Ablowitz M.J., Fokas A.S. — Complex Variables: Introduction and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

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 $(\Gamma(z))$       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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