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| Churchill R.V. — Operational mathematics |
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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  in 111
Shear, modulus 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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