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Henrici P. — Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.
Henrici P. — Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.

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Название: Applied and Computational Complex Analysis. I: Power Series, Integration, Conformal Mapping, Location of Zeros.

Автор: Henrici P.

Аннотация:

This volume, after laying the necessary foundations in the theory of power series and complex integration, discusses applications and basic theory (without the Riemann mapping theorem) of conformal mapping and the solution of algebraic and transcendental equations.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 350

Добавлена в каталог: 06.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's limit theorem      82 145 565
Abel's limit theorem, applications of      83
Absolute value      5
Accumulation, point of      73 88 146 147 152 655
Addition theorem for Bessel function      223 228
Addition theorem for exponential function      107 110
Addition theorem for exponential series      21 122
Algebra      70
Algebra complete normed      70; see “Banach algebra normed”
Algebraic complement      16 17 593
Algorithm      see also “Quotient-difference algorithm”
Algorithm for computing poles of meromorphic function      608—651
Algorithm for computing winding number      239
Algorithm for evaluating derivatives of polynomial      433—437
Algorithm for partial fraction decomposition      553 557 562 656
Algorithm for starting Bernoulli's method      589
Algorithm for zeros of polynomials      497—551
Algorithm for zeros of polynomials, conditionally convergent      489
Algorithm for zeros of polynomials, convergent      498 549
Algorithm for zeros of polynomials, globally convergent      498
Algorithm for zeros of polynomials, locally convergent      498
Algorithm for zeros of polynomials, unconditionally convergent      498
Algorithm for zeros of polynomials, uniform convergence of      498 506 513 517 522 549
Almost unit      45 47 49
Amount of work in methods of search      505
Amount of work in Weyl's exclusion algorithm      521
Amount of work to construct Hadamard polynomials      634
Amount of work, for partial fraction decomposition      559 561
Anomaly eccentric      119
Anomaly mean      119
Apolar polynomial      472 473 474
ARC      165 187 230 231
arc, analytic      391
arc, differentiable      166
arc, geometrically equivalent      166 192
arc, homotopic      167
arc, initial point of      165
arc, opposite      192
arc, piecewise differentiable      166 190 191
arc, piecewise regular      166 191 232 233
arc, regular      166
arc, terminal point of      165
Area      339
Argument      5
Argument, continuous      230 485
Argument, increase of      231
Argument, principal value of      294 521 563
Argument, principle of      234 276 278 383 485 515
Arithmetic, circular      475 479 483 500 534 551
Arrangement, combinatorial      578—580
Associative law      2 3 11 45 46 303
Astroid      430
Asymptotic expansion      81
Bairstow's method      500 559
Banach algebra      71 72 77 81 87 89 90 90 92 93 95 99 101 103 133 143
Banach space      67 69 74 75
Basis of natural logarithms      107
Bernoulli numbers      13 64 111 112 269 661
Bernoulli polynomials      276
Bernoulli's law (in hydrodynamics)      365 368
Bernoulli's method      500 588 589 653 663
Bessel function      28 164 185 220 221 607 619
Bessel function, addition theorem for      223 228
Bessel function, asymptotic behavior of      228
Bessel function, complex zeros of      651 662
Bessel function, Poisson's integral for      228
Bessel function, zeros of      138 284
Bessel's integral      221 227
Binary representation      581
Binomial coefficient      21 461
Binomial coefficient, generalized      22
Binomial series      23 41 50 92 93 102 569
Binomial theorem      22 23
Birkhoff's theorem on polynomial zeros      456 512
Blasius, formula of      367
Boundary free      368
Boundary layer theory      425
Boundary of set      203 235
Boundary point accessible      385
Boundary point of set      235
Boundary, mapping of      382
Breakthrough electrostatic      422
Cable, capacity of condenser      350
Cable, excentric      346
Cable, per unit length      350
Cable, suspended      354
Cardano, formulas of      121
Cardoid      194
Casorati — Weierstrass theorem      215 216 218 378
Cauchy inclusion radius      58 459 462
Cauchy index      443
Cauchy index for interval      444 485 486 487
Cauchy integral formula      211 230 245 388 389 600 629
Cauchy integral formula for holomorphic functions      331 332
Cauchy kernel      207
Cauchy product      10 11 41 46 90 219 226
Cauchy sequence      69 134
Cauchy sequence, convergent      69
Cauchy — Hadamard formula      77 142 155 157 571 656
Cauchy — Riemann equations      326 328 336 544
Cauchy's estimate      84 86 90 91 96 98 134 156 159 211 332 530 597 657
Cauchy's integral theorem      232
Cauchy's integral theorem for disks      198
Cauchy's integral theorem for holomorphic functions      329 333
Cauchy's integral theorem for homotopic curves      200 207
Cauchy's integral theorem for simply connected regions      199 201 202 203 204
Cauchy's integral theorem, extended form of      204
Center of mass      341
Chain rule for formal power series      40 50 58
Channel with corner      412
Channel, flow through      357
Channel, suddenly narrowing      412
Channel, turnabout      413
Characteristic of field      8
Circle generalized      309 317 318 389
Circulation      361 370
Circulation, necessity of      365
Closed curve homotopic      199
Closure      73
Cluster of polynomial zeros      499 514
Coefficient of formal power series      10
Combinatorial analysis      578 662
Commutative law      2 8 11 50 70 303
Complex plane, extended      301
Component of open set      145 146 234
Component of set      637 638
Composition of analytic functions      95 116 404
Composition of formal power series      36 45 46 50 55 132
Composition of functions      94
Condenser      349
Condenser, cylindrical      351
Condenser, plate      344 355
Condenser, semi-infinite      409 426
Conductor      342
Confluence, method of      599 603 608 624
Conjugate of complex number      7
Continuation analytic      146 148
Continuation analytic by continuous continuation      387
Continuation analytic by functional relation relationships      152
Continuation analytic by patching      149
Continuation analytic by power series      149 150 170
Continuation analytic by rearranging power series      150 170
Continuation analytic by reflection      389
Continuation analytic by removing singularities      148
Continuation analytic, along arc      166
Continuation, fundamental lemma on      150
Continued fraction      490 614 663
Continuity, modulus of      190
Continuity, of zeros of polynomial      281
Control theory      487
Convergence function      501 503
Convergence function of exclusion test      518
Convergence of series      75
Convergence, cubic      538
Convergence, function linear      506
Convergence, locally uniform      160 161 184
Convergence, order of      498
Convergence, quadratic      535 537
Convergence, speed of      526
Convergence, uniform      74 133 134
Convergence, uniform of power series      81
Convex hull, closed      464
Corner, concave      423 425
Corner, convex      429
Corner, re-entrant      423
Corner, rounding of      422
Cosine function      110
Cotangens function      110 111 137 660
Covering of set      160 503
Covering, optimal      512
Cross, mapping of      413
Crosscut      385
Curvature      186
Curve, closed      195 233
Curve, rectifiable      188
Curve, simple      235
Curve, starlike      205
Cycloid      186
Deflation      438
Derivative of analytic function      142
Derivative of complex function of real variable      180 181
Derivative of formal Laurent series      53
Derivative of formal power series      18 135 141 142
Derivative of function      129
Derivative of polynomial, with respect to point      466
Derivative, complex      327
Derivative, logarithmic      276 464 478
Descartes, rule of signs of      442
Descent function      542 546
Descent function, continuous      542 543 545
Descent function, Kellenberger's      548 549
Descent function, Nickel's      547
Descent function, Ward's      547
Descent, steepest      544 546 552
Determinant      16 17 496 591 592 663
Determinant of product of matrices      594
Determinant of sum of matrices      593 597
Determinant, Laplacian expansion of      592 593 601
Determinant, minor of      592
Determinant, minor of, algebraic complement of      593
Determinant, minor of, complement of      592
Determinant, Vandermondian      648
Diffeomorphism, piecewise      204 246
Difference equation      584 588 663
Difference equation of infinite order      589
Difference equation, basis of solution space of      586
Difference equation, solution of      585
Difference of polynomial      439
Difference operator      154
Difference scheme      608
Difference, divided      247 248
Differential      324 333
Differential equation, formal      20
Differentiation rules      181
Dirichlet integral      340
Dirichlet problem      337 342 343 350 373
Distance      310
Distance, chordal      311
Distance, Euclidean      523
Distributive law      2 3 11 46
Distributive law, right for composition      37 38
Divisor function      162
Divisor of zero      2 11
Dixon's formula      33 43 44
Domain of definition      72
Domain of values      72 286
Drawer problem      578—580
Eigenvalue of matrix      636 638—640
Eigenvalue, continuity of      636 663
Eigenvector      637
Electrostatics      342
Element regular      72
ellipse      194 206 263 295
Ellipse, circumference of      417
Emergency step      547
Enestroem's theorem      284 462 497
Epicycloid      194
Equation, analytic      101
Equation, biquadratic      121
Equation, cubic      118
Equation, Diophantine      582 584
Equation, trinomial      118 121
EQUIVALENCE      299
Estimate, a posteriori      498
Euclidean algorithm      487 489 490
Euclidean algorithm for rational functions      447
Euler's constant      275
Euler, first identity of      32 44
Euler, formulas of      110
Euler, result of (on representation of integers)      582
Euler, second identity of      40 150
Evolute      186
Exclusion algorithm      500
Exclusion test      517 518—522
Exclusion test, convergent      518
Exclusion test, one-sided      520
Exponential function      87 106 107 284 293
Exponential of matrix      122
Exponential series      20 50
Exponential, differential equation satisfied by      123
Extension, analytic      144 145—147
Factorial, generalized      24
Fast Fourier Transform      549 552
Fibonacci sequence      13 587 590
Field      3
Field of complex numbers      3
Field strength complex      346
Fixed point of analytic function      523—528
Fixed point of Moebius transformation      304 306
Flow, against dam      407
Flow, against rounded dam      424
Flow, around airfoil      365
Flow, around tilted blade      367
Flow, irrotational      356
Flow, past obstacle      358
Flow, potential      356
Flow, through cascade of airfoils      371
Flow, through circular grid      371
Flux      330 340
Force, complex      365
Force, complex, moment exerted by      369
Force, exerted on obstacle      365 367
Form factor      346
Fourier series      224 225 226 229 251 374 377 577
Fourier series with coefficients that are rational functions      269
Fourier series, absolutely convergent      71 72
Fourier series, considered as Laurent series      223 224
Fourier transforms of rational functions      254
Fourier-Budan, theorem of      443
Fresnel's integral      205
Function      72
Function, analytic      139
Function, analytic, abstract      138
Function, analytic, at infinity      216
Function, analytic, at point      87
Function, analytic, composition of      95
Function, analytic, defined by definite integral      183
Function, analytic, defined by limit process      161
Function, analytic, inversion of      97
Function, analytic, on set      144
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