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Forsyth A.R. — Theory of differential equations. Part 1
Forsyth A.R. — Theory of differential equations. Part 1



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Название: Theory of differential equations. Part 1

Автор: Forsyth A.R.

Аннотация:

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1959

Количество страниц: 340

Добавлена в каталог: 28.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Mansion      183 230 306
Maximowitch      58
Mayer      1 59 62 67 72 76 81 86 200 215 230 233 257 258 294 331
Mayer's establishment of equations of tangential transformation      233 238
Mayer's establishment of equations of tangential transformation modification and simplification of Lie's theorem      237
Mayer's establishment of equations of tangential transformation will not apply to systems of Pfaffians      331
Mayer's method of integrating system of exact equations      59
Mayer's method of integrating system of exact equations in its simplest form      61
Mayer's method, of solving complete system of linear homogeneous partial differential equations      72—76
Mayer's method, of solving complete system of linear homogeneous partial differential equations, of obtaining at least one integral      76—78
Memoirs on systems of Pfaffians      299
Minimum number of integrals, general for non-integrable system      312—316
Minimum number of integrals, general for single equation      89 113 114 145 146
Minimum, conditions that the number of equations in the integral equivalent be less than the general by Clebsch      207
Minimum, conditions that the number of equations in the integral equivalent be less than the general by Lie      255
Minimum, conditions that the number of equations in the integral equivalent be less than the general in Grassmann's symbolical form      123—127
Minimum, conditions that the number of equations in the integral equivalent be less than the general obtained by Natani      166 168
Modification of incompletely integrable system by use of its exact integrals      311
Monge      80 102 307
Monge's view of inexact equations      80
Monomial equation of Grassmann, if extensive, includes a system of simultaneous equations in several dependent variables      122
Monomial equation of Grassmann, if numerical, includes a single partial differential equation of the first order      122
Monomial equation of Grassmann, relation of, to integrals of Pfaffian      123
Monomial equation of Grassmann, transformation of      137 141
Multipliers of system of exact equations      40
Multipliers of system of exact equations, partial differential equations satisfied by      42
Multipliers of system of exact equations, quotient of two is a solution, with other properties      41 43
Natani      27 30 32 55 56 59 78 82 83 85 86 143 180 187 190 191 200 208 278 312
Natani's method of integration, of exact equation      27
Natani's method of integration, of exact equation of system of exact equations      56
Natani's method of integration, of exact equation, compared with du Bois-Reymond's      32
Natani's method of integration, of exact equation, compared with Euler's      30
Natani's method of integration, of exact equation, developed by Mayer      59—62
Natani's method of treatment of Pfaff's problem      chap. vi
Natani's method of treatment of Pfaff's problem, abstract and character of      85 86
Natani's method of treatment of Pfaff's problem, application of, to solution of single partial differential equation      187 188
Natani's method of treatment of Pfaff's problem, generalised to system of Pfaffians to determine number      313
Natani's method of treatment of Pfaff's problem, inapplicable to determine integrals      322
Natani's method of treatment of Pfaff's problem, to solution of system of partial differential equations      190
Non-integrable systems      301
Non-integrable systems, arbitrary integrals used to modify      319
Non-integrable systems, minimum number of equations in integral equivalent of      312—316
Non-integrable systems, number of arbitrary integrals in equivalent of      316
Non-integrable systems, three fundamental problems relating to      311
Normal form involving even number of functions      194
Normal form involving even number of functions, Clebsch's generalisation of      196
Normal form involving odd number of functions      221
Normal form involving odd number of functions, Clebsch's generalisation of      222
Normal form of conditioned expression deduced from that of transformed unconditioned expression      259—266
Normal form reduction of expression to a, by Lie      248
Normal form relations between elements of equivalent      252
Normal form used by Frobenius to make expressions equivalent      285 289
Normal form, character of, to be inferred from results of Natani and Frobenius      278 (note)
Normal form, conditions which determine character of      253
Normal form, construction of      see "Gradual construction"
Normal form, equations of Frobenius which determine      291 292
Normal form, invariantive persistence of character of      249
Normal form, unaltered in character when Cauchy substitution is applied      258 269
Number of equations in most general integral equivalent of non-integrable system      312—316
Number of equations in most general integral equivalent of non-integrable system, application of result to simultaneous partial equations in several dependent variables      317 329
Number of exact integrals of incompletely integrable system      304
Number of independent solutions of a complete system of linear and homogeneous partial differential equations      69
Odd invariantive integer in Frobenius' theory      287
Odd number of variables, unconditioned expression involving, treated by Clebsch's method      219
Odd number of variables, unconditioned expression involving, treated by Lie's method      268
Odd number of variables, unconditioned expression involving, treated by Natani's method      157—165
Odd reduction      111
Odd reduction can always be applied to expression involving odd number of variables      111
Odd reduction, not unique      111
Osculational transformations      280
Partial differential equation of first order, a single, integration of, by Pfaff      181—183
Partial differential equation of first order, a single, only one integration necessary in Natani's method      154
Partial differential equation of first order, a single, Pfaff's integration improved by Jacobi      183—187
Partial differential equation of first order, a single, Pfaff's integration improved by Natani      187 188
Partial differential equation of first order, a single, special case of Pfaffian equation      122
Partial differential equation of second order, conditions for intermediary integral of      307
Partial differential equation of second order, nature of integral equivalent of general      320
Partial differential equations, solution of simultaneous system of, by Natani      190
Partial differential equations, solution of simultaneous system of, by Natani, application to solution of      chap. vii 238
Partial differential equations, system of, coextensive with system of exact equations      67 69 71
Persistence of character of normal form      249
Pfaff      81—83 89 180
Pfaff's method of reduction      Chap. iv
Pfaff's method of reduction, additions to, by Gauss and Jacobi      81 82
Pfaff's method of reduction, general theory      81 90
Pfaff's Problem, why so called      81
Pfaff's solution of partial differential equation of first order      181
Pfaff's solution of partial differential equation of first order, simplified by Jacobi      183
Pfaff's theorem as to transformation of an expression, applied to deduce a later theorem of Jacobi's      83 115
Pfaff's theorem as to transformation of an expression, completion of proof of      112
Pfaff's theorem as to transformation of an expression, simplified by Jacobi      117—120
Pfaff's theorem as to transformation of an expression, stated      89
Pittarelli      35
Principal integrals, of system of equations      118 151
Principal integrals, of system of equations of subsidiary system used for transformation by literal transcription      120 152 153 157 170 171
Pujet      33
Raabe      33 193
Reciprocation a particular case of tangential transformation      230 232
Reduced form, integral equivalent derived from      116 117
Reduced form, integral equivalent derived from, equivalence of, containing even number of independent functions      203 255
Reduced form, integral equivalent derived from, equivalence of, to another reduced form      195 219 249
Reduced form, integral equivalent derived from, generalisation of      194 220
Reduced form, integral equivalent derived from, generalisation of, containing odd number of independent functions      219 268
Reduced form, integral equivalent derived from, generalisation of, normal form of      222
Reduction of expression by Pfaff's method, completed by Gauss for all cases      112—114
Reduction of expression by Pfaff's method, procedure in, when number of variables is odd      106—111
Reduction of expression by Pfaff's method, subsidiary equations for      89—94
Reduction of expression by Pfaff's method, three cases of      95 100 103
Reduction of two equations in four variables to canonical form      325—327
Reduction, even      105
Reduction, neither unique      105 111
Reduction, odd      111
Reduction, simplified by use of principal integrals      117—120
Sarrus      33
Scott      81 95 106 275
Second Method, applies only to equation in even number of variables, if unconditioned      210
Second Method, Clebsch's      209—218
Second Method, or if Pfaffian determinant alone vanishes      214
Second order, partial differential equation of conditions that it may possess intermediary integral      307—310
Second order, partial differential equation of nature of integral equivalent of      320 321
Simplification of Pfaff's reduction, by Jacobi      117—120
Simplification of Pfaff's reduction, by Jacobi, of process when some coefficients vanish      153
Simultaneous partial differential equations of first order in a single dependent variable, conditions of coexistence      191 and note
Simultaneous partial differential equations of first order in a single dependent variable, solution of, by Natani      190—193
Simultaneous partial differential equations of first order in several dependent variables, included in extensive monomial equation      122
Simultaneous partial differential equations of first order in several dependent variables, number of integral equations equivalent to      317 329
Simultaneous variations used by Binet      148
Simultaneous variations used by Darboux      295
Simultaneous variations used by Frobenius      273
Simultaneous variations used by Natani      148 149 157 174 178
Single exact equation      chap. i
Single integration of subsidiary system sufficient for partial differential equation of first order      154
Solution of partial differential equation, connected with Natani's general result      187
Solution of partial differential equation, improved by Jacobi      183—187
Solution of partial differential equation, Natani's method of      188—190
Solution of partial differential equation, note on history of      188 (note)
Solution of partial differential equation, Pfaff's method of      181—183
Solution of system of equations by Mayer      72—78
Solution of system of equations by Natani's method      190—193
Solution of system of equations in Clebsch's method      215
Stodockiewicz      58
Stoffel      33
Subsidiary equation for transformation of Grassmann's monomial form      128—130
Subsidiary equation for transformation of Grassmann's monomial form, integration of solved equation      136 137
Subsidiary equation for transformation of Grassmann's monomial form, interpreted numerically      133
Subsidiary equation for transformation of Grassmann's monomial form, solution of      130—136
Subsidiary equations constructed by use of simultaneous variations      148
Subsidiary equations for conditioned expression an exact system      54 170
Subsidiary equations for conditioned expression an exact system, integration of      170—172
Subsidiary equations for Pfaff's reduction, formation of      89—94
Subsidiary equations, when number of variables is even, alternative cases      94 296
Subsidiary equations, when number of variables is even, Cayley's symbolical form of      100
Subsidiary equations, when number of variables is even, principal integrals of      118
Subsidiary equations, when number of variables is even, solution of, in most general case      96
Subsidiary equations, when number of variables is even, still valid, if determinant alone vanish      101
Subsidiary equations, when number of variables is odd in general inconsistent      110
Subsidiary equations, when number of variables is odd, effect of satisfaction of      109
Subsidiary equations, when number of variables is odd, formed by Natani      157—159
Subsidiary equations, when number of variables is odd, Jacobi's condition for consistency of      107
Subsidiary equations, when number of variables is odd, principal integrals of, used to transform expression      151 160
Subsidiary equations, when number of variables is odd, solution of      160 164
Subsidiary equations, when number of variables is odd, verified by Natani's results      164
Subsidiary system, modified by more than two integrals      179
Subsidiary system, modified by one of its integrals      173—175
Subsidiary system, modified by two integrals of original equation      178
Subsidiary system, modified by two of its integrals      176 177
Summary of methods of treatment of Pfaff's problem      chap. iii
Symbolical solution by Cayley of subsidiary system      100
System of equations, completely integrable      300
System of equations, incompletely integrable      301
System of equations, non-integrable      301
System of equations, what is meant by exact integral of      300 301
System of exact equations      chap. ii
System of Pfaffians      chap. xiii
System of Pfaffians, memoirs relating to      299
System of Pfaffians, represented by a single extensive monomial equation      122 329
Tangential transformations      chap. ix 298
Tangential transformations, applied by Lie to Pfaff's problem      252
Tangential transformations, note on history of      230
Tanner      117 142 299
Tanner's symbolical forms similar to Grassmann's      142
Transformation of expression to monomial form      122
Transformation of expression when number of variables is even, completed      113
Transformation of expression when number of variables is even, three cases of      99 100—102 103—105
Transformation of expression when number of variables is odd, completed      114
Transformation of expression when number of variables is odd, two cases of      107—109 110—111
Transformation of expression, by Cauchy substitutions when it is conditioned      258 269
Transformation of expression, by principal integrals      118 152 157
Transformation, gradual, of monomial form      127—141
Uniqueness, want of, in reductions even or odd      105 111
Unsolved problems, connected with non-integrable systems of equations      330
Valyi      321
Vanishing coefficients, effect of, in simplifying construction of normal form      153
Vanishing Pfaffian determinant, effect of, on transformation of expression      102 105
Variable, extensive      121
Voss      33 34 299
Weiler      32
Winckler      33
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