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| Авторизация |
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| Поиск по указателям |
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| Forsyth A.R. — A Treatise on Differential Equations |
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| Предметный указатель |
Abel 249
Ampere’s method of solving the generalised form of Monge’s equation 406—410
Bessel’s equation 159—168
Bessel’s equation, derivable from Legendre’s equation 169
Bour 347
Cauchy’s method of integrating Euler’s equation 241
Cayley 36 92 213 243
Charpit’s method of integration of partial differential equations of the first order in two independent variables 317—324
Clairaut’s equation 27 312
Classification of the integrals of a partial differential equation 287—299
Classification of the integrals of a partial differential equation, every integral is included in one of the three classes 291
Complementary function 49 52—55 66 384 389
Complete Integral of a partial differential equation 288 356
Cuspidal Locus 33
Darboux 36 297
Definite Integrals, solution of linear equation whose coefficients are of first degree in independent variable by means of 217—223
Definite Integrals, solution of linear equation whose coefficients are of first degree in independent variable by means of, proposition relating to solution of general equation by means of 223—227
Definite Integrals, solution of linear equation whose coefficients are of first degree in independent variable by means of, solution of a partial differential equation in 397
Degree, definition of 8
Depression of order of equation when one or more particular integrals are known 50 115
Depression of order of equation when one or more particular integrals are known, when one variable is absent 77
Duality between partial differential equations, analytical 313 376
Duality between partial differential equations, analytical, corresponds to geometrical principle of duality 315
Envelope Locus 33
Envelope Locus, the only Singular Solution 35
Equation of first order and first degree has only one independent primitive 15
Equations giving relation between differential coefficients 74—76
Equivalence of linear equations of second order, conditions for 95
Euler 234 360
Euler’s equation 239—243
Euler’s equation, generalisation of 243—249
exact equations 82—85
Ferrers 159
First Integrals, definition of 9
First Integrals, number of independent, belonging to equation of  order 9
Functions, conditions for relations between 11
Gauss 186 212
Gauss’s n function 155 161 198
General Integral of a partial differential equation 291
Generalisation of any integral of a partial differential equation containing constants 410—415
Glaisher, J.W.L. 39 176 178
Goursat 213
Graindorge 342 417
hankel 151 167
Heine 159 169 170
Hicks 153
Homogeneous ordinary equations of first order 20
Homogeneous ordinary equations of first order, in general 79
Homogeneous ordinary equations of first order, linear of order 66
Homogeneous ordinary equations of first order, partial equations 392
Hypergeometrie series, definition of 185
Hypergeometrie series, definition of, as a definite integral 230
Hypergeometrie series, definition of, casps when expressible in a finite form 204—212
Hypergeometrie series, definition of, differential equation satisfied by 187
Hypergeometrie series, definition of, particular solutions of this equation 189—194
Hypergeometrie series, definition of, relations between these solutions 194—203
Imschenotsky 342 411 417
Independence of Particular Integrals of general linear equation, conditions for 110
Intermediary integral 356
Invariant of coefficients of linear equation of second order 89
jacobi 92 213 234 249 942
Jacobi’s method for the integration of the general partial differential of the first order in n independent variables 325—342
Jacobi’s method of integrating the generalised form of Euler’s equation 243
Kummer 92 213
Lagrange 92 301 317 411
| Lagrange’s linear partial differential equation 299—303
Lagrange’s linear partial differential equation, generalised form 304
Laplace’s transformation of the linear partial differential equation of the second order 377—382
legendre 360
Legendre’s equation 143—159
Linear equation with constant coefficient, ordinary Chapter III
Linear equation with constant coefficient, ordinary, partial 383—393
Lobatto 234
Lomwel 170 176
Malet 90
Mansion 342
Monge’s form of solution of total differential equations 255
Monge’s method of integrating the equation of the second order which is linear in the partial differential coefficients 358—371
Motion of particle under central force, integration of equations of 278’
Neumann 170
Nodal Locus 33
Normal form of linear equation of second order 90
Normal form of linear equation of second order, of equation of hypergeometric series 188
Order, definition of 8
Particular integral 49 57—66 67 385 391
Petzval 234
Poisson’s method for a form of homogeneous partial equation 382
Primitive, definition of 8
Quotient of two solutions of linear equation of second order, equation satisfied by 92
Rayleigh 169
Relation between linearly independent solutions of a differential equation 99 112 155 168 201
Riccati’s equation 170—176
Riccati’s equation, reducible to Bessel,s equation 173
Richelot 248
Richelot’s method of integrating Euler’s equation 239
Riemann 400
Routh 170 342’
Schwarz 92 204 213
Schwarzian derivative 92 204—212
Series, possibility of integration in 132
Series, possibility of integration in, form when such a factor occurs in the numerator 141
Series, possibility of integration in, form, of solution when a vanishing factor occurs in the denominator of a coefficient 139
Series, possibility of integration in, integration of partial equations in 394—396 401—405
Simultaneous equations (ordinary), linear, with constant coefficients 265—272
Simultaneous equations (ordinary), linear, with variable coefficients 272—278
Simultaneous partial differential equations in one dependent variable 347—352
Singular Integral of a partial differential equation 290
Singular Integral of a partial differential equation, derived from the differential equation 296
Singular Solutions of ordinary equations of first order 30—39
Solution of ordinary equation, what is to be considered a 6
Species, definition of 7
Spitzer 234
Standard Forms of ordinary equations , they are particular cases in which Charpit’s method (q. v.) proves effective 322—324
Standard Forms of ordinary equations of first order 16—30
Standard Forms of ordinary equations of partial differential equations of first order 306—312
Sturm 170
Symbolic Operations 43—48 384 395 399
Symbolical method for partial equations due to Laplace and Poisson 398
Symbolical Solutions 176
Tac — Locus 35 298
Thomson, Sir William 108
Todhunter 159 170
Total differential equations, which are linear 249—257
Total differential equations, which are linear, case of n variables 261
Total differential equations, which are linear, equations which are not linear 268
Total differential equations, which are linear, geometrical interpretation of linear equatione with three variables 258—261
Total differential equations, which are linear, they separate into two classes 255
Trajectories, general 119
Trajectories, general, orthogonal 120
Variation of parametrs 98 112 116 411
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