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Bliss G.A. — Calculus of Variations
Bliss G.A. — Calculus of Variations



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Название: Calculus of Variations

Автор: Bliss G.A.

Аннотация:

This book is the first of a series of monographs on mathematical subjects which are to be published under the auspices of the Mathematical Association of America and whose publication has been made possible by a very generous gift to the Association by Mrs. Mary Hegelek Carus as trustee for the Edward C. Hegeler Trust Fund. The purpose of the monographs is to make the esse features of various mathematical theories accessible and attractive to as many persons as possible who have an interest in mathematics but who may not be specialists in the particular theory presented, a purpose which Mrs. Carus has very appropriately described to be " the diffusion of mathematical and formal thought as contributory to exact knowledge and clear thinking, not only for mathematicians and teachers of mathematics but also for other scientists and the public at large".


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1925

Количество страниц: 189

Добавлена в каталог: 16.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abbatt      181
Barnett      80 182
Barrow      1
Bernoulli, James      10 54 175 181
Bernoulli, John      10 42 54 181 182
BLISS      183
Bolza      9
Borda      78 182
Brachistochrone problem      9 41—84 182
Brachistochrone problem, auxiliary formulas      62
Brachistochrone problem, construction of a field      55—62
Brachistochrone problem, descriptive summary of results      42—43
Brachistochrone problem, extremals are cycloids      50—54
Brachistochrone problem, first necessary condition      47
Brachistochrone problem, from a curve to a point      78
Brachistochrone problem, from a point to a curve      70
Brachistochrone problem, initial velocity zero      68
Brachistochrone problem, integral to be minimized      45
Brachistochrone problem, sufficient conditions for a minimum      66
Brachistochrone problem, the invariant integral      65
Byerly      181
Catenaries      85 89
Catenaries, envelope of the family      86 97
Catenaries, family through a point      92 95
Catenaries, through two points      96
Cauchy      3
Cavalieri      1
Clebsch      179
Conjugate points for catenaries      86 94 103
Conjugate points, in general      131 148 165
Corner conditions for brachistochrones      50
Corner conditions, for catenaries      92
Corner conditions, in general      143
Cycloids      42 52
Cycloids, through two points      55
Darboux      87 178 182
Descartes      1
Dienger      181
Dirksen      181
Du Bois Reymond      183
Envelope theorems for brachistochrones      72
Envelope theorems for shortest distances      32
Envelope theorems, for catenaries      87 102 124
Envelope theorems, for more general cases      131 140 168
Envelope theorems, references      183
Erdmann’s comer condition      143 183
Euler      48 175—76 181 182
Euler, his equation      48 130
Extremals for shortest distances      22
Extremals, for minimum surfaces of revolution      89
Extremals, for more general cases      131 145
Extremals, for the brachistochrone problem      50
Fermat      1
Fields of extremals for shortest-distance problems      27 33
Fields of extremals, for minimum surfaces of revolution      104 112 124
Fields of extremals, for more general cases      100 132 151 154 172
Fields of extremals, for the brachistochrone problem      57 76
Fields of extremals, properties of field functions      60 106 152 156
Focal points      79 124 169
Focal points, geometric constructions      79 125
Fundamental auxiliary, formulas for shortest-distance problems      23
Fundamental auxiliary, formulas, for more general cases      98 136
Fundamental auxiliary, formulas, for the brachistochrone problem      62
Fundamental lemma      20 182
Galileo      13 42 174 182
General theory      128—179
General theory, analytic proof of Jacobi’s condition      161
General theory, construction of a field      154—157
General theory, descriptive summary of results      130—136
General theory, formulation of the problem      128
General theory, fundamental auxiliary formulas      98 136
General theory, fundamental lemma      20 182
General theory, historical re-remarks      174
General theory, necessary conditions for a minimum      47 130 136 138 140 143
General theory, regular problems      154 160—161
General theory, sufficient conditions for a minimum      133 157—159
General theory, the envelope theorem      131
General theory, the extremals      145
General theory, when both end-points are variable      172
General theory, when one end-point is variable      166
Goldschmidt      88
Goldschmidt, his discontinuous solution      111 116 182
Goursat      180 181
Goursat — Hedrick      183
hadamard      178 180 181
Hahn      180
Hancock      181
Hilbert’s differentiability condition      144 178 183
Hilbert’s invariant integral for shortest-distance problems      25
Hilbert’s invariant integral, for minimum surfaces of revolution      108
Hilbert’s invariant integral, for more general problems      100 141 178 183
Hilbert’s invariant integral, for the brachistochrone problem      64
Historical remarks      174
Huygens      53
Isoperimetric problems      15
jacobi      41 87 177 181 182
Jacobi, his necessary condition for shortest-distance problems      32
Jacobi, his necessary condition, an analytic proof      161
Jacobi, his necessary condition, for minimum surfaces of revolution      87 102 124
Jacobi, his necessary condition, for more general cases      132 140 169
Jacobi, his necessary condition, for the brachistochrone problem      74
Jellett      181
Kneser      87 178 180 181 182
Lagrange      78 174 181 182
Lecat      179 180
legendre      131 176 181
Legendre, his necessary condition      138
Leibniz      2 3
Light paths      14
Lindeloef      181 183
Lindeloef, his conjugate point construction      94 102 183
l’Hospital      11
Maclaurin      5
MacNeish      89 118 182 183
Maxima and minima      3
Maxima and minima, criteria      4
Mayer      179
Moigno — Lindeloef      181
Moore, E.H.      182
Necessary conditions for a minimum for shortest-distance problems      18 33
Necessary conditions for a minimum, for brachistochrone problems      50—51
Necessary conditions for a minimum, for minimum surfaces of revolution      92 103 124
Necessary conditions for a minimum, for more general cases      48 130—131 136 143—145 161 166 173
Newton      2 3 174
Newton, his resistance problem      8 182
notes      182
Ohm      181
Osgood      183
Ostwald’s Klassiker      182
Pascal, B.      1
Pascal, E.      181
references      180
Relative minima      134
Relative minima, sufficient conditions      154
Riemann      3
Roberval      1
Schwarz      43
Shortest distances      17—40
Shortest distances, between two curves      38
Shortest distances, between two points      17—30
Shortest distances, extremals are straight lines      21
Shortest distances, from a point to a curve      30
Shortest distances, from a point to an ellipse      34
Shortest distances, sufficiency proofs      21 27 33—34
Sinclair      80 89 121 126 182 183
Soap films      7 119 126
Stegmann      181
Strauch      181
Sufficiency theorems for shortest-distance problems      21 27 33
Sufficiency theorems, for brachistochrone problems      66 75
Sufficiency theorems, for minimum surfaces of revolution      108 112 124
Sufficiency theorems, for more general cases      133 151 154 169
Surfaces of revolution of minimum area      7 85—127
Surfaces of revolution of minimum area, continuity of the extremal integral      113
Surfaces of revolution of minimum area, descriptive summary of results      85—89
Surfaces of revolution of minimum area, generated by straight lines      110
Surfaces of revolution of minimum area, necessary conditions for a minimum      89 102 124
Surfaces of revolution of minimum area, sufficient conditions for a minimum      109 124
Surfaces of revolution of minimum area, the absolute minimum      115
Surfaces of revolution of minimum area, with one end-point variable      122—126
Todhunter      180 181
Tonelli      179 181
Transversality conditions for shortest distances      32
Transversality conditions, for minimum surfaces of revolution      123
Transversality conditions, for more general cases      167
Transversality conditions, for the brachistochrone problem      72
Wallis      1
Weierstrass      3 132 177 183
Weierstrass, his comer condition      143 183
Weierstrass, his necessary condition      131 138
Weierstrass, his sufficiency proofs      27 66 88 108 124
Woodhouse      181
Zermelo      87 178 189 182
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