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| Simmons G.F. — Differential Equations with Applications and Historical Notes |
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| Предметный указатель |
 -body problem 267
Abel, N. H. 196 204 220n 347 415 417
Abel, quoted on Gauss 198
Abel’s integral equation 41 1
Abel’s mechanical problem 410
Absolute convergence, improper integral 393
Achieser, N. I. 209n
action 378
Adams, J. C. 158n
Admissible function 356
Airy functions 158
Airy, G. B. 158n
Airy’s equation 158 241
Analytic function 145
Andronow, A. A. 333n
Arago, F. 108
Asymptotically stable critical point 704
Autonomous system 292
Auxiliary equation 84
Auxiliary equation, of a system 277 306
Baldwin, G. C. 18n
Barrow, Isaac 112
Bell, E. T. 201n
Bendixson, I. O. 341
Bernoulli, Daniel 31 128 232
Bernoulli, Jakob 30
Bernoulli, Johann 25 31 108 113 353
Bernoulli’s equation 49
Bernoulli’s solution, wave equation 129
Bertrand’s postulate 211
Bessel expansion theorem 245
Bessel functions 232
Bessel functions, first kind 233
Bessel functions, generating function 261
Bessel functions, integral formula 263
Bessel functions, integrals of 243
Bessel functions, order  83 174 241
Bessel functions, order 0 147 166 234 404
Bessel functions, order 0, graph 234
Bessel functions, order 1 173 234
Bessel functions, order 1, graph 234
Bessel functions, orthogonality 244
Bessel functions, oscillation 121 123 124
Bessel functions, second kind 174 237 239
Bessel functions, spherical 243n
Bessel functions, vibrating membrane 259 260
Bessel functions, zeros 123 124 244 247
Bessel series 245
Bessel, F. W. 232 263
Bessel, Gauss’s letters to 203 204
Bessel’s equation 3 160 232
Bessel’s equation,  , solution 147 166 234 403
Bessel’s equation, , solution, second solution 174
Bessel’s equation,  , solution 173 234
Bessel’s equation,  , solution 83 174 241
Bessel’s equation, general solution 237 239
Bessel’s equation, generalization 241
Bessel’s equation, normal form 121 123
Bessel’s equation, point at infinity 1 82
Bessel’s equation, vibrating chain 133
Bessel’s equation, vibrating membrane 259
Bessel’s integral formula 263
Binomial coefficient 150n
Binomial series 150
Binomial theorem 150n
Birkhoff, G. D 348
Bliss, G. A. 363n
Bochner, S. 377n
Bolyai, J. 203
Bolyai, W. 203
boundary conditions 124
Boundary value problems 124
Boyer, C. B. 108n
Brachistochrone problem 25 113 353 363
Brahe, Tycho 103n
Cajori, F. 109n
Cantor, G. 215
Carath odory, C. 356n
Cartan, E. 387
Catenary 54 362
Cauchy, A. L. 416
Cauchy’s equidimensional equation 86n
Center 300
Central force 102
Central gravitational force 103
Cesari, L. 321n 325n 341n
Chaikin, C. E. 333n
Chebyshev polynomials 158 180 204 210
Chebyshev polynomials, orthogonality 208
Chebyshev problem 208
Chebyshev series 208
Chebyshev, P. L. 210 211
Chebyshev’s equation 138 138 179 207
Cheney, E. W 209n
Churchill, R. V. 401n
Circular membrane 257
Closed interval 73n
Coleridge, S. T. 387
Comparison test, improper integral 393
Comparison theorem, Sturm 122
Conant, J. B. 32n
Confluent hypergeometric equation 181 183
Confluent hypergeometric function 183
Confocal conics 32
Conservation of energy 20 382
Conservative force 377
Conti, R. 321n
Continued fractions 264
Convergence, improper integral 392
Convolution 408
Cooling, Newton’s law of 19
Coordinates, generalized 381
Copernicus, N. 113
Courant, R. 239n 386n
Crelle, A. L. 416 417
Critical point 293
Critical point, asymptotically stable 304
Critical point, isolated 293
Critical point, simple 324
Critical point, stable 303
Critical point, unstable 304
Critically damped vibration 96
Curve, stationary 359
Curves, integral 6
Curves, one-parameter family of 7
Cycloid 29 31 52 363 412
Damped vibration 95
Damping force 95 332 333
Darwin, G. H. 347
Dating, radiocarbon 17 18
Davis, P. J. 109n
Dedekind, R. 200
Degrees of freedom 381
Descartes, R. 30
Differential equation 1 (see also Equation)
Differential equation, linear 47 72
Differential equation, normal form 119
Differential equation, order 2
Differential equation, ordinary 2
Differential equation, ordinary point 151
Differential equation, partial 3
Differential equation, singular point 151 159
Differential equation, singular point, irregular 160
Differential equation, singular point, regular 160
Differential equation, standard form 119
Dirac delta function 397
Dirac, P. A. M. 397n
Dirichlet problem 254
Dirichlet, P. G. L. 59n 214 216
Douglas, J. 386
| Dunnington, G. W. 200n
Dynamical problems, variable mass 63
d’Alembert, Jean le Rond 132n
D’Alembert’s formula 132
D’Alembert’s Solution, Wave Equation 132
Eccentricity, physical meaning 105
Eddington, A. 268n
Eigenfunction 125 136 195
Eigenfunction expansion 129 137
Eigenvalue 125 136 195
Einstein relativity impossible without Gauss 200 201
Einstein, A. and Poincar 348
Einstein, A. on doubting the obvious 254
Einstein, A. on future of mathematical physics 291n
Einstein, A. on Riemannian geometry 217
Einstein, use of calculus of variations 354
Einstein, variable mass and  64
Electrostatic dipole potential 254
Electrostatic potential 250
Elliptic integral, first kind 23
Elliptic integral, second kind 23
Energy, conservation of 20 382
Energy, kinetic 20 105 320 378
Energy, potential 20 105 320 378
Equation(s), Airy’s 158 241
Equation(s), Bernoulli’s 49
Equation(s), Bessel’s see Bessel’s equation
Equation(s), Chebyshev’s 138 158 179 207
Equation(s), differential see Differential equation
Equation(s), equidimensional, Cauchy’s 86n
Equation(s), equidimensional, Euler’s 86 161
Equation(s), Euler’s, calculus of variations 358
Equation(s), exact 39
Equation(s), heat 3 250
Equation(s), Hermite’s 138 158 187
Equation(s), homogeneous 36 74
Equation(s), hypergeometric, confluent 181 183
Equation(s), hypergeometric, Gauss’s 174 181 211
Equation(s), hypergeometric, generalized 214
Equation(s), integral see Integral equation
Equation(s), Lagrange’s 382
Equation(s), Laguerre’s 138 183
Equation(s), Laplace’s 3 249
Equation(s), Legendre’s 3 83 138 153 160 182 220 253
Equation(s), Linard’s 343 349
Equation(s), linear differential 47 72
Equation(s), nonhomogeneous 74
Equation(s), prey-predator 285
Equation(s), Riccati see Riccati equation
Equation(s), Riemann’s 214
Equation(s), Sturm — Liouville 136
Equation(s), van der Pol 291 294 331 344 346
Equation(s), wave see Wave equation
Equidimensional equation, Cauchy’s 86n
Equidimensional equation, Euler’s 86 161
Erdyi, A. 141n 176n 397n
Escape velocity 24
Euclid’s theorem 110
Euler and Lagrange 376
Euler calculus of variations 355 358 377
Euler Fourier coefficients 128 129
Euler hypergeometric function 178
Euler identity for primes 1 10 2 17—2 18
Euler irrationality of  139
Euler law of quadratic reciprocity 198
Euler method 66
Euler method, improved 68
Euler minimal surfaces 385
Euler on sequence of primes 210
Euler sums of series 220
Euler vibrating membrane 232 255
Euler, L. 86 107 111 112
Euler’s equation, calculus of variations 358
Euler’s equidimensional equation 86 161
Euler’s formula 84
Euler’s formula, for Fourier coefficients 129
Euler’s identity for primes 110 217—218
Euler’s theorem, homogeneous functions 382
Ewing, G. M. 356n
Exact differential 39
Exact equation 39
Expansion theorem, Bessel 245
Expansion theorem, Fourier 130
Expansion theorem, Legendre 229n
Exponential order, function of 394
Exponents 170
Extremal 359
Fermat, P. 30 109
Fermat’s principle of least time 27 387
Fermi, E. 64n
First-order reaction 15
Focal property, parabolas 46
Fomin, S. V. 356n 429n
Force, central 102
Force, conservative 377
Force, damping 95 332 333
Force, gravitational 103
Forced vibration 98
Fourier expansion theorem 130
Fourier sine series 129
Fourier — Bessel series 245
Fourier, J. 129n
Fredholm, L 138 285n
Free vibration 98
Frobenius series 163
Frobenius, F. G. 163n
Frobenius, method of 163
Function(s), admissible 356
Function(s), Airy 158
Function(s), algebraic 140
Function(s), analytic 145
Function(s), Bessel see Bessel functions
Function(s), Dirac delta 397
Function(s), elementary 140
Function(s), exponential order 394
Function(s), gamma 234
Function(s), Hermite 192 194
Function(s), homogeneous 36
Function(s), homogeneous, Euler’s theorem 382
Function(s), hypergeometric 176
Function(s), hypergeometric, confluent 183
Function(s), Legendre 155
Function(s), Liapunov 318
Function(s), negative definite 317
Function(s), negative semidefinite 317
Function(s), orthogonal 137 229
Function(s), piecewise continuous 393
Function(s), positive definite 317
Function(s), positive semidefinite 317
Function(s), special 140
Function(s), spherical Bessel 243n
Function(s), stationary 359
Function(s), transcendental, elementary 140
Function(s), transcendental, higher 140
Function(s), unit impulse 397
Fundamental lemma, calculus of variations 358n
Fundamental theorem of calculus 5n
Galileo 25 32n 113
Gamma function 234
Gauss and Abel 416
Gauss hypergeometric function 178
Gauss on Riemann’s dissertation 215
Gauss potential theory 250
Gauss prime number theorem 210 21 1
Gauss, C. F. 108 196 204 214
Gauss, complex numbers and quaternions 387
Gauss, Helen W. 197n
Gauss, Riemannian geometry 216
Gauss’s hypergeometric equation 174 181 211
Gelfand, L M 356n
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