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| Hildebrand F.B. — Advanced Calculus for Applications |
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| Предметный указатель |
Power series, operations with 122 512
Power series, solutions of differential equations 119
Pressure, fluid 309
Principal normal vector 273
Principal value, of improper integral 558
Principal value, of logarithm 515
Principal value, of power function 518
Proper strip 403
Pulsating cylinder 458
Pulsating sphere, steady-state solution 498 (62)
Pulsating sphere, transient solution 505 (80)
pure imaginary number 509
Quasi-linear equations 357 376 388
Quasi-linear equations, characteristics of 380
Quasi-linear equations, classification of 388
Raabe’s test, for infinite series 120
Radiation, from rod 479 (6)
Radius, of convergence 120 512 530
Radius, of curvature 273
Radius, of torsion 274
Ratio Test 119 511
Rational function 123 511 538 543 546
Real number 509
Real part, of complex quantity 438 509
Rectifying plane 275
Recurrence formula, for Bessel functions 152
Recurrence formula, for Gamma function 79
Recurrence formula, for Legendre functions 162
Recurrence formula, in Frobenius method 131
Reducible curve 287
Reduction of order, of differential equation 29
Reflection, of plane 606 (96)
Reflection, of waves 469
Regular function 122
Regular singular point, of differential equation 128 168
Removable singular point 538
Residue 547
Residue at infinity 594 (60) 595
Residue at pole 548
Resistive force 88 (35) 497
Resonance 70 499
Riccati's equation 50 (48)
Riemann surface 537
Right-handed coordinate system 299
Rod, deformation of 320 (38)
Rodrigues' formula 164 182 232
Rotating shaft 193
Rotating string 189
Rotation, of axes 318 (29) 329 605
Rotation, of fluid 294
Rouche’s Theorem 593 (55)
Runge — Kutta method 102
Saddle point 351
scalar 262
Scalar product 265
Scale factor 299
Schwarz — Christoffel transformation 574
Semiconvergent series 171
Separable differential equation 33 36 433
Separation constant 433
Separation of variables 1 428 430
Series, asymptotic 170
Series, Fourier Fourier — Bessel 226 see
Series, Frobenius 129
Series, geometric 166
Series, hypergeometric 165
Series, power 119
Series, semiconvergent 171
Series, Taylor 94 122 348
Shaft, rotating 193
Shear lines 412
Shearing force 194 320
Simple pole 548
Simple region 284
Simply connected region 284
Simpson’s rule 117 (25) 118 27)
Simultaneous differential equations 19
Sine-integral function 32
Single-valued function 283 521
Singular curve, on integral surface 406
Singular point, of differential equation 127 168
Singular solution 5 34
Singularities, of analytic functions, at infinity 542
Singularities, of analytic functions, branch point 132 516 535 540
Singularities, of analytic functions, essential 540 541
Singularities, of analytic functions, isolated 538
Singularities, of analytic functions, pole 132 538
Singularities, of analytic functions, removable 538
Singularities, of analytic functions, significance of 545
Singularity functions 63
Sink 291
Sliding clamped end support 195
Smooth curve 281
Smooth surface 288
Solution, of differential equation 1
Solution, of differential equation, complementary 7 388
Solution, of differential equation, complete 4
Solution, of differential equation, homogeneous 7
Solution, of differential equation, particular 6 388
Solution, of differential equation, singular 5 34
Sonic velocity 311
Source 291 569
Source function, in heat flow 501 (71) 503
Source, strength of 569
Space curve 271
Specific heat 428
Speed 273
Spherical coordinates 304
Spherical waves 455
| Spring constant 68
Square-wave function 83 (9)
Stability 199
Stagnation point 490 (38) 572
Standard form, of linear ordinary differential equation, first order 4
Standard form, of linear ordinary differential equation, second order 127
Steady state 429
Stirling’s formula 81 90
Stodola — Vianello method 200 214
Stokes’s theorem 295
Straight line, equations of 315 (5)
Stream function 307 480 566
Streaming 572
streamline 306 480 566
Stress function 427
Stretching, of plane 605 (95)
String, deflection of 189
String, rotating 189
String, vibrating 244 (7)
Strip 401
Strip condition 401
Strip, characteristic 404
Strip, proper 403
Sturm — Liouville problem 208 373
Sturm — Liouville problem, proper 209
Substantial derivative 310
Superposition integral 451
Supersonic fluid flow 312 475
Surface area 288 300 370
Surface charge 584 615
Surface integral 287
Surface, conical 384
Surface, cylindrical 383
Surface, equation of 287
Surface, equipotential 286
Surface, normal to 287
Surface, Riemann 537
Table, of Bessel functions of order n + 1/2 77
Table, of Gamma function 619
Table, of Laplace transforms 74
Table, of zeros of Bessel functions 619
Tangent vector 272
Tangential acceleration 274
Taylor series 94 122 348 528
Taylor series with remainder 123 349
Taylor series, uniqueness of 590 (34)
Telegraph equations 427 464
Temperature, steady state, in circular annulus 433
Temperature, steady state, in circular cylinder 487 (30—32) 488
Temperature, steady state, in half-plane 460
Temperature, steady state, in rectangle 430
Temperature, steady state, in rectangular parallelepiped 441 488
Temperature, steady state, in rod 450
Temperature, steady state, in sphere 439
Temperature, steady state, inside circle 436
Temperature, steady state, outside circle 437
Tension 189 320 446
thermal conductivity 428
Thermal diffusivity 429
Torsion 274
Torsion, radius of 274
Torsional stiffness 320 (38)
Total differential 335
Transform, Fourier 240
Transform, Fourier — Bessel 242
Transform, Laplace 51
Transient solution, heat flow 450
Translation properties, of Laplace transforms 59
Translation, of axes 329 (86) 605
Traveling waves 454
Triangular-wave function 83 (10)
Trigonometric functions 512
Triple scalar product 268
Twisting moment 320 (38)
Undetermined coefficients, method of 11 19
Unit doublet function 65
Unit impulse function 64
Unit step function 87 (27)
Unit vector 263
Variation 356
Variation of parameters 25
Vectors 262
Vectors, algebra of 262
Vectors, differentiation of 270 278
Vectors, products of 265
Velocity 273
Velocity deviation potential 311
Velocity potential 305 566
Vianello see "Stodola — Vianello method"
vibrating beam 244 (10)
Vibrating membrane 446
Vibrating string 244 (7)
Vibration 68
Vibration, natural modes of 70
Viscosity, coefficient of 334 (105)
Viscous fluid 334 (105)
Volume, element of 300 346
Vortex 305 570
Vortex, strength of 570
Wave equation 327 (78) 391 427 446 464
Waves 454
Waves, standing 496 (58)
Weber’s function 146
Weighting function 206
Work 281
Wronskian determinant 4 27 29 31 41 179 370
Youno’s modulus 194
Zero vector 263
Zeros, of Bessel functions 154 617
Zeros, of Bessel functions table of 619
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