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Simmons G.F. Differential Equations with Applications and Historical Notes
Simmons G.F.  Differential Equations with Applications and Historical Notes









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: Differential Equations with Applications and Historical Notes

: Simmons G.F.

: en

: /

:

ed2k: ed2k stats

: 1972

: 478

: 25.11.2012

: | | ID
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$n$-body problem      267
Abel, N. H.      196 204 220n 347 415 417
Abel, quoted on Gauss      198
Abels integral equation      41 1
Abels 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
Airys 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
Bernoullis equation      49
Bernoullis solution, wave equation      129
Bertrands 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 ${}^{1}/{}_{2}$      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, Gausss letters to      203 204
Bessels equation      3 160 232
Bessels equation, $p = 0$, solution      147 166 234 403
Bessels equation, $p = 0$, solution, second solution      174
Bessels equation, $p = 1$, solution      173 234
Bessels equation, $p = {}^{1}/{}_{2}$, solution      83 174 241
Bessels equation, general solution      237 239
Bessels equation, generalization      241
Bessels equation, normal form      121 123
Bessels equation, point at infinity      1 82
Bessels equation, vibrating chain      133
Bessels equation, vibrating membrane      259
Bessels 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$\acute{e}$odory, C.      356n
Cartan, E.      387
Catenary      54 362
Cauchy, A. L.      416
Cauchys 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
Chebyshevs 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, Newtons 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
dAlembert, Jean le Rond      132n
DAlemberts formula      132
DAlemberts 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$\acute{e}$      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 $E = mc^{2}$      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), Airys      158 241
Equation(s), Bernoullis      49
Equation(s), Bessels      see Bessels equation
Equation(s), Chebyshevs      138 158 179 207
Equation(s), differential      see Differential equation
Equation(s), equidimensional, Cauchys      86n
Equation(s), equidimensional, Eulers      86 161
Equation(s), Eulers, calculus of variations      358
Equation(s), exact      39
Equation(s), heat      3 250
Equation(s), Hermites      138 158 187
Equation(s), homogeneous      36 74
Equation(s), hypergeometric, confluent      181 183
Equation(s), hypergeometric, Gausss      174 181 211
Equation(s), hypergeometric, generalized      214
Equation(s), integral      see Integral equation
Equation(s), Lagranges      382
Equation(s), Laguerres      138 183
Equation(s), Laplaces      3 249
Equation(s), Legendres      3 83 138 153 160 182 220 253
Equation(s), Li$\acute{e}$nards      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), Riemanns      214
Equation(s), Sturm Liouville      136
Equation(s), van der Pol      291 294 331 344 346
Equation(s), wave      see Wave equation
Equidimensional equation, Cauchys      86n
Equidimensional equation, Eulers      86 161
Erd$\acute{e}$yi, A.      141n 176n 397n
Escape velocity      24
Euclids 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 2 172 18
Euler irrationality of $e$      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
Eulers equation, calculus of variations      358
Eulers equidimensional equation      86 161
Eulers formula      84
Eulers formula, for Fourier coefficients      129
Eulers identity for primes      110 217218
Eulers 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
Fermats 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, Eulers 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 Riemanns 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
Gausss hypergeometric equation      174 181 211
Gelfand, L M      356n
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