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| Ablowitz M.J., Fokas A.S. — Complex Variables: Introduction and Applications |
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| Предметный указатель |
Function, doubly periodic 185
Function, elliptic modular 382 396
Function, entire 38 95
Function, error 283
Function, exponential 4 11
Function, exponential integral 494
Function, factorial 276
Function, gamma (r(g)) 276 427
Function, gamma (r(z)) 436
Function, generalized analytic 601
Function, Green's 286
Function, Hankel 457
Function, harmonic 39
Function, Heaviside 471
Function, hyperbolic 12
Function, inverse trigonometric and hyperbolic 53 55
Function, Jacobian elliptic 359
Function, Kronecker delta 203 208
Function, meromorphic 217
Function, multivalued 46
Function, periodic 4
Function, piecewise continuous 72
Function, power 10 52
Function, principal branch 48
Function, range 10
Function, rational 11 150
Function, residue 206
Function, Schwarzian S 389
Function, Schwarzian triangle 190 382 389
Function, sin (sine) 12
Function, square integrable 267
Function, stream 40 324
Function, symmetric 539
Function, trigometric 12
Function, uniformly continuous 23
Function, univalent 319
Function, zeros of 123 259
Fundamental theorem of algebra 96 264
Gaier 410
Gakhov 516
Gamma function  171 276 427 436
Gaussian 279
Gel'fand — Levitan — Marchenko equation 613
Generalized analytic function 601
Geometric interpretation 3 6
Glasser 504
Gohberg 560 605 607
Goursat 83 105
Gradient 34 43
Green 500
Green's function 286 288
Green's theorem 81
Group velocity 295 475
Halphen's (Darbaux — Halphen) system 188—189 190 195
Handelsmac 455
hankel 506
Hankel function 457
Harmonic 39
Harmonic conjugate 39
Harmonic function 39
Harmonic motion 28
Heat equation 303
Heat flow 325
Heat flow, steady state conduction 39
Heaviside function 471
Helmholtz equation 570
Hilbert problem 546
Hilbert transform 255
Hille 174 180
Holder condition 517
Holomorphic 38
homogeneous differential equations 26 180
Hopf 476
Hyperbolae 39 57 366 402
Hyperbolic function 12
Hypergeometric equation 183 305
ideal fluid flow 40 323 329ff
Identities, hyperbolic function 12
Identities, trigonometric 5 12
Image 14
Images on the sphere 17
Imaginary part 3 11
IMT (inverse Monodromy transform) 618
Ince 174 180
Incompressible 40
Indicial equation 182
Individual indices 580
Inequality derivatives 95
Inequality integral 78
Inequality, triangle 6
Infinite products 158ff
Integrable 70
Integral equation 538
Integral equation with Abel 553
Integral equation with displacement kernel 558
Integral equation with logarithmic kernel 556
Integral representation 298 299
Integral, independence of path 73
Integration (complex) 70ff
Integration by parts 423
Interior point 8
Invariance of the cross-ratio 369
Inverse Fourier transform 267
Inverse function 53 55
Inverse hyperbolic function 53 55
Inverse Laplace transform 274
Inverse mapping 317ff
Inverse Monodromy transform (IMT) 618
Inverse points (circle) 372—373 374
Inverse scattering 515 609
Inverse scattering transform 484 565
Inverse tangent function 52
Inverse transformation 57
Inverse trigonometric functions 53 55
Inviscid 40
Irrotational 40 324
Isolated singular point 144
Isolated zero's 123
Isothermal lines 325
IST (inverse scattering transform) 484
Jacobi/Jacobian elliptic function 186 359
Jeffreys 300 500
Jordan arc 71
Jordan contour 72
Jordan curve 71
Jordan's lemma 222
Joukowski profiles 404
Kadomtsev — Petviashvili equation 615
KdV (Kortewg — deVries) 480 613
Kernel 538
Kernel degenerate 539
Kernel displacement 558
Kernel logarithmic 556
Keyhole contour 246
Korteweg — deVries (KdV) equation 480 613
KP (Kadomtsev — Petviashvili) 615
Krein 560 605 607
Kronecker delta function 203 208
Kruskal 494
Kurta condition 551
L R circuit 301
l'Hopital's rule 29 242
Laplace transform and inverse 274 510
Laplace type integrals 422ff 423
Laplace's equation 39
Laplace's formula 431
Laplace's method 430ff 431
Laplacian operator 288
Laurent expansion 206
Laurent series 121 127 196
| Least upper bound (l.u.b.) 117
Legendre's equation 183
Lemulscate 367 402
Level curves 41
Lift 335 337
Lighthill 270
Limit at infinity 21
Limits 20ff
Line integral 72 74
Linear fractional transformation 366
Linear homogeneous differential equations 26 180
Linear integral equation 538
Linearize 192
Liouville 500
Liouville's theorem 95
Lipschitz condition 517
Logarithm 48 49
Logarithmic kernel 556
Lower half plane 224
M mapping: one-to-one 319
Majorants 175
Mapping 14
Mapping, conformal 31
Mapping: inverse 317ff
Marginally stable 14
Matching solution 296
Maximum principles 97
Maximum-modulus theorem 97
Mean value formula 96
Mellin transform 504 510
Meromorphic function 150 217
Mittag — Leffler expansion 165 228
Mittag — Leffler theorem 166 167
MKdV (modified KdV) 480
Modified Bessel function 298
Modified KdV 480 484
Modulus 4 406
Moebius transformation 366
Monodromy problem 618
Monodromy theorem 155
Morera's theorem 95
Movable branch point 180
Mtest 112 139
Multiple solutions 5 27
Multiplication of series 120
Multiply connected 79
Multivalued function 4 46
Multivaluedness 10
Muskhelishvili 516 522 540
N-soliton 615
NACA 550
Natural barrier (boundary) 155 392
Necessary condition 33
Nehari 344 348 359 393 398
Neighborhood 8 15
Neumann problem 40 326
Nonisolated singularity 155
Nonlinear differential equation 174
Nonlinear wave propagation 98
Nonviscous 40
Normal (unit vector) 77
Normalization constants 611
North pole 15 18
o notation 413
One-to-one, mapping 319
Open set 8
Open sets map to open sets 341
Orientation of contour, standard 254
Orthogonality of level curves 39
Osgood — Caratheodory theorem 344
Painleve equation 193 174
Painleve transcendents 187
Painleve type ODE 184
Parallelogram law 6
Parseval formula 272
Parseval formula for Mellin transforms 510
Parseval identity 272
Partial differential equations 37 39 285
Partial indices 580
PDE (partial differential equation) 37
Periodic function 4
periodicity 5
Phase 47
phase diagram 63
phase velocity 475
Picard's theorem 149
Piecewise continuous function 72
Piecewise smooth 268
PIV (Painleve IV equation) 617
Plemelj 516
Plemelj formula 518 540
Poincare — Bertrand transposition formula 577
Point at infinity 15 18
Point at infinity, cluster 151
Point vortex 58
Poisson formula (circle) 104
Poisson formula (half plane) 287
Polar coordinates 3
Polar form 4
Polar representation 14
Polar, exponential 4
Pole 146
Pole at infinity 150
Pole, double 146
Pole, movable 180
Pole, N'th-order 145
Pole, simple 145
Pole, strength of 145
Pole, triple 145
Polygon, curvilinear 382
Polygon, mapping 348ff
Polynomial 10 11 25 30
Polynomial equation 5
Polynomial equation, zeros (roots) of 5 96 264
Potential, complex velocity 40
Potential, electrostatic 326
Power function 10 52
Power series 13 114
Power spectrum 272
Principal branch 49
Principal part 130 164 206
Principal value at infinity 218
Principal value integral 237ff
Principle of the argument 259
Product, infinite 158ff
Projection operators 255
Projection, stereographic 15
Proper factorization 560
Punctured z-plane 37
Radiation condition 571
Radius of convergence 13 117 202
Radon transform 515 564—566
Range of a function 10
Ratio Test 120
Rational function 150
Rays of maximum dominance 493
Real part 3 11
Recessive (part of asymptotic expansion) 492
Recursion relation (differential equation) 183
Reduced wave equation 570
Reflection principle (Schwarz) 346 379
Region, bounded 8
Region, closed 8
Region, compact 23
Regular singular point 182
Removable singularity 144
Residue 130 206
Residue at infinity 211
Residue theorem 206 207
RH (Riemann — Hilbert) 514
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