 1 63 93 102 126 256 378
Node 297
Nonhomogeneous equation 74
Nonhomogeneous linear system 269
Normal form, differential equation 119
Ohm, G. S. 59n
Ohm’s Law 59
One-dimensiona 1
One-dimensional wave 131
One-parameter family of curves 7
Open interval 73n
Order, differential equation 2
Ordinary differential equation 2
Ordinary point 151
Ore, O. 417n
Orthogonal functions 137 229
Orthogonal trajectories 1 1
Orthogonality, Bessel functions 244
Orthogonality, Chebyshev polynomials 208
Orthogonality, Hermite functions 192
Orthogonality, Legendre polynomials 226 230 231
Overdamped vibration 96
Parabolas, focal property 46
Partial differential equation 3 (see also Heat equation; Laplace’s equation; Wave equation)
Particular solution 7
Pascal, B. 30
Peano, G. 428n
Peano’s theorem 428
Pendulum 21 291 329 334 337
Periods of revolution of planets 106
Phase plane 292
Phase portrait 294
Philosophers 199 204
Picard, E. 420n
Picard’s method of successive approximations 420
Picard’s Theorem 6 266 423
Piecewise continuous function 393
Planck, M. 379
Planets, periods of revolution of 106
Plateau, J. 386
Plateau’s problem 386
Poincar — Bendixson Theorem 341
Poincar, H. 196 290 325 341 346 349
Point, at infinity 180
Point, critical 293
Point, critical, asymptotically stable 304
Point, critical, isolated 293
Point, critical, simple 324
Point, critical, stable 303
Point, critical, unstable 304
Point, ordinary 151
Point, singular 151 159
Point, singular, irregular 160
Point, singular, regular 160
Polynomials, Chebyshev 158 180 204 210
Polynomials, Hermite 159 187 196
Polynomials, Laguerre 183
Polynomials, Legendre see Legendre polynomials
Positive definite function 317
Positive semidefinite function 317
Potential 249
potential energy 20 105 320 378
Potential theory 250
Potential, electrostatic 250
Potential, electrostatic dipole 254
Potential, gravitational 250
Power series 142
Power series, interval of convergence 143
Power series, radius of convergence 143
Prey-predator equations 285
Prime number theorem 211
Principle of least action 379
Problem,  -body 267
Problem, Abel’s mechanical 410
Problem, air pressure 18
Problem, bacteria 18
Problem, bead on circle 33
Problem, brachistochrone 25 113 353 363
Problem, brine 32 62
Problem, bugs on table 34
Problem, buoy 100
Problem, chain on table 33
Problem, chemical reaction 1 8
Problem, clepsydra 32
Problem, confocal conics 32
Problem, destroyer hunting submarine 34
Problem, dog-rabbit 55 58
Problem, earth explodes 107
Problem, escape velocity 24
Problem, falling raindrop 64
Problem, football 32
Problem, geodesics on cone 365
Problem, geodesics on cylinder 366
Problem, geodesics on sphere 365 374
Problem, hanging chain 52 375
Problem, hole drilled through earth 24
Problem, isoperimetric 366 370 371 375
Problem, Lambert’s law of absorption 19
Problem, minimal surface of revolution 54 361
Problem, mirror 45
Problem, mothball 32
Problem, Newton’s law of cooling 19
Problem, one-dimensional wave 131
Problem, path of boat 57 58
Problem, Plateau’s 386
Problem, President and Prime Minister 33
Problem, radioactive decay 62
Problem, relativity 64
Problem, rocket 64
Problem, rope wound around post 33
Problem, rotating can of water 33
Problem, snowplow 31
Problem, tank 33
Problem, tapered column 33
Problem, tautochrone 31 52 411
Problem, Torricelli’s law 32 33
Problem, tractrix 54
Problem, tunnel through earth 100
Problem, vibrating chain 132
Quantized energy levels 196
Rad , T. 386
Radioactive decay 16 62
Radiocarbon 17
Radiocarbon datiag 17 18
Radius of convergence 143
Rainville, E. D. 214n
Ratio Test 143
Reaction, first-order 15
Reaction, second-order 18
Recursion formula 154
Recursion formula, three-term 157 158
Recursion formula, two-term 157
Refraction, Snell’s law of 27
Regular singular point 160
|
|
|
| Реклама |
|
|
|
|
|
О проекте