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Churchill R.V. — Operational mathematics
Churchill R.V. — Operational mathematics

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Название: Operational mathematics

Автор: Churchill R.V.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1958

Количество страниц: 344

Добавлена в каталог: 31.08.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's Test      219 282
Abel, Niels      102
Abelian property      67
Adjoint      258
Analogue, electrical      87—91 245
Analogue, mechanical      90
Analytic continuation      165 166
Analytic function      150—152
Analytic transforms      169—172
Angular displacements      see "Vibrating shaft"
Antiperiodic function      56
Bar, temperature in      138 139 144 199—222 See
Beam, shear in      92
Beam, static deflection of      91—94
Beam, vibrating      see "Vibrating beam"
Bessel's equation      49—52 223
Bessel's function      50 223 285
Bessel's function, Bessel's zeros of      224
Boundary value problem      112 See "Temperature" "Vibration"
Boundary value problem in differential equations      259—264
Boundary value problem with variable coefficients      116 117 309
Boundary value problem, superposition of solutions of      218
Boundary value problem, verification of solution of      114 201 245 282
Brake band, temperature in      135
Branch cut      164
Branch of function      163—166
Cauchy — Riemann conditions      151
Cauchy's integral formula      156
Cauchy's integral formula, extension of      166—168
Cauchy's integral theorem      156
Cauchy, A.L.      3
Characteristic function (eigenfunction)      265 266
Characteristic number (eigenvalue)      264
Composite solid, temperature in      141—143 145 146
Concentration      129 See
Continuity by subregions      31
Continuity, sectional      5
Convolution for Fourier transforms      296—298 312
Convolution for Laplace transforms      35—41
Convolution for Laplace transforms, generalized      69 70
Convolution, properties of      38 68
Cooling fin      139
Cosine-integral function      98
Cycloid      102
Cylinder, temperature in      222—226
Damping, viscous      72
Deflection in plate      319
Deflection, static, beam      91—94
Deflection, static, of string      260
Difference equation      26—30
Difference-differential equation      30
Differential equations      19 42
Differential equations of first order      48
Differential equations with variable coefficients      48—52 67
Differential equations, boundary value problem in      259—264
Differential equations, existence of solution of      259
Differential equations, initial-value problem in      259
Differential equations, partial      108
Differential equations, self-adjoint      258
Differential equations, system of      20—22 45 74 81—91
Differential form      2 313
Differential form, adjoint of      258
Differential form, self-adjoint      258
Differential form, transformation of      7—10 290 295 311—320
Diffusion in composite solid      145 146
Diffusion in evaporation plate      139 145
Diffusion in semi-infinite body      226—228 231
Diffusion in slab      309
Diffusion, coefficient of      128
Diffusion, equation of      128—130
Diffusivity      129
Dirac delta symbol      27
Dirichlet integral      173
Distributions      28
Duhamel's formula for temperature      212 229—232
Duhamel's formula in vibrations      254 255
Eigenfunction      265
Eigenfunction, orthogonality of      266
Eigenvalue      264
Eigenvalue problem      264
Eigenvalue problem of fourth order      270
Eigenvalue problem, reduced      268 270
Elastic support      254 255 260 284
Electric circuit      73—75 80 87—91
Electric circuit, Kirchhoff's laws of      87
electronics      302
Entire function      152
Equipment, mortality of      104—107
Equipment, replacement of      105—107
Error function      38
Error function, complementary      67
evaporation      139 145 226
Exponential function      27 152
Exponential order      6
Exponential-integral function      97
Factorial function      11
Faltung      see "Convolution"
Fourier constants      267
Fourier integral formula      181 310
Fourier integral formula, generalized      228
Fourier series      206 289 294
Fourier series, generalized      267 276—287
Fourier transform      288
Fourier transform, convolution for      296—298 312
Fourier transform, cosine      310—312 317
Fourier transform, cosine, finite      294—301
Fourier transform, cosine, finite, tables of      300
Fourier transform, exponential      312 317
Fourier transform, generalized      313—320
Fourier transform, sine      310—312 317
Fourier transform, sine, finite      288—309
Fourier transform, sine, finite, tables of      299
Frequency, natural      72
Gamma function      11
Green's function      219 260—263 268
Green's function, transform of      293 320
Hankel transformation      317
heat capacity      129
Heat conduction      128 199 See
Heat equation      129 130
Heat source      136
Heaviside's expansion      58
Hooke's law      71 110
Hyperbolic functions      153
Hyperbolic functions, identities in      154
Image      2
Impulse function      26
Impulse symbol      27 77
Initial-value problem      259 262
Initial-value problem, existence theorem for      259
Integral equation      43 274 286
Integral equation of convolution type      44 101
Integral equation, Abel's      44
Integral transformations      2 313—320 See "Laplace
Integral transformations, successive      304
Integrals, evaluation of      94—100
Integrals, inversion      see "Inversion integral"
Integrals, principal value of      167
Integrals, probability      38
Integrals, properties of      30—35 68 69 155
Integrals, uniform convergence of      32
Integrals, uniform convergence of, Weierstrass test for      33
Integrodifferential equation      46
Inverse transformation, cosine      310
Inverse transformation, cosine, finite      294 295
Inverse transformation, Fourier, exponential      312
Inverse transformation, Fourier, generalized      315
Inverse transformation, Laplace      13 176—183
Inverse transformation, sine      310
Inverse transformation, sine, finite      289
Inversion integral      169
Inversion integral, alteration of      193—197
Inversion integral, derivative of      184—186
Inversion integral, properties of      178—186
Inversion integral, real form of      177
Inversion integral, series representation of      186—193
Laplace transform      3
Laplace transform, analytic      169—171
Laplace transform, convolution for      35—41 69 70
Laplace transform, derivatives of      46—48
Laplace transform, integration of      52 53
Laplace transform, order properties of      172—176
Laplace transformation      3
Laplace transformation of derivatives      7 8
Laplace transformation, inverse of      13 176—183
Laplace transformation, linear substitution in      15 24
Laplace transformation, table of properties of      323
Laplace transformation, translation property of      23 24
Laplace, P.S.      3
Laurent series      158
Leibnitz formula      31
Lerch's theorem      14 184
Longitudinal displacements      see "Vibrating bar"
Mortality of equipment      104—107
Motion of a particle      100—102 106 107
Multiple-valued function      163—166
Natural frequency      72
Norm      266
Orthogonal functions      266
Orthonormal functions      266
Oscillation, stable      63—65 90
Oscillation, unstable      190
Partial differential equation      108 See
Partial fractions      15—18 57—65
Partial fractions for linear factors      57—62
Partial fractions for quadratic factors      62—65
Periodic extension of function, even      295
Periodic extension of function, odd      291
Periodic function      54
Periodic function, rectification of      55—57
Periodic temperature      233
Plate, deflections in      319
Poisson's equation      301 307
Poisson's integral formula      319
Pole      160
Potential      See also "Steady temperature"
Potential in cylindrical region      285
Potential in half plane      318
Potential in semicircle      319
Potential in slot      301—304
Prism, steady temperature in      284 306
Probability integral      38
Products of transforms      see "Convolution"
Propeller shaft      257
Quadrant, steady temperature in      318 319
Reflection principle      166
Replacement of equipment      105—107
Residue      159
Resonance      77—80
Resonance in bar      239—244 250 251 255 269
Resonance in beam      253 256 257
Resonance in shaft      257
Resonance type      190
Riemann — Lebesgue lemma      174
Schwarz integral formula      318
Sectionally continuous      5
Semi-infinite slab, temperature in      234 304 309
Semi-infinite solid, temperature in      130—145 231—233 317 318
Semi-infinite strip, steady temperature in      279—283 302—304 306 307
Separation of variables      270 279
Servomechanism      103 104 106
Shaft      see "Vibrating shaft"
Shear in beam      92
Shear in string      108 109
Shear, modulus $E_{8}$ in      111
Shear, modulus $E_{8}$ in, for steel      257
Sine-integral function      53
Singular point      49 159 160
Slab, temperature in      137 143 215—222 224 225 309
Soil, temperature in      233
Square-wave function      54
Stability      245
Stable oscillation      63—65 90
Staircase function      25
Steady temperature in prism      284 306
Steady temperature in quadrant      318 319
Steady temperature in semi-infinite strip      279—283 302—304 306 307
Steel bar      126 127
Step functions      25—30
String, shear in      108 109
String, static deflection of      260
String, vibrating      see "Vibrating string"
Sturm — Liouville problem      264
Sturm — Liouville problem, reduced form of      268 270
Surface-heat transfer      130 139
Tables of transforms      322
Tables of transforms, Fourier      299 300 313
Tables of transforms, Laplace      17 324—331
Tauberian property      68
Tautochrone      100—102
Taylor's series      157
Telegraph equation      111 244 245
Temperature      128
Temperature functions, product of      233 234
Temperature in bar      138 139 144 199—222
Temperature in brake band      135
Temperature in composite solid      141—143 145 146
Temperature in cooling fin      139
Temperature in cylinder      222—226
Temperature in semi-infinite slab      234 304 303
Temperature in semi-infinite solid      130—145 231—233 317 318
Temperature in slab      137 143 215—222 224 225 309
Temperature in soil      233
Temperature in wall      215—217
Temperature in wire      145
Temperature, Duhamel's formula for      212 229—232
Temperature, periodic      233
Temperature, properties of      206—208
Temperature, steady-state      see "Steady temperature"
torque      111
Transfer function      89
transform      2 See "Laplace "Tables
Translated function      24
Transmission line equations      244 245
Transverse displacements      see "Vibrating beam" "Vibrating
Triangular wave      55
Uniqueness of inverse transform      14 183 289 295
Uniqueness of solution      208 248 259 264
Unit step function      5 6
UNITS      138 224
Unstable oscillation      190
Variables, separation of      270 279
Vibrating bar, equations for      110
Vibrating bar, finite      121—127 235—248 250—256
Vibrating bar, loaded      250
Vibrating bar, nonuniform      285
Vibrating bar, resonance in      239—244 250 251 255 269
Vibrating bar, semi-infinite      115—119
vibrating beam      251—257 308
Vibrating beam, resonance in      253 256 257
Vibrating membrane      255 257
Vibrating shaft      127 243 257
Vibrating shaft with flywheel      250
Vibrating shaft, resonance in      257
Vibrating shaft, torque in      111
Vibrating spring      71—87
Vibrating string, equations for      108 109
Vibrating string, finite      124 241—254 284 307 308
Vibrating string, infinite      128 318
Vibrating string, semi-infinite      111—121
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