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| Ablowitz M.J., Fokas A.S. — Complex Variables: Introduction and Applications |
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| Предметный указатель |
Abel equation 553
Absolute value 4
Accessory parameters 386
Airfoil 404 550
Airy's equation 296
Airy's function 297
Algebraic equation 14 27
Analytic 24
Analytic continuation 123 152
Analytic function 24 37 38
Analytic in a region 37
Analytic, zero's of 123
Annulus 8 79
Antiderivative 76 84
Antistokes lines 492
ARC 71 313
Arc, Jordan 71
Arc, simple 71
Arc, smooth 72
Argument 4
Argument principle 259
Associative law 6
Asymptotic behavior 423
Asymptotic expansion 414
Asymptotic power series 417
Asymptotic power series, sequence 414
Asymptotic power series, zero's of 123
Automorphic function 190 395
Barrier 43
Barrier, circular 43
Bernoulli equation 331
Berry 494
Bessel function 136 216 283
Bessel's equation 183
Bibliography 445
Bilinear transformation 328 366
Binomial coefficients 25
Biot 550
Bleistein 455
BMO (bounded mean oscillations) 268
Boundary 8
boundary conditions 38 326
Boundary point 8
Boundary value problems 326
Boundary, correspondence points 408
Boundary, jump discontinuity 152
Boundary, natural 155
Bounded mean oscillations 268
Bounded region 8
Branch 47
Branch, cut 47
Branch, movable point 180
Branch, point 46
Branch, principal 48
Bromwich contour 274
Burgers equation 476
Camper line 550
Canonical factorization 560
Capacitance 407
Carleman 516 555
Cassinians 402
Cauchy (Type) Integrals 517ff
Cauchy integral formula 91
Cauchy Principal Value at Infinity 218
Cauchy Principal Value Integrals 237ff
Cauchy residue theorem 207
Cauchy sequence 137
Cauchy — Euler type equation 192
Cauchy — Goursat theorem 70 105
Cauchy — Riemann conditions 33 34
Cauchy — Riemann conditions in polar form 34
Cauchy's theorem 70
Cavitation 337
Chain rule 57 73 98
Chazy 188
Chazy's equation 188
Circular barrier 43
Circulation 77 81 324
Clarkson 610 611
Closed contour 72
Closed contour, simple 72
Closed region 8
Cluster point 151
Cole 476
Commutative law 6
Compact 9
Compact region 23
Compactified 16
Comparison Test 120
Complementary domains (circle) 372
Complementary error function 293
COMPLEX 3
Complex conjugate 5 22
Complex conjugate pairs 27
Complex electrostatic potential 326
Complex electrostatic potential, velocity potential 40
Complex imaginary part 1
Complex integration 70ff
Complex logarithm 49
Complex logorithm 48
Complex logorithm, exponential 11
Complex number 1
Complex number exponential form 4
Complex number, properties 5 6
Complex number, real part 1
Complex plane 3
Complex plane compactified (closed) 16
Complex plane extended 15 16
Complex temperature 325
Computerized tomography (CT) 564
Conduction 39
Conduction, steady state heat 39
Conductivity 325
Conformal mapping 57 311ff
Conformal transformation 312 314
Conjugate (complex) 5 22
Conjugate mapping 15
Conjugate, harmonic 39
Connected 9
Connected at infinity 22
Connection functions 504
continuous 22
Continuous everywhere 24
Continuous function 22 72
Continuous in a region 23
contour 72
Contour Bromwich 274
Contour deformed 86 87
Contour dogbone 257
Contour integral 72
Contour integral, Jordan 72
Contour integral, keyhole 246
Contour integral, two-keyhole 257
Convergence 217 222
Convergence, absolute 159
Convergence, radius of 117
Convergence, uniform 110 222
Convolution product - Fourier 271
Convolution product - Laplace 277—278
coordinates 3
Coordinates, polar 3
Cos (cosine) 12
Cosine transform 273
Critical point 317 449
Cross ratio 369
Crosscut 76 85
CT 564 see
Curl 40
Curve 71
Curve, Jordan 71
| Curve, simple 71
Curve, simple closed 71
Curvilinear polygon 382
Cylinder 42
Damped and stable 14
Darboux 184 188 190 195
Darboux — Halphen system 188—189 190 195
DBAR  problem 516 598
Debye 455 464
Deformation of contours 213
Deformed contour 86 87
Degenerate kernel 539
Delta function 270
Derivative, definition 23
Derivative, Schwarzian 190 194 383
dielectric constant 325
Difference equation 277
Difference quotient 24
Differentiable 23 24
Differentiable function 34
Differentiable, nowhere 24
Differential equations 174ff
Diffusion equation 288
Dingle 494
Dirac delta function 270
Dirichlet problem 40 326 546
dispersion relation 295 475
Dispersive 476
Dispersive solution 475
Displacement kernal 558
Distributive law 6
Divergence 40
Divergence theorem 82
Dogbone contour 257
Domain 9
Domain multiply connected 79
Domain of definition of a function 10
Dominant (part of an asymptotic expansion) 492
Doublet 45 69
Doubly periodic function 185
Doughnut 79
Dual space 267
Eigenfunction 539
Eigenvalues 539
Electrodes 407
Electrostatics 39 325
Elliptic function 185 186 359
Elliptic integral 358
Elliptic modular function 382 396
Entire function 38 95 149 185
Equation, Abel 553
Equation, Airy's 296
Equation, Bernoulli 331
Equation, Bessel's 183 192
Equation, Cauchy — Euler type 192
Equation, Chazy 188
Equation, Darboux — Halphen 188—189 190 195
Equation, diffusion 288
Equation, Fredholm 484
Equation, Fredholm integral 538
Equation, Gel'fand — Levitan — Marchenko 613
Equation, heat 303
Equation, Helmholtz 570
Equation, hypergeometric 189 305
Equation, indicial 182
Equation, integral 538
Equation, Kadomtsev — Petviashvili 615
Equation, Korteweg — deVries (KdV) 480
Equation, Laplace's 39
Equation, Legendre's 183 192
Equation, linear homogeneous differential 26 180
Equation, linear integral 538
Equation, modified KdV 480 484
Equation, Painleve 174 184 617
Equation, polynomial 5
Equation, reduced wave 570
Equation, Riccati 184
Equation, Schroedinger 411 474 609
Equation, self-dual Yang — Mills 566
Equation, Theodorsen's integral 409
Equation, Volterra integral 538
Equation, wave 293
Equilibrium states 14
Equipotential lines 326
Erdelyi 417 443
Erf (error function) 283
Error function 283
Essential singular point 148 149
Essential singularity 149
Euclidean geometry 18
Euler constant 420
Euler formula 18
Euler method 198
Euler notation 3
Euler numbers 125
Expansion, asymptotic 414
Expansion, Laurent 206
Expansion, Mittag — Leffler 165
Expansion, Taylor (series) 114ff
Expansion, Weierstrass expansion 169
Exponential function 4 11
Exponential function, order 274
Exponential integral 494
Exponential integral, polar 4
Extended complex plane 15
Factorial function 276
Factorization, canonical 560
Factorization, problem 560
Factorization, proper 560
FFT (fast Fourier transform) 197
Field, flow and velocity 41
Flow field, uniform 41
Fluid ideal flow 39 40 323
Flux 77
Flux lines 326
Forcing 293
Fornberg 410
Four dimensions 14
Fourier coefficients 269
Fourier sine transform 291
Fourier transform 267
Fourier transform, cosine 273
Fourier transform, discrete 197
Fourier transform, fast (FFT) 197
Fourier transform, inverse 267
Fourier transform, pair 267
Fourier transform, sine 273
Fourier type integrals 439ff
Fredholm equation 484
Fredholm integral equation 538
Friction zero 40
Frobenius 182
Fuchs 182 184
Function 10
Function of exponential order 274
Function, absolutely integrable 268
Function, Airy 297
Function, analytic 24 37 38
Function, automorphic 190 395
Function, Bessel 136 216 283
Function, branch of 47
Function, complementary error 293
Function, complex logarithm 49
Function, continuous 22 72
Function, continuous in a region 23
Function, cos (cosine) 12
Function, differentiable 34
Function, differentiable nowhere 24
Function, Dirac delta 270
Function, domain 10
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