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| Simmons G.F. — Differential Equations with Applications and Historical Notes |
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| Предметный указатель |
Regular Sturm — Liouville problem 138
Resonance 99
Riccati equation 62
Riccati equation, special 63n 248
Riccati, J. F. 62n
Riemann, B. 108 214 218
Riemann’s equation 214
Riemann’s identity 214
Ritt, I. F. 5n 139n 243n
Rodrigues, O. 223n
Rodrigues’ formula, Hermite polynomials 191
Rodrigues’ formula, Legendre polynomials 223
Runge — Kutta method 69
Runge, C. 69n
Saddle point 299
Sansone, G. 321n
Sarton, G. 376n
Scarborough, J. B. 66n 70n
Schr dinger wave equation 194
Schrdinger wave functions 194
Schrdinger, E. 194n 354
Schuster, M, L 348n
Scribner, C., Jr 348n
Second-order reaction 18
Separation constant 252
Separation of variables, method of 127 252 258
Separation theorem, Sturm 118
Series, Bessel 245
Series, binomial 150
Series, Chebyshev 208
Series, Fourier sine 129
Series, Fourier — Bessel 245
Series, Frobenius 163
Series, Hermite 193
Series, hypergeometric 175
Series, Legendre 228
Series, power 142
Series, Taylor 145
Simple critical point 324
Singular point 151 159
Singular point, irregular 160
Singular point, regular 160
Singular Sturm — Liouville problem 138
Smith, D. E. 198n 216n
Snell, W. 27n
Snell’s law of refraction 27
Solution, general 7 271
Solution, particular 7
Solution, trivial 75
Special functions 140
Special Riccatti equation 63n 248
Spherical Bessel functions 243n
Spiral 300
Stable critical point 303
Standard form, differential equation 119
Stationary curve 359
Stationary function 359
Stationary value 359
Stoker, J. J. 333n
Sturm comparison theorem 122
Sturm separation theorem 118
Sturm — Liouville equation 136
Sturm — Liouville expansion 138
Sturm — Liouville problem, regular 138
Sturm — Liouville problem, singular 138
Sturm, J. C. F. 118n
System, autonomous 292
System, auxiliary equation of 277 306
| System, linear homogeneous 269
System, linear nonhomogeneous 269
Szeg, G. 372n
Tautochrone problem 31 52 411
Taylor series 145
Taylor’s Formula 145
terminal velocity 21
Tietze H. 197n
Titchmarsh, E. 218n
Torricelli, E. 32n
Torricelli’s law 32
Tractrix 54 58
Transcendental functions, higher 140
Transcendental numbers 139
Transform, inverse Laplace 399
Transform, Laplace 390
Transformation, integral 389
Transformation, inverse Laplace 399
Transformation, Laplace 389
Transformation, linear 389
Tricomi, F. G. 296n 325n
Trivial solution 75
Truesdell, C. 251n
Turnbull, H. W 112n
Two-dimensional wave equation 257
Uncoupled linear system 280n
Undamped vibration 93
Underdamped vibration 96
Undetermined coefficient 88
Unit impulse function 397
Universe, Euler’s use of 110
Universe, Jeans’ definition of 268n
Unstable critical point 304
van der Pol equation 291 294 331 344 346
Van der Pol, B. 344n
van der Waerden, B. L. 366n
Variable mass 63
Variation of parameters for linear equations 90
Variation of parameters for linear systems 283
Vavilov, S. I. 114n
Velocity, escape 24
Velocity, terminal 21
Vibration, critically damped 95
Vibration, damped 96
Vibration, forced 98
Vibration, free 98
Vibration, undamped 93
Vibration, underdamped 96
Vicar of Bray 414
Voltaire 108
Volterra, V. 285n
Volterra’s prey-predator equations 285
Waltershausen, W. Sartorius von 197n
Watson, G. N. 63n 214n 232n 239n 243n 245n
Wave equation 126 386
Wave equation, one-dimensional 126 386
Wave equation, one-dimensional, Bernoulli’s solution 129
Wave equation, one-dimensional, d’Alembert’s solution 132
Wave equation, Schrdinger 194
Wave equation, two-dimensional 257
Weber, W. 202
Whittaker, E. T. 214
Wordsworth, W 387
Wronski, H. 78
wronskian 78 271
Zero of a function 76
Zeros of Bessel functions 244
Zeuner, F. E. 16n
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