Lovitt W.V. — Linear integral equations :: Электронная библиотека попечительского совета мехмата МГУ

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Lovitt W.V. — Linear integral equations

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Название: Linear integral equations

Автор: Lovitt W.V.

Аннотация:

In the present volume I have tried to present in a readable and systematic manner the general theory of linear integral equations with some of its applications. The applications given are to differential equations, calculus of variations, and some problems in mathematical physics. The applications to mathematical physics herein given are to Neumann's problem, Dirichlet's problem, and certain vibration problems which lead to differential equations with boundary conditions. The attempt has been made to present the subject matter in such a way as to make the volume available as a text on this subject in Colleges and Universities.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1950

Количество страниц: 279

Добавлена в каталог: 20.11.2012

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Предметный указатель

Abel's problem      2
Associated equation      70
Associated equation, fundamental functions of      60
Associated equation, homogeneous      56
Associated kernel, determinant for      57
Associated kernel, minors for      58
Associated kernel, the function H(x,y) for      61
Baltzer      30 31
Bar, flow of heat in      229
Bessel's inequality      149 160
Bessel's inequality, function      217
Bilinear formula      141 144 152
Bocher      2 20 69 207
Calculus of variations      192
Cauchy      5
Characteristic constants      7 56 60 183 185 186 202 211 212 235 244 247
Characteristic constants, reality of      129
Conjugate point      208
Cramer      25 69
Curve, smooth      85
Derivative, directional      87
Dirichlet's problem      100 196 205
Dirichlet's problem, solution of      105
Elastic string, free vibrations of      73
Elastic string, free vibrations of, constrained vibrations of      81
Elastic string, free vibrations of, differential equation of      73
Elastic string, free vibrations of, reduction to one-dimensional boundary problem      74
Elastic string, free vibrations of, solution of boundary problem      74
Equations, completeness proof of solutions of      54
Equations, differential, relation with integral equation      4
Equations, homogeneous, solution of when $D(\lambda)=0$ , $D^{'}(\lambda)\neq 0$       42 43 45
Equations, integral      see "Integral equation"
Equations, q independent solutions of      52 55
Equations, solution when $D(\lambda)=0$       46
Equations, system of linear, replacing integral equation      23
Euler's differential equation      193
Euler's rule for isoperimetric problems      195
Fourier series      212 245
Frechet      22 46
Fredholm      7 100
Fredholm, determinant      25 38
Fredholm, determinant, convergence proof      32
Fredholm, equation      9 69
Fredholm, equation, Volterra's solution Of      19
Fredholm, first fundamental relation      27 34
Fredholm, first fundamental theorem      41
Fredholm, first minor      26 38
Fredholm, first minor, convergence proof      33
Fredholm, generalization of      47 49
Fredholm, minors for the associated kernel      58
Fredholm, second fundamental relation      28 34
Fredholm, second fundamental relation, generalization of      47 49
Fredholm, second fundamental theorem      55
Fredholm, theory, application of      73
Fredholm, third fundamental theorem      66
Functions, iterated      17
Functions, reciprocal      17 19
Fundamental functions      7 56 247
Fundamental functions of the associated equation      60
Fundamental functions, normalized      132 136 137 138 141 183 212 235 237 244
Fundamental numbers      7
Green's formula      172 217
Green's formula, function      76 174 176 187 191 201 211 218 228 234 237 241 245
Green's formula, function, physical interpretation of      247
Green's formula, theorem      86 241
Hadamard's Theorem      28 31 32
Harmonic functions      85
Heywood — Frechet      22 46
hilbert      7 116 189 191 196 204 240
Hilbert's fundamental theorem      176

Hilbert's fundamental theorem, third fundamental theorem      180 187 191 199
Homogeneous integral equation      3
Homogeneous integral equation, associated      56
Homogeneous integral equation, completeness proof of solutions of      54
Homogeneous integral equation, q independent solutions of      52 55
Homogeneous integral equation, solution when $D(\lambda)=0$       46
Homogeneous integral equation, solution when $D(\lambda)=0$ , $D^{'}(\lambda)\neq 0$       42 43 45
Horn      96 98
INDEX      212 244
Index of $\lambda_{0}$       52 131
Integral equation with a parameter      3
Integral equation, homogeneous      3
Integral equation, linear, first kind      1
Integral equation, more than one variable      6
Integral equation, non-homogeneous, when $D(\lambda)=0$       62
Integral equation, non-linear      5
Integral equation, Schmidt's solution      162 166
Integral equation, second kind      3
Integral equation, second kind, Volterra      3 5
Integral equation, singular      6
Integral equation, third kind      4
Iterated functions      17
Jacobi's condition      207
Kernel      1
Kernel, closed      187
Kernel, expansion of      141
kernel, symmetric      117 127 131 137 145 234
Kernel, symmetric, characteristic constants of      129
Kernel, symmetric, iterations of      123
Kernel, symmetrizable      190
Kneser      118 121 141 142 192 215 222 245 247 248
Kowalewski      117 155
Lalesco      5 189
Liouville      7
Marty      189 190
Minors, for the associated kernels      58
Minors, Fredholm first      26 38
Minors, p-th minors      46
Multiplicity of $\lambda_{0}$       51 131
Neumann      7
Neumann's problem      110
Neumann's problem, solution of      114
Orthogonality theorem      61 128
Pierpont      44
Potential, logarithmic, of a double layer      92
Potential, logarithmic, of a simple layer      107
Reciprocal functions      17
Ring, flow of heat in      243
Rope, rotating      222
Schmidt      7 116 162
Schmidt, auxiliary theorem of      155
Schwarz's inequality      125 159
Schwarz's inequality, application of      126
Solutions of homogeneous equation      42
Solutions, discontinuous      20
Solutions, Fredholm's solution when $D^{'}(\lambda)\neq 0$       39
Solutions, types of      7
Solutions, uniqueness of      16
String, elastic, constrained vibrations of      81
String, free vibrations of      73
String, vibrating      138 209
Sturm's oscillation theorem      207
Successive approximations      15
Successive substitutions      9
Vibrations, of a rope      215
Vibrations, of a string      209
Volterra      3 7
Volterra, equation      13
Volterra, solution of Fredholm's equation      19
Weber      209 229

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