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Bak J., Newman D.J. — Complex Analysis
Bak J., Newman D.J. — Complex Analysis

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Название: Complex Analysis

Авторы: Bak J., Newman D.J.

Аннотация:

This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. "Complex Analysis" offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. Stressing motivation and technique, and complete with exercise sets, this volume may be used both as a basic text and as a reference. For this second edition, the authors have revised some of the existing material and have provided new exercises and solutions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1996

Количество страниц: 312

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      6
Absolutely convergent, product      217
Absolutely convergent, sum      11
Analytic, branch of log z      99
Analytic, continuation      228
Analytic, function      37
Analytic, part      111
Analytic, polynomial      21
Angle between curves      157
Annulus      107
Arclength      48
Argand, J.      4
Argument      6
Argument, Principle      122
Associative law      2
Automorphism      170
Axis, imaginary      4
Axis, real      4
Barrier      180
Bilinear transformation      165
Binomial coefficients      142
Boundary      12
Boundary natural      230
Bounded set      12
C-analytic      77
C-harmonic      202
Canonical regions      183
Cardan, J.      1
Casorati — Weierstrass theorem      105
Cauchy Integral Formula, for analytic functions      69
Cauchy Integral Formula, for entire functions      58 65
Cauchy integral formula, generalized      125
Cauchy — Riemann equations      23 34 35
Cauchy, product      27 32 33
Cauchy, Residue Theorem      120
Cauchy, sequence      10
Circle of convergence      26 228
Circulation      178 258
Closed curve      50
Closed Curve Theorem, for analytic functions      69 96
Closed Curve Theorem, for entire functions      54
Closed Curve Theorem, general      97
Closed set      12
Closure      12
Commutative law      2
Compact      12
Complement      12
Complex, integral      43
Complex, number      1
Complex, plane      4
Conformal, equivalence      157 175
Conformal, mapping      158 163
conjugate      5
Connected set      12
Continuation, analytic      228
Continuous function      13
Convergence, absolute      11 217
Convergence, circle of      26 228
Convergence, radius of      25
Convergence, uniform      14 86
Convergent, integral      130 132 134
Convergent, sequence      10
Cross-ratio      174
Curve, closed      50
Curve, Jordan      118
Curve, level      214
Curve, piecewise differentiable      43
Curve, regular closed      120
Curve, simple closed      50
Curve, smooth      44
Curves, smoothly equivalent      44 54
Cyclotomic equation      18
Define integral, complex      43 224
Define integral, real      130
Deleted neighborhood      103
Dense set      105
Derivative, complex      24 34
Derivative, partial      22
Descartes, R.      1
Differentiable function      24
Differential equation      197
Dirichlet problem      205
disconnected set      12
Distributive law      2
Entire function      37
Equicontinuous set of functions      186
Erdoes, P.      78
Essential singularity      104
Euler constant      238
Euler, L.      1
Exponential function      39
Extended plane      16
Fiadamard      vi
Field of complex numbers      2
Fixed point      173
Fluid flow, locally irrotational and source-free      178
Fluid flow, totally irrotational and source-free      180
Flux      178 258
Fourier Uniqueness Theorem      247
Fraction, partial      112
Function, analytic      37
Function, complex continuous      13
Function, differentiable      24
Function, entire      37
Function, even      64
Function, exponential      39
Function, Gamma      235
Function, harmonic      200
Function, inverse      38
Function, locally 1-1      158
Function, logarithm      99
Function, meromorphic      121
Function, of z      20
Function, rational      112 130 134
Function, trigonometric      40
Function, zeta      238
Functional equation      75
Functions, equicontinuous      186
Fundamental theorem of algebra      63 79
Fundamental theorem of calculus      49
Gamma function      235
Gauss, C      1
Hamilton, W.      2
Harmonic function      200
Heat equation      207 258
Hurwitz's theorem      126
Imaginary, axis      4
Imaginary, part      5
Infinite product      215
Infinity, point at      16
Integral Theorem, for analytic functions      69 97
Integral Theorem, for entire functions      52
Integral, complex definite      43 224
Integral, real definite      130
Inverse function      38
Isolated singularity      103
Isomorphism      3
Jordan curve theorem      118
Kelvin's theorem      182
Kernel function      250
Kernel function, Poisson      203
Laplace, equation      207
Laplace, transform      234
Laurent expansion      107
Laurent expansion, analytic part      111
Laurent expansion, principal part      111
Laurent series      107
Level curve      214
Levels of polygonal path      95
lim sup      25
Line integral      44
Liouville's theorem      62 84 192
Liouville's theorem, extended      63
Liouville's Theorem, for Re f      210
Locally      1—1 158
Logarithm function      99
M-L Formula      47
M-test      14
Mapping, bilinear      165
Mapping, conformal      158 163
Mapping, Theorem      183
Maximum Modulus Theorem, for analytic functions      76
Maximum Modulus Theorem, for harmonic functions      202
Maximum Modulus Theorem, generalized      190
Mean-Value Theorem, for analytic functions      76
Mean-Value Theorem, for harmonic functions      202
Meromorphic function      121
minimum modulus theorem      77
Modulus      6
Moments      232
Morera's theorem      85
Neighborhood      12
Neighborhood, deleted      103
Open mapping theorem      80
Order, in the complex plane      4
Order, of entire function      211 214
Order, of pole      104
Order, of zero      64 66
Partial derivative      22
Partial fraction decomposition      112
Partition problem      243
Phragmen — Lindelof theorem      193
Picard's theorem      106
Piecewise differentiable curve      43
Plane, complex      4
Plane, extended      16
Point, at infinity      15
Point, fixed      173
Point, regular      229
Poisson Integral Formula, for a disc      203 204
Poisson Integral Formula, for a half-plane      205
Poisson kernel      203
Polar coordinates      8
Pole      104
Polygonal line      12
Polygonal path      14
Polygonal path, levels of      95
Polygonally connected      12 13
Polynomial, analytic      21
Polynomial, real      17 65
Power series      25 27 70
Prime number theorem      250
Principal part      111
Quadratic equation      4
Radius of convergence      25
Rational function      112
Real, axis      4
Real, part      5
Real, polynomial      17 65
Rectangle Theorem, for analytic functions      67
Rectangle Theorem, for entire functions      50 56
Reflection principle      89
Region      13
Region, convex      101
Region, simply connected      92
Regular closed curve      120
Regular point      229
Removable singularity      104
Residue      115
Residue theorem      120
Riemann, Mapping Theorem      184
Riemann, Principle of Removable Singularities      104
Riemann, sphere      15
Rotation      163
Rouche's theorem      123 128
Schwarz, Lemma      81
Schwarz, Reflection Principle      89
Sequence, Cauchy      10
Sequence, convergent      10
Series      11
Simply connected      92 256 257
Singularity      229
Singularity, essential      104
Singularity, isolated      103
Singularity, removable      104
Sphere, Riemann      15
Square root      3 41
Stereographic projection      15
Tangent to a curve      157 257
Taylor Expansion, for an analytic function      70
Taylor Expansion, for an entire function      60
Tchebychev estimates      260
Triangle inequality      6 11 18
Uniform convergence, on a set      14
Uniform convergence, on compacta      86
Uniqueness Theorem, for analytic function      74
Uniqueness Theorem, for power series      30
Value, absolute      6
Variation      245
Vector sum      4
Velocity vector      179
Wallis, J.      4
Weierstrass Product Theorem      219
Winding number      117
Zero of multiplicity k      64 66
Zeroes of entire functions      212 219
Zeta function      238
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