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| Авторизация |
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| Polya G., Latta G. — Complex Variables |
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| Предметный указатель |
 roots of a complex number 50
Absolute convergence 63
Absolute value 4
Analytic continuation 231
Analytic continuation, along a curve 233
Analytic continuation, reflection principle 240
Analytic functions 75 97
Analytic functions at infinity 138 205
Analytic functions, derivative of 75
Analytic functions, singularities of 202
Arcs 134
Argument (phase) 4
Argument principle 226
Asymptotic series 291
Bernoulli's equation 266
Bessel function 68
beta function 239
Bilinear transformation 120
Binomial series 107
Branch cut 165
Branch cut, principal 220
Branch point 48
Branch point, integration around 220
Cauchy inequalities 186
Cauchy integral formula 177
Cauchy integral formula, theorem 146
Cauchy principal value 182 222
Cauchy — Riemann conditions 80
Cauchy — Riemann conditions in polar coordinates 84
Circle of convergence 63
Circulation of a fluid 282
Closed curve 146
Complex number(s) 5
Complex number(s), conjugate 15
Complex number(s), imaginary part 4
Complex number(s), plane 3
Complex number(s), polar form 42
Complex number(s), real part 4
Complex number(s), roots of 50
Complex potential 267
Conformal mapping 87
conjugate 15
Connected domain 169
Continuity 100
Contour integral 146
Convergence 63
Critical point 129
Cross ratio 125
Curl 91
Curve(s) orientation 134 168
Curve(s), closed 169
Curve(s), simple 161
de Moivre's formula 11
Degenerate polygons 255
Derivative, of Cauchy integral 185
Dipole 270
Divergence 91 155
domains 54
Domains, multiply connected 158
Domains, simply connected 158 168
Entire functions 187
Essential singularity 203
Essential singularity, behavior near 220
Essential singularity, residue at 210
Euler's formula 39
Exponential function 36
Exponential function, inverse of 46
Exponential function, mapping by 129
Fixed point 126
Fluid flow, about cylinder 280
Fluid flow, in channels 275
Flux 143
Fourier series 202
Free boundaries 282
Functions, analytic 75
Functions, beta 239
Functions, entire 187
Functions, gamma 235
Functions, inverse 46
Functions, limits of 20
Functions, multiple valued 54 140
Fundamental theorem of algebra 188
Gamma function 235
Gauss' theorem on zeros of polynomials 70
Geometric series 21
Green's identity 175
Harmonic functions 96
Hodograph plane 285
Hydrodynamics 265
Hyperbolic functions 69
identities 43
Image 85
| Imaginary axis 4
Imaginary axis, part 4
Indefinite integral 162
Independence of path 159
Integrals, contour 146
Integrals, line 147
Integrals, principal value 182
Inverse point 127
Inversion of series 227
Irrotational flow 90
Irrotational flow, vector field 93
Isolated point 206
Isolated point, singular point 206
Jensen's theorem 229
Joukowski airfoil 139
Lagrange's formula 22
Laplace's equation 95
Laplace's equation, asymptotic formula 302
Laurent series 195
Level curves 57
Limits 20
Line integral 147
Linear fractional transformation 120
Liouville's theorem 187
Logarithm 46
Logarithm, inverse of 46
Logarithm, mapping by 131
Logarithm, principal branch of 47
Machin's formula 24
Maclaurin's series 188
Magnification 105
Majorant 262
Mapping, conformal 87
Mapping, Mercator 131
Mapping, Ptolemy (stereographic) 113
Mapping, Schwarz — Christoffel 250
Mapping, univalent 110
Maximum modulus theorem 187
Meromorphic function 99
Natural boundary 235
One to one function 110
Order of zeros 205
Order, of poles 203
Phase (argument) 4
Point at infinity 114
Poisson's integral formula 219 24:
Poles 203
Poles order 205
Polynomial 36
Power series 63
Power series, algebra of 192
Power series, convergence of 63
Power series, differentiation of 78 101
Power series, integration of 192
Powers 49
Principal part of Laurent expansion 203
Punctured plane 55
Quaternions 29—33
Real axis 4
Real axis, part 4
Reflection principle 240
Removable singularity 203
Residue theorem 206
Residues 204
Residues, computation of 208
Riemann mapping theorem 243
Rouche's theorem 227
Saddlepoint method 314
Schwarz — Christoffel formula 250
Schwarz' inequality 205 220
Series inversion 227
Singular points 202
Sink 270
Source 91 270
Stagnation point 274
Stereographic mapping 113
Stream function 267
Stream function, streamlines 267
Taylor's series 188
Triangle inequality 7 25
Trigonometric functions 38
Trigonometric functions, identities 40 43
Trigonometric functions, inverse 52
Univalent 110 244
Vector(s) 2 6
Vector(s) fields 88
Vectorial operations 17
Velocity potential 267
Vena contracta 288
Weierstrass 220
Work 143
Zeros, order 205
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