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

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Предметный указатель

Riccati equation      184
Riemann mapping theorem      344
Riemann surface      65
Riemann surface, infinitely sheeted      66
Riemann surface, n-sheeted      66
Riemann surface, two-sheeted      65
Riemann zeta function      142
Riemann — Hilbert (RH) problem      514
Riemann — Lebesgue lemma      439
RK4 (Runge — Kutta method)      199
Root test      117
Roots of unity      5 410
Rouche's theorem      263
Rudin      268
Runge — Kutta methods      199
Saddle point      449
Savart      550
Scattering theory      98 515 609
Schroedinger equation      411 474 609
Schwarz reflection principle      346 379
Schwarz symmetry principle      346 379
Schwarz — Christoffel theorem (formula)      348
Schwarz-Christoffel transformation      312 346
Schwarzian derivative      190 383
Schwarzian S-function      389
Schwarzian triangle function      190 382 389
Sectionally analytic      520 528
Sector      10
Segur      484 613
Self-dual Yang — Mills equation      161
SEQUENCE      109
Sequence, asymptotic      484
Sequence, Cauchy      137
Series asymptotic power      417
Series expansions      18
Series methods (numerical)      201
Series, Laurent      121 127 146
Series, power      164
Series, Taylor      70 114ff
Sheet (Riemann surface)      65
SHM (simple harmonic motion)      28
Shock condition      479
Shock wave      479
Simple arc      71
Simple closed contour      72
Simple closed curve      71
Simple curve      71
simple harmonic motion      28
Simple pole      145
Simply connected      79
Sin (sine)      12
Sine transform      273 291
Singular integral equations      538ff
Singular point      38 98
Singular point, essential      179
Singular point, fixed      179
Singular point, isolated      145
Singular point, regular      182
Singularity, fixed      179
Singularity, movable      179
Singularity, nonisolated      155
Singularity, removable      144
Sink      60 69
Smooth arc      72
Sommerfeld contour      463
Sommerfeld diffraction problem      570
Sommerfeld radiation condition      294
Source      60 69
South pole      15
SP (singular point)      179
Special ends      535
Sphere      15
Square integrable function      267
Square root      46
Stable      14
Stable marginally      14
Stagnation point      43
Standard orientation of contour      254
Stationary phase method      443ff
Steepest descent method      448ff
Stereographic projection      15 50 62
Stirling's formula      436 495
Stokes lines      493
Stokes phenomenon      418 488
Stream function      40 324
Stream lines      41 324
Strength of a pole      145

Sufficient condition      33
Supremum (sup)      117 202
Symmetric function      539
Tangent (unit vector)      77
Taylor series      30 114ff
Temperature distribution      56
Temperature distribution, steady state      67
Test comparison      120
Test ratio      120
Theodorsen's integral equation      409
thermal conductivity      325
Thin airfoil theory      550
Time independent Schroedinger equation      609
Time-stepping methods      198
Titchmarsh      440
To all orders      430
Tomography      564
Total index      608
Transcendental      14
Transform space      267
Transform, Fourier      267
Transform, Hilbert      255
Transform, Laplace      274
Transform, Mallin      504
Transformation      14
Transformation, bilinear      328 366
Transformation, conformal      314
Transformation, critical point      317
Transformation, inverse Monodromy      618
Transformation, inverse scattering      484
Transformation, Laplace      274
Transformation, linear fractional      366
Transformation, Mellin      504
Transformation, Moebius      366
Transformation, Radon      515 564
Transformation, Schwarz — Christoffel      312 346
Triangle inequality      6
Triangular region      315 319
Trigonometric functions      12
Trigonometric identifies      5
Trilateral      405
Turning point      501
Turning solution (function)      296 504
Two-keyhole contour      257
Unbounded region      15
Uniform convergence      222
Uniform flow      41
Uniformly continuous      23
Uniqueness of analytic inverse      320 342
Uniqueness of Laurent series      132
Uniqueness of Taylor series      118
Univalent      319
Unstable system      14
Upper half plane      14 224
Values at infinity      15
Vector      3
Vector gradients      34
Vekua      583 601
Velocity field      41
Velocity potential      40
Velocity, fluid      40 324
Vibrations of beams      28
Volterra integral equation      538
Vortex, point      60
Watson      389 393
Watson's Lemma 426ff      427
Watson's Lemma in the complex plane      490
Wave      98
Wave equation      293
Wave nonlinear propagation      98
Wedge product      598
Wegmann      410
Weierstrass      149
Weierstrass elliptic function      185
Weierstrass Factor Theorem      169 228
Weierstrass M test      112 139
Whitham      476 477
Whittaker      389 393
Wiener — Hopf method      516 570
Winding number      213 260
WKB (Wentzel — Kramner — Brillouin)      500
wronskian      189
Z plane      4 11
z plane, punctured      37
Zero friction      40
Zeroes of a function      123 259
Zeta function      142

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