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Nehari Z. — Conformal mapping
Nehari Z. — Conformal mapping

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Название: Conformal mapping

Автор: Nehari Z.

Аннотация:

In the preface to the first edition of Courant-Hilbert's "Methoden der mathematischen Physik," R. Courant warned against a trend discernible in modern mathematics in which he saw a menace to the future development of mathematical analysis. He was referring to the tendency of many workers in this field to lose eight of the roots of mathematical analysis in physical and geometric intuition and to concentrate their efforts on the refinement and the extreme generalization of existing concepts. In the intervening years, this trend has become much more pronounced, and it has led to an increasing division of the workers in mathematical analysis into "pure" and "applied" mathematicians. One may deplore this development or welcome it—and many, notably among the "pure" variety, do welcome it—but it seems inevitable that fields like conformal mapping, whose methods are mathematical while their subject matter is derived from physical and geometric intuition, are bound to suffer in such a division.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 396

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"Modern Analysis"      206 316
Absolute convergence      57
Absolute convergence of an infinite product      285
Absolute value      53
Accessory parameters      202
Addition theorem, exponential function      71 280
Addition theorem, logarithm      80 93
Addition theorem, trigonometric functions      74 277 279
Analytic continuation      103—105
Analytic curve      42 186 341
Analytic function, branch of      76
Analytic function, definition of      59
Analytic function, definition of, global      102
Analytic function, element of      104
Approximation      256
Approximation in the mean      245
Area of a conformal map      154 362
Area theorem      210
Argument of a complex number      53
Argument principle      130
Automorphic functions      313
Bergman kernel function      250—260 367—376 389 391
Bessel functions      116
Bessel inequality      245
Bilinear transformation      156
Boundary point      1
Boundary point, inaccessible      178
Boundary value problem      14 19 23 181 357
Bounded functions in multiply-connected domains      378—392
Bounded functions in the unit circle      166—168
Branch of an analytic function      76
Branch point      78 152
Canonical domains      189 333
Canonical mappings, existence of      342
Capacity      183
Cassinian      270
Cauchy integral formula      94
Cauchy — Riemann equations      28 62
Cauchy's inequality      100
Cauchy's theorem      84
Circle of convergence      66 99
Circle with circular slits      336
Circular ring      336 373
Circular slit mapping      335
Closure      1
Closure, cn z      281
Compactness      141
Complement      1
Complete sets of functions      245 370
complex numbers      49
Complex numbers, argument of      53
Complex numbers, conjugate of      51
Complex numbers, modulus of      53
Complex numbers, sequences of      55—56
Complex plane      53
Complex variable      58
Confocal conies      270 274
Confocal conies, domains bounded by arcs of      299—308
Conformal equivalence      174
Conformal map, area of      154 362
Conformal mapping, definition of      149
Conformal type      333
Conjugate of a complex number      51
Conjugate of a harmonic function      28 62
Connected set      2
Connectivity of a domain      3
Continuous deformation      32 90
Continuous function      58
Continuous functional      144
contour      84
Contour integration      90
Convergence of a product      285
Convergence of a sequence      55
Convergence of a series      57
Convergence, absolute      57
Convergence, uniform      66 96
Convex domains      222—224
cos z      72 274
Critical point      133 150 153
Cross ratio      158
Crosscut      2
Curvilinear polygon      198 204
Curvilinear triangle      207
Derivative      59
Diagonal process      142
Differentiable function      59
Dirichlet problem      14 354
Discontinuity      21
Distortion theorems      214
dn z      281
Domain      2 153
domain functions      42
Domain of definition      58
Doubly periodic functions      282 288 298
Doubly-connected domains      3 33 334
Element of an analytic function      104
ellipse      258 270 279 295 300
Elliptic function      280—299
Elliptic function, Jacobian      281
Elliptic function, modulus of      292 319
Elliptic integrals      281
Elliptic modular function      318—332
Entire functions      118 321
Equicontinuity      137
Essential singularity      112 113
Existence of canonical mappings      342
Exponential function      70—74 273—274
Extremal problems      145
Fixed points of a linear transformation      161
Fourier coefficients      244 373
Function element      104
Functional      144
Functional equation, permanence of      106—107
Fundamental theorem of algebra      118 121 135
Gamma function      109
Gauss' theorem      6
Global definition of an analytic function      102
Goursat's lemma      87
Green's formula      8 9 12 240
Green's function      13 38 133 181 187 357
Green's function, symmetry of      14
Green's function, variation of      42
Group of linear transformations      160 313
Hadamard's three-circle theorem      120
Hadamard's variation formula      46
Harmonic conjugate      28
Harmonic function, conjugate of      28 62
Harmonic function, definition of      4
Harmonic function, maximum principle for      9
Harmonic measure      38 357
Holomorphic function      59
Horizontal slit mapping      362
Hyperbola      269 270 307
Hyperbolic functions      79
Hypergeometric series      206 314
imaginary numbers      49
Imaginary part      51
Inaccessible boundary point      178
Infinite products      284—286
Infinite series      56—58
Inner product      241
Integration      81—84
Interior point      1
Inverse function      74 281 308
Inverse points      162
inversion      184 190 310
Inversion principle      184
Jacobian elliptic functions      281
Jordan curve      2
Joukowsky profile      271
Kernel function      250—260 367—376 389
Laplace equation      4
Laurent series      110—111
Legendre polynomial      97
Lemniscate      270
Limit point      1 56 137
Line integral      6
Linear independence      242
Linear transformation      155—165
Liouville's theorem      117
Local uniform boundedness      138
Log z      74—77 273
Logarithmic residue      128
Many-valued functions      74
Mapping theorem, Riemann      175
Maximum principle      119
Maximum Principle for harmonic functions      9
Meromorphic part      116
Modular surface      320
Modulus of a complex number      53
Modulus of a doubly-connected domain      334
Modulus of an elliptic function      292 319
Monodromy theorem      108
Montel's theorem      141
Morera's theorem      95
Multiply-connected domains      2 7 32 89 333
Natural boundary      108 311
Nearly circular domains      47 263—265
Neighborhood      1
Neumann function      23
Neumann problem      25 31
Norm of a function      241
Normal families      140 217
Odd function      213 328
Open set      1
Order of a branch point      78 153
Order of a pole      112
Order of a zero      113
Orthogonal circle      309
Orthogonal functions      242
Orthogonalization process      242
Orthonormal sets of functions      243 370 389
Outer area      361
parabola      269 279 305—307
Parallel slit mappings      334
Parameters, accessory      202
Parseval's identity      100
Partial fractions      116
Period      35 73
Period parallelogram      290
Period rectangle      283
Permanence of a functional equation      106—107
Picard's theorem      321
Piecewise smooth curve      2
Point at infinity      3 112
Poisson formula      17 97
Poisson kernel      17
Pole      112 128—131
Polygon      189
Polynomial      60
Positive real part, functions with      169—171
Potential      4
Power series      65—70
Power, general      77
Principal part      116
Principal value      75
Principle of permanence      106—107
Radial slit mapping      335
Radius of convergence      66 69
Radius of convexity      224
Radius of starlikeness      354
Rational functions      60 114
Rational functions of second degree      266—273
Real part      51
rectangle      280
Reflection principle      184
Regular function      59
Reproducing property      250 361 368 389
Residue      122
Residue theorem      122
Riemann      173
Riemann mapping theorem      175
Riemann moduli      334 354
Riemann surface      76 78 80 231 266
Ring with circular slits      336
Robin constant      183
Rouche's theorem      131
Schlicht domain      154
Schlicht function      209
Schmidt orthogonalization process      242
Schwarz lemma      165
Schwarz — Christoffel formula      194
Schwarzian derivative      199 226
Schwarzian s-functions      308—318
Sequences of analytic functions      140—143
Sequences of complex numbers      55—56
Simple pole      123
Simply-connected domains      2
sin z      72 274—277
Single-valued functions      59 76
Singular point      5 59 99
Smooth curve      2
sn z      280
Starlike domains      220—222
Subordination      227
Symmetry principle      184
Szegoe kernel function      389
tan z      277—278
Taylor series      69 98
Tchebichef polynomials      258
Three-circle theorem      120
Transcendental entire functions      118
Transfinite diameter      183
triangle      194
Triangle functions      308
Triangle, curvilinear      207
Trigonometric functions      72 274—280
Typically real functions      225
Uniform boundedness      138
Uniform convergence      66 96
Unimodular linear transformations      331
Univalent functions      146 209—226
Variation of the Green's function      46
Vertical slit mapping      362
Whittaker — Watson      206 316
Zeros of an analytic function      113 128—132
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