Forsyth A.R. — A Treatise on Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Forsyth A.R. — A Treatise on Differential Equations

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Название: A Treatise on Differential Equations

Автор: Forsyth A.R.

Аннотация:

Classic 19th-century work considered one of the finest treatments of the topic. Differential equations of the first order, general linear equations with constant coefficients, integration in series, hypergeometric series, solution by definite integrals, many other topics. Over 800 examples. Index.

Язык:

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1888

Количество страниц: 424

Добавлена в каталог: 06.04.2005

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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 $n^{th}$ 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 $n^{th}$ 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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