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| Sokolnikoff I.S. — Higher Mathematics for Engineers and Physicists |
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| Предметный указатель |
 48—51 54
 250
 48—55
 336
 337
 46
Absolute convergence of series 16 17 20 21
Absolute value of complex number 441
Addition of series 21
Addition of vectors 393
Addition, parallelogram law of 394
Adiabatic process 224
Aerodynamics 133 431
Algebra, fundamental theorem of 92
Algebraic theorems 92—94
Alternating series 15
am u 51
Ampere's formula 52
Amplitude function 51
Amplitude of complex number 441
Analysis, harmonic 545
Analytic functions 451—491
Angle as a line integral 195
Angle of lap 240
Angle of twist 485
Angle, direction 146 398
Angle, solid 195
Angular velocity 61 191 236 404 424
Applications of conformal representation 479—491
Applications of line integrals 217—224
Applications of scalar and vector products 404—406
Approximate formula for n! 509
Approximate formula for probability of most probable number 511
Approximate formula in applied mathematics 55
Approximation, Laplace's or normal 515
Approximations to binomial law 512
Arc length 143
Arc length of ellipse 475
Arc length of sinusoid 55
Area 172
Area as a double integral 178
Area as a line integral 199—202
Area, element of 183 184 190 437
Area, positive and negative 200
Area, surface 188—196
Argument of complex number 441
Associative law for series 18
Associative law for vectors 394
Asymptotic formula for n! 509
Asymptotic series 524
Atmosphere, thickness of 61
Attraction of cone 196
Attraction of cylinder 196
Attraction of sphere 196 232
Attraction, law of 218 232
Attraction, motion under 58 218
Augmented matrix 118
Auxiliary equation 292
Averages, method of 534
Axes, right- or left-handed 397
Base vectors 396
Beam 240—242 307
Belt on pulley, slipping of 239
Bending moment 241
Bernoulli — Euler law 241 397
Bernoulli's equation 286
Bessel functions 273 336 381
Bessel functions, expansion in 339
Bessel's equation 332 380
beta function 276
Binomial law 502
Binomial law, approximations to 512
Binomial series 40
Biot and Savart, law of 52
boundary conditions 242 351 363 370
Buckling 299
Cable, flexible 244
Cable, flow of electricity in 386
Cable, supporting horizontal roadway 242
Cartography 479
Catenary 247 252
Cauchy — Riemann equations 221 450 455
Cauchy's equation 2
Cauchy's integral formula 461
Cauchy's integral test 12
Cauchy's integral theorem 455
Center of gravity 177 182 183 187 190 191 196 522
Change of variables in derivatives 154
Change of variables in integrals 183—188
Characteristic equation 292
Charge, distribution of 487
Charts, distribution 506
Chemical reaction 258
Circular functions 247
Circulation of a liquid 475 477
Circulation of a vector 418 419
Closed curve, area of 199—201
Closed curve, direction around 200
Closed curve, integral around 201 203 206 216 421
Closed curve, simple 200
cn u 51
Coefficients, Fourier 65
Coefficients, metric 437
Cofactor 111 112
Combinatory analysis, fundamental principle of 493
Commutative law 394 399 400
Comparison test for series 9
Complementary function 290 292
Complete elliptic integrals 48
Complex number 440
Complex number, absolute value of 441
Complex number, argument of 441
Complex number, conjugate of 444 488
Complex number, vector representation of 440
Complex roots of unity 87
Complex variable 440—491
Complex variable, functions of 444—491
Complex variable, functions of, analytic 451—491
Complex variable, functions of, derivative of 449
Complex variable, functions of, integration of 453
Complex variable, functions of, line integral of 454
Complex variable, functions of, Taylor's expansion for 464
Components of force 217
Composite function 134 137
Condenser 283 299 305 308 387
Conditionally convergent series 16 17 21
Conditions for exact differential 212 216
Conditions, Cauchy — Riemann 221 450 455
Conditions, Dirichlet 65
Conductivity 367 426
Conductor 486 489
Conformal mapping 465 471
Conformal representation, applications of 479—491
Conformal transformation 467
Conjugate functions 468 470
Conjugate of a complex number 444 488
Conservation of matter, law of 429
Conservative field of force 219 411
Consistent systems of equations 117—122
Continuity of functions 23 28 124 448
Continuity, equations of 221 429 481
Contour line 144
Convergence of series 4 7
Convergence of series, tests for 9 11 12 15 20 27 31 33
Convergence, absolute 16 17 20 21 33
Convergence, conditional 16 17 21
Convergence, interval of 31 33
Convergence, radius of 31 33
Convergence, uniform 23—30 33
Cooling, law of 254
| Coordinate lines 434
Coordinate surfaces 434
Coordinates, curvilinear 433—439
Coordinates, cylindrical 152 185 190 191 378 386 434 438
Coordinates, ellipsoidal 433
Coordinates, parabolic 439
Coordinates, polar 183 184 276 279 386 438
Coordinates, spherical 152 185 382 386 434 439
cos x 46 250
cosh 247
Cosine series 73
Cosine, hyperbolic 247
Cosine, power series for 38 40
Cosines, direction 146 147 151 188 194 398
coth 249
Cramer's rule 113
Cross product 400
Cubic equation, algebraic solution of 86
Cubic equation, graphical solution of 83
Curl 418 422 423 438
Current 386 427
Curve fitting 525—560
Curve, distribution 504 516
Curve, elastic 240 307
Curve, map of 466
Curves, integral 226 228 279
Curves, orthogonal 277 468
Curvilinear coordinates 433—439
Cylinder functions see “Bessel functions”
Cylindrical coordinates 152 185 190 191 378 386 434 438
Dam, gravity 483
Damping, viscous 302
De Moivre's theorem 90 442
Dead-beat motion 304
Decomposition of vectors 396
Definite integrals 172
Definite integrals, change of variable in 183—188
Definite integrals, evaluation of 172
Definite integrals, mean-value theorem for 210
Deflection 299
Degree of differential equation 225
Del,  see “Nabla”
Delta amplitude, dn 51
Dependence, functional 2
Dependence, linear 116
Dependent events 495
Derivation of differential equations 231—247
Derivative 125
Derivative of functions of a complex variable 449 452 463
Derivative of hyperbolic functions 255
Derivative of series 29 33
Derivative, directional 143 151 219
Derivative, normal 144 146 152
Derivative, partial 125—143 153
Derivative, total 130—143
Descartes's rule of signs 94
Determinants 102—114
Determinants of matrix 115
Determinants, cofactors of 111
Determinants, expansion of 10
Determinants, functional or Jacobian 183
Determinants, laplace development of 111
Determinants, minors of 110
Determinants, product of 110
Determinants, properties of 107—112
Determinants, solution of equations by 102—114
Determinants, Wronskian 317
Deviation, standard 523
Diagonal term of determinant 107
Diagram, pv 223
Differences 527
Differentia equations of electric circuits 301 305 386
Differentia equations of heat conduction 367
Differentia equations of membrane 377
Differentia equations of vibrating spring 308
Differentia equations of vibrating string 361
Differentia equations with constant coefficients 287—315 357
Differentia equations with variable coefficients 284 315—349
Differentia equations, general solution of 230 290 292 350 358
Differentia equations, homogeneous 259 261
Differentia equations, homogeneous linear 290
Differentia equations, integral curve of 226 228
Differentia equations, integrating factor of 265
Differentia equations, Laplace's 369 382 385 386 439 451 470 481
Differentia equations, Legendre's 342 384
Differentia equations, linear 226 283—349 357
Differentia equations, numerical solution of 346
Differentia equations, order of 225
Differentia equations, ordinary 225—349
Differentia equations, partial 225 350—391
Differentia equations, particular integral of 290 292 297 318 359
Differentia equations, particular solution of 230
Differentia equations, second order 269 295
Differentia equations, separation of variables in 257
Differentia equations, simultaneous 312—315
Differentia equations, singular solution of 279
Differentia equations, solution in series 228 325 349 364
Differentia equations, solution of 226
Differential equations 225—391
Differential equations, Bernoulli's 286
Differential equations, Bessel's 332 380
Differential equations, Cauchy — Riemann 221 450 455
Differential equations, Cauchy's 32
Differential equations, definition of 225
Differential equations, degree of 225
Differential equations, derivation of 231—247
Differential equations, Euler's 322 430
Differential equations, exact 262
Differential equations, first order 256 267
Differential equations, Fourier 425
Differential expression 225
Differential of area 184 190
Differential of volume 185 187 190
Differential operators 287—299 357 406
Differential, exact 211 212 216 222 224 262 411 418 420
Differential, partial 128—143
Differential, total 127—143
Differentiation of implicit functions 132—142
Differentiation of series 29 33 34 80
Differentiation under integral sign 167
Differentiation, partial 123—171
Differentiation, term by term 33 34 80
Diffusion 369 427
Diffusivity 36
Direction angles 146 398
Direction components 146
Direction cosines 146 147 151 188 194 398
Direction ratios 150 151
Directional derivative 143 151 219;
Dirichlet conditions 65
Discharge of condenser 299
Discontinuity, finite 64
Discriminant of cubic 89
Distance, element of 435
Distribution charts 506
Distribution curve 504 516
Distribution of charge 487
Distributive law 399 400
Divergence of a vector 411 423 438
Divergence of series 5 8 20
Divergence theorem 191 415 425 428
dn u 51
Dot product 399
Double integrals 173 192 202 275
Drying of porous solids 369
Dynamics, laws of 231
e 42
Effects, superposition of 129 223
Elastic curve 240 307
Elasticity 241 422 484—486
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