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Ablowitz M.J., Fokas A.S. — Complex Variables: Introduction and Applications
Ablowitz M.J., Fokas A.S. — Complex Variables: Introduction and Applications

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Название: Complex Variables: Introduction and Applications

Авторы: Ablowitz M.J., Fokas A.S.

Аннотация:

Part I provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2003

Количество страниц: 660

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $(\bar{\partial})$ 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
1 2 3
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