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Hancock H. — Theory of Maxima and Minima
Hancock H. — Theory of Maxima and Minima

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Название: Theory of Maxima and Minima

Автор: Hancock H.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 212

Добавлена в каталог: 05.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian transcendents      169
Algebra, fundamental theorem of      165
Algebraic curve expressed through power series      36 53
Algebraic function at a singular point      180 et seq.
Algebraic function, its development in series      177
Algebraic structures      176 et seq. 181
Ambiguous case, the      iv 27.
Analytic dependence      166 et seq. 169
Analytic function      73
Analytic function defined      138
Analytic structure      74 174
Appell      180
Area, maximum area      143
Asymptotic approach      138
Auxiliary variable      101 173
Baltzer      2
Bauer      107
Bertrand      v 33
Biermann      136 155 168
Bocher      148
Bohlmann and Schepp      iv
Bois-Reymond, Paul du      2 7 74
Bolzano      12 136
Borchardt      107
Boundary      136 et seq. 156
Brand      126 et seq.
Burnside      89 106
Calculus of variations      iv 171
Cantor, Geschicte etc.      15
Cartesian oval      133
Cauchy      3 7 92
Cavalieri      27
Center of curvature      117 125
Christoffel      107
Complete differential quotient      6
Contact of indefinitely high order      36
Continuation of an analytic function      174
Continuous function      161 162
Convergence      166 167 168 172 178
Cremona      144
Curvature      117
Cusps, appearance of      30
Cylinder, trace of      31
Dantscher, method of      39 62 72
Dantscher, Victor von      v 36 69
Definite form      19
Definite form, conditions for      91
Definite form, necessary condition      21 49 50 51 64 68 82 83 91 109 111 114;
Derivative, existence of a      161 162 166
Descartes      iv 165
Determinant orthogonal      149
Determinant, the sign of the      25 et seq. 28 29 30 32 33 51 52 59 60 83 85 90 91 92 93 97 100 107 111;
Differentiation, one-sided      iv 7 11
Dini      12 136 167
Distinctness as characteristic of an extreme      37 38 47 50
Double curve      54
Double point      101
Double point isolated      29 30 31
Double point with distinct tangents      29
Element of a complete structure      74
Equation of secular variations      107
Euclid      iii 15 135
Euler      16 18 107
Euler, theorem of, for homogeneous functions      84 155
Exceptional cases involving a squared factor      54 58 68 97
Existence of an extreme, proof of      135 146
Extraordinary cases of extremes      iv 19
Extraordinary maxima or minima      1 et 17 19 43 74
Extreme curves      53 54
Extreme, criteria for      4 6 26 92.
Extreme, or extreme value      v 2 53
Failure of general criterion      55
Fallacious conclusions      See Incorrectness of earlier theories
Fermat      iii iv 15 132
Fermat, method of determining maximum and minimum      iii
FORM      See Definite form
FOURIER      iii
Fourier series      74
Fractional powers      178 182
Fuchsian functions      171
Function many-valued      169
Function, one-valued      166
Function, rational      166
Function-element      138 174
Fundamental theorem of algebra      49
Gauss      19
Gauss, principle of      151 et seq.
Genocchi-Peano      1
Geometrical interpretations      6 24 31 46 69 71 97 125
Geometrical mechanics      139
Geometry of numbers      174
Gergonne      19
Goursat      6 28 27 29 31 126 170 177 180
Greatest value      1 48 94.
Hachette      107
hadamard      147 148 160
Hancock      123 166
hankel      74
Harkness      12
hermite      89 106 180
hilbert      170
homogeneous functions      49 155
Homogeneous quadratic forms      82 85 103
Homogeneous quadratic forms expressed as a sum of squares      86 89 91
Homogeneous quadratic forms with subsidiary conditions      114
Hudde      165
Huygens      16
Hypergeometric series      170
Improper maxima and minima      See Maxima and minima
Incorrectness of earlier theories      33 et seq. 52
Indefinite form      19 49 50 51 64 68 82 106 116
Indeterminate coefficients      172
Inflection, point of      6
Integral rational function      168
Isolated point      29 31
jacobi      107
JORDAN      75
Koenigsberger      180
kronecker      106
Kummer      106 107
Lagrange      iii v 4 18 22 26 38 43 77 86 92 99 107 114 127 131 148 172
Laplace      iii 107
Least squares      26
Least value      1 50 94.
Left-hand differential quotient      7 11
legendre      135
Leibnitz      3 15
Limitation expressed through an equation      150
Lipschitz      2 74
Lower limit      63 See
Lueroth      See Dini
Maclaurin      iii 3 4 15 22 77
Maxima and minima (see also Extreme value), one of the most admirable applications of fluxions      iv
Maxima and minima, absolute      2
Maxima and minima, condition for improper extremes      41 42 140
Maxima and minima, condition for proper extremes      40 42
Maxima and minima, conditions for      iv 4 40 99
Maxima and minima, criteria for      4 7—12 et 48 51 55 64 67 68 77 80 81 82 92 100 102 115 116
Maxima and minima, criteria for relative maxima and minima      115
Maxima and minima, erroneous criteria      33
Maxima and minima, extraordinary      (see under Extraordinary etc.)
Maxima and minima, geometrical interpretation of      6
Maxima and minima, improper      2 5 23 26 31 50 59 60 63 75 140 164
Maxima and minima, inaccuracies in      v
Maxima and minima, maximum defined      1
Maxima and minima, minimum      1
Maxima and minima, ordinary      (see under Ordinary etc.)
Maxima and minima, proper      2 5 17 23 26 44 45 60 61 63 74 75
Maxima and minima, relative      2 21 96
Mayer      iv v 2 79
Mechanics, derivation of the ordinary equations of      152
Mechanics, problems in      139 150
Minimal surfaces      123
Minkowski      174
Morley      See Harkness
Neighborhood of, in the      65 173
Newton, discoverer of the calculus      iii
One-sided differential quotient      7 11
Orbits of planets      107
Order of a curve      54
Ordinary maxima and minima      1 et seq. 17
Osculating circle      117
Osgood      167 170
Panton      See Burnside
Pappus      15 164
Pascal, Exercici etc.      11
Pascal, Repertorium etc.      130
Peano      iv v 2 6 21 31 33 34 62 61 68 94
Pendulum      150
Petzval      107
Picard      170 180
Pierpont      3 7 15 34 37 177
Poincare      170 180
Poison      107
Polygon      See Regular polygon
POSITION      135 et seq.
Power-series      171 et seq. 175 179
Proper maxima or minima      See Maxima and minima
Puiseux      180
Quadratic form      19
Quadratic form, application of      92 et seq. See Homogeneous quadratic forms
Quadratic form, expressed as a sum of squares      86 et seq. 89
Radius of curvature      117
realm      135 174
Reflection of a ray of light      126 et seq.
Refraction of a ray of light      131 et seq.
Regiomontanus      16
Region of convergence      167 168
Regular function      73
Regular point      177
Regular polygon      140 142 147
Relative maxima and minima      See Maxima and minima
Reversion of series      153 et seq.
Richelot      106
Right-hand differential quotient      7 11
Roots of unity      180
Salmon      107 120 122
Scheeffer      v 19 27 35 36 39 46 48 50 62 70
Scheeffer's method      37
Scheeffer's theorem      43 46 55 59 60 61 62 70 72
Scheeffer's theory      43 et seq.
Schepp      See Bohlmann ; see also Dini
Secular variations, equation of      107
Semi-axes of a central section      165
Semi-definite case      iv
Semi-definite form      19 49 50 51 52 64 65 68 70 82 83 92 93 106 116
Serret      v 33 104 106 136
Severus      16
Shortest distance to a given surface      v 101 123
Simple point      177
Simpson      16
Singular point      164 177 180 183 184
Sluse, Rene F. W. de      16
Smallest value      1
Smith, Edward      107
Spherical triangle      136
Squared factor      See Exceptional cases
Stolz      v 2 6 11 43 45 46 60 60 70 79 91 100 136 166 164 180 181 187 189
Stolz's added theorem      46 60
Stolzian theorems      39 et seq. 66 68 70 72
Structure of the first kind etc.      175
Sturm's theorem      61 106
Surfaces of second degree      107
Sylvester      89 107
System of m equations, solution of      171 et seq.
Tangent, common to two curves      34 35 36
Tangent, parallel to x-axis      6
Tangential plane      28 31
Tartaglia      16
Taylor's development in series      v 4 5 9 10 19 24 33 75 79 80 97 152 159
Taylor-Lagrange theorem      43 47 77
Todhunter      33
Transcendental curves      36
Transcendental functions      167 169
uniform      See Convergence
Upper and lower limits      2 12 55 57 94 104 136 137
Variations, calculus of      iv 171
Von Dantscher      See Dantscher
Voss      2
Weierstrass      iv 73 79 86 107 138 167 168 169 174 181
Wilson, E. B.      12
Wirtinger      148
Zajaczkowski      106
Zenodorus      142 147
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