Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Goursat E. — A course in mathematical analysis. Volume 2, part 2: Differential equations
Goursat E. — A course in mathematical analysis. Volume 2, part 2: Differential equations

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: A course in mathematical analysis. Volume 2, part 2: Differential equations

Автор: Goursat E.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1945

Количество страниц: 306

Добавлена в каталог: 26.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abel's theorem, applied to Euler's equation      28 15
Abelian integral      18 11
Abell      28 15
Adjoint equation, polynomial      115 42; 42
Adjoint system of equations      156 166 62
Algebraic critical points      178 63; 67; 71; 71
Algebraic differential equations      180 66; 67
Analytic extension of integrals      101 37; 56; 182 67; 68
Analytic integrals      45 22; 22; 23; 24; 25; 25; 26; 26; 26; 29; 37; 64; 84; 94
Anharmonic ratio of integrals      18 7
Antomari      246
Appell      41; 115 42;
Approximate integration of differential equations      64
Arbitrary constants      74 31 see
Asymptotic lines      43 ex. 35; ex.6
Auxiliary equation, polynomial      12 6; 43; 45; 60
Auxiliary equation, polynomial, for a system of equations      158 58; 60
Auxiliary equation, polynomial, roots of      119 43
bernoulli      11 6
Bernoulli's equation      11 6
Bertrand      41; 232 80; ex.
Bertrand's method      282 80; ex.
bessel      126 46; 62; ex.
Bessel's equation      126 46; 52; ex.8
Boole      212 ex.
Bounitzky      44 ex.
Bracket [u, v]      234 81; 83
Briot and Bouquet      45 21; 26; 64; 64; 64; 64; 65;
Briot and Bouquet's equation      178 64
Briot and Bouquet's method, analytic integrals      50; 59 26
Briot and Bouquet's theorem      175 64; 64; 64; 65
Calculus of limits      45 21 50
Calculus of limits, (system of equations)      48
Calculus of limits, (system of)      56 26; 94; 94
Calculus of limits, equations of the nth order      49 22; 37
Calculus of limits, non-linear equations      174 64
Calculus of limits, partial differential equations      58 25
Calculus of limits, system of linear equations      50 23
Calculus of limits, total differential equation      51 24
Canonical form, of a system of linear equations      161 59; 179 65
Canonical form, of substitutions      181 48; 48
Cauchy      85 18; 21; 22; 27; 30; 30; 30; 39; 46; 63; 67; 71; 71; 75; 75; 84; 86; 85; 85; Note; 86; Note; 87; 87
Cauchy — Lipschitz method      61 27; 30; 30
Cauchy's equation      257 ex.
Cauchy's first proof      68 30; 30
Cauchy's method non-homogeneous linear equations      108 39;
Cauchy's method non-homogeneous linear equations, (extended)      261 87
Cauchy's method non-homogeneous linear equations, (system of)      154
Cauchy's method non-homogeneous linear equations, partial differential equations      249 85; Note; 86; Note
Cauchy's problem      246 84; 87
Cauchy's theorem      45 22; 68; 67; 71; 71
Cauchy's theorem, (system of equations)      48 217 76
Cauchy's theorem, partial differential equations      54 26
Center, of integral curves      180 66
Center, of similitude      8 3
Characteristic curves      219 76; 77; 86; 86; 86; 87
Characteristic curves, Cauchy's method      249 257 Note; 86; Note; 87
Characteristic curves, congruence of      219 76; 76; 77
Characteristic curves, derivation from complete integral      259 86
Characteristic curves, differential equations of      219 76; 77; 77; 86 see
Characteristic developable surface      252 85; 86; Note
Characteristic direction      250 85
Characteristic equation      180 189 50; 61; 63; 54; 61; 775 66
Characteristic equation, elementary divisors      132
Characteristic equation, roots of      130 47; 48; 60; Note
Characteristic exponents      147 64; 66
Characteristic numbers      147 54
Characteristic strip      252 86; 86; Note; 87
Characteristic strip, differential equation of      262 87
Circles, differential equation of      5 1;
Circles, differential equation of, of double contact with a conic      206 ex.4
Cissoid      206 ex.
Clairaut      17 41; ex. 72; 74; ex.
Clairaut's equation      17 41; ex. 72
Clairaut's equation, generalized      212 74; ex.
Clebsch      267 88
Complete integral      236 82; 241 83; 84; Note; 91; 92
Complete integral of involutory systems      277 91 see
Complete integral, generalization of theory      272 90
Complete integral, geometric interpretation      288
Complete systems      267 88
Complete systems, change of variables      267 89
Complete systems, equivalent      268 89
Complete systems, Jacobian systems      269 89; 89; ex.; 91; 92
Complete systems, method of integration      270 89
Completely integrable total differential equations      52 24; 78
Completely integrable total differential equations, system of equations      58 24;
Complex of curves      259 86
Condition for incompressibility of a fluid      86 33
Condition for integrability of total differential equations      52 24; 78; 80
Condition for integrability of total differential equations, invariance of      281 80
Condition for integrability of total differential equations, involutory systems, Poisson's parenthesis      274 91
Condition for integrability of total differential equations, the bracket [u, v]      284 81; 83
Condition for integrability of total differential equations, the parenthesis (u, v)      234 81
Conformal representation      22 13
Congruence of curves      209 74; 76; 77
Congruence of curves, focal points of, focal surface      209 74; 77 see
Conical point      257 85
Conics, differential equation of      5 1
Conics, differential equation of, having circles of double contact      206 ex.
Conoids      220 ex.
Constant coefficients in differential equations      117 43
Constant coefficients in differential equations, (system of equations)      157 68; 68
Constant coefficients in differential equations, D'Alembert's method      122 44; 68
Constants of integration      74 31;
Continuous one-parameter groups      87 34;
Corresponding homogeneous linear equation      107 39
Cotton      64
Covariant      80 Note
Cremona transformation      198
Critical points, algebraic      178 63; 67; 71; 71
Critical points, algebraic, infinite number of      185
Critical points, algebraic, linear equations      129 47
Critical points, algebraic, non-linear equations      173 63
Critical points, algebraic, permutation of integrals about      129 47; 49;
Critical points, algebraic, transcendental      197 70
Curves, asymptotic lines      48 ex. 36; ex.
Curves, asymptotic lines, circles see Circles; cissoid      206 ex.
Curves, asymptotic lines, complex of      259 86
Curves, asymptotic lines, congruence of      see "Congruence of curves"
Curves, asymptotic lines, conics      see "Conics"
Curves, asymptotic lines, cycloid      41 20
Curves, asymptotic lines, edge of regression      209 74; 74; ex.
Curves, asymptotic lines, elastic space curve      99 ex.
Curves, asymptotic lines, ellipse      75 10
Curves, asymptotic lines, envelope      see "Envelope"
Curves, asymptotic lines, family of      8 1
Curves, asymptotic lines, helices      220 ex.
Curves, asymptotic lines, isothermal      45 ex.
Curves, asymptotic lines, orthogonal      14 7; 17; 78;
Curves, asymptotic lines, parabola      6 1
Curves, asymptotic lines, parallel      42 ex.
Curves, asymptotic lines, similar      8 3
Curves, asymptotic lines, straight lines      4
Curves, asymptotic lines, trajectories      14 7; 17; 36
Curves, asymptotic lines, unicursal quartic      19 ex. 72; "Lines "Locus"
Cusps of integral curves      41 20; 71; 71; 73; 74; ex. see
D'Alembert      122 44; 68
D'Alembert's method      122 44; 68
Darboux      29 16; 21; ex. 85
Darboux's theorems      29 16
Definite integrals as solutions, of Bessel's equation      126 46; ex.
Definite integrals as solutions, of Laplace's equation      124 46
Delassus      286 94
Depression of order      36 19; 40
Derivative in non-linear equations, indeterminate      178 64; 65;
Derivative in non-linear equations, infinite      172 63
Developable surfaces      240 82; 85; ex. also
Differential equations      3 1
Differential equations of characteristic curves      219 76; 77; 77; 85
Differential equations of characteristic strip      262 87
Differential equations of circles      5 1
Differential equations of conics (Halphen's method)      5 1
Differential equations of first order      6 2; 66
Differential equations of higher order      85 18; 70
Differential equations of incompressible fluid      84 33
Differential equations of isothermal curves      48 ex.
Differential equations of orthogonal trajectories      14 7; 17; 78
Differential equations of parabolas      6 1
Differential equations of similar curves      8 3
Differential equations of straight lines      4 1
Differential equations of the nth order      4 1; 2; 22; 37
Differential equations of trajectories      see "Trajectories" "Special
Differential equations with periodic coefficients      see "Periodic coefficients"
Differential equations, admitting a group of transformations      89 35; 35; 36; 36; 36; ex.
Differential equations, algebraic      180 66; 67
Differential equations, algebraic, of deficiency zero or one      18 11
Differential equations, Bernoulli's      11 6
Differential equations, Bessel's      126 46; 52; ex.
Differential equations, Cauchy's      257 ex.
Differential equations, Clairaut's      see "Clairaut's equation"
Differential equations, Darboux's theorems      29
Differential equations, depression of order of      36 19; 40
Differential equations, Differential equations, Briot and Bouquet's      173
Differential equations, differential notation      7 2
Differential equations, elastic space curve      99 ex.
Differential equations, equations F(x,y')— 0, F(y,y') = 0      18 11
Differential equations, Euler's see Euler's equation; Euler's linear      128 45
Differential equations, existence theorems      see "Existence theorems"
Differential equations, Gauss's      140 51
Differential equations, geometric representation of      14 8
Differential equations, homogeneous      8 16; 19; 35
Differential equations, integrals of      see "Integral curves" "Integral
Differential equations, Jacobi's      see "Jacobi's equation"
Differential equations, Lagrange's      16 9; 72; 72
Differential equations, Lamp's      146 53
Differential equations, Laplace's linear      124 46
Differential equations, Legendre's      112 ex.
Differential equations, linear      9 4; 36
Differential equations, Liouville's      79 3
Differential equations, order of      4 1
Differential equations, Painlev^'s      196 70; 70
Differential equations, Picard's      148 53
Differential equations, raising order of      41 Note
Differential equations, regular      184 50
Differential equations, Riccati's      see "Riccati's equation"
Differential equations, singular points of      see "Singular points"
Differential notation      7 2
Differential operators      97 36; 38; 41
Differential operators, bracket [u, v]      284 81; 83
Differential operators, Poisson's parenthesis      274 91
Differential operators, the parenthesis (u, v)      284 61
Differential operators, X[Y(f)]-Y[X(f)]      97 36; 88; 92
Dixon      44 ex.
Dominant functions      45 47 22; 23; 55 188 60; 64
Doubly periodic functions of the second kind      145 68
Edge of regression      209 74; 74; ex 2; 86
Elastic space curve      55 ex 7
Element      86; 261 87
Elementary divisors      182
Elimination, of arbitrary functions      222 77; 82; 86; 90; 93
Elimination, of constants      3 1; 74; 82; 90
Ellipsoid, lines of curvature of      41 Note
Elliptic functions      28 14
Elliptic functions as coefficients of a linear equation      144 63; 64
Elliptic functions as integrals      19 ex 3; 20; 63;
Elliptic functions existence proof from Euler's equation      28 14; 69
Elliptic functions Picard's equation      144 63
Envelope, of asymptotic lines      206 ex 6
Envelope, of integral curves      17 10; 71; 72; 74; ex 8
Envelope, of integral surfaces      288 82; 93
Envelope, of straight lines      18 10
Equations of first order, higher order      see "Differential equations and special classes of equations"
Equivalent complete systems      268 89
Essentially singular points      181 47; 49
Essentially singular points, movable      196 70
Euler      19 12; 14; 14; 15; 16; ex 17; 43; 45; 69; 72; ex 3
Euler's equation      28 28 15; 69; 72
Euler's equation, Abel's theorem      28 15
Euler's equation, existence of elliptic functions      28 14; 69
Euler's equation, Lagrange's integral of      48 ex.
Euler's equation, Stieltjes's general integral      27 14
Euler's linear equation      128 45
Euler's relation for homogeneity      221 ex 3
Exceptional initial values      172 63; 64; 65
Existence theorems      45 22; ex.
Existence theorems for elliptic functions      28 14; 69
Existence theorems for integrating factors      57 26
Existence theorems for systems of partial differential equations in normal form      283 94;
Existence theorems, analytic integrals      see "Analytic integrals" and "Briot and Bouquet's method"
Existence theorems, calculus of limitss      see "Calculus of limits"
Existence theorems, successive approximations      see "Successive approximations"
Extended group      94 36
First integrals      74 31; 31; 32; 32; 67; lb
Fixed singular points      181 66; 67
Floquet      151
Focal point      209 74
Focal surface      209 74; 77
Focus      180 65
Fuchs      134 50;
Fuchs' theorem      134 50
Functions defined by differential equations      182 67
Fundamental characteristic equation      189 50;
Fundamental system for a system of linear equations      158 56
Fundamental system of integrals      103 38; 38; 47; 47; 54
Gauss      140 51
Gauss's equation      140 51
General integral      3 1; 59 26; 31
General integral of a system of equations      57 26; 56
General integral of homogeneous linear equations      108 38; 38
General integral of partial differential equations      217 16; 82; 90
Goursat      88 170 ex. 15;
Group, differential equations admitting a      89 35; 35; 36; 36; 36; ex.
Group, differential equations of a      88
Groups of infinitesimal transformations      94 36; 36
Groups of translations      89 34;
Groups, application to differential equations      89 35; 36;
Groups, functions admitting      96 36
Groups, invariants      96 36
Groups, one-parameter continuous      86 34; 36
Groups, similar      15 34
Halphen      5 1; 42
Hedrick      255
Helices      220 ex. 83
Helicoid      220 ex. 83
Helicoid lines of, curvature of      91 36
hermite      99 ex. 63; ex.
Hoiiel      212 ex.
Homogeneity of functions, Euler's relation      221 ex.
Homogeneous equations      8 3; 19; 36
Homogeneous linear equations      102 38;
Homogeneous linear equations, (D'Alembert's method)      122 44
Homogeneous linear equations, adjoint equation, polynomial      116 42
Homogeneous linear equations, analogies with algebraic equations      113 41
Homogeneous linear equations, analogies with the Galois theory, with symmetric functions of roots      445 41
Homogeneous linear equations, auxiliary equation, polynomial      117 43
Homogeneous linear equations, Bessel's equation      126 46; 62; ex.
Homogeneous linear equations, common integrals of two equations      444 41
Homogeneous linear equations, constant coefficients      117 43
Homogeneous linear equations, corresponding      107 39
Homogeneous linear equations, critical points      129 47
Homogeneous linear equations, depression of order      400 40
Homogeneous linear equations, elliptic coefficients      444 53; 54
Homogeneous linear equations, Euchs* theorem      134 60
Homogeneous linear equations, Euler's linear equation      123 45
Homogeneous linear equations, fundamental system of integrals      103 38; 38; 47
Homogeneous linear equations, Gauss's equation      140 51
Homogeneous linear equations, general integral      103 38; 38
Homogeneous linear equations, greatest common divisor      113 41
Homogeneous linear equations, group of substitutions      132 48; 48
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2018
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте