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Kaplan W. Ч Introduction to analytic functions
Kaplan W. Ч Introduction to analytic functions

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Ќазвание: Introduction to analytic functions

јвтор: Kaplan W.

јннотаци€:

The present volume can be considered as a revised and considerably enlarged version of the author's A First Course in Functions of a Complex Variable, which was essentially a reprint of Chapter 9 of the author's Advanced Calculus. The material of that chapter has now been broken up into eight separate chapters, many of the references to other chapters of advanced Calculus have been avoided by rewriting, and a large new chapter has been added on analytic functions of several complex variables. This book is therefore a self-contained introduction to the theory of analytic functions of one or more complex variables.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1966

 оличество страниц: 212

ƒобавлена в каталог: 07.12.2009

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel summation of series      144Ч145 (Prob. 5)
AbelТs theorem      65
Absolute convergence      10 172 176 178 180 182 184
Absolute value      2
Addition      2
AiryТs stress function      148
Algebraic branch point      162
Algebraic equation      115 (Prob. 5)
Amplitude      2
Analytic at a point      39
Analytic at infinity      94
Analytic continuation      49 75 159Ч163 166 189Ч195 201Ч202
Analytic function      35 54 74 123 166Ч167
Analytic, along a curve      39
angle      2 4Ч5
Annular domain      89 184Ч185
Arc length      31
Argument of complex number      2 54Ч55
Argument, Principle      112 197
Arithmetic mean      72 82
Associated radii of convergence      184 (Probs. 7 8)
Average value      72 82
Biharmonic equation and functions      148Ч150 151
Boundary, conditions      136Ч137
Boundary, points      14 91 168
Boundary, value problem      135Ч145
Bounded function      77 (Probs. 7 8) 201
Branch      53Ч61 159
Branch, point      54 59 60 162
Cauchy Ч Riemann equations      27Ч28 (Probs. 9 10) 33 36 83 146 175
Cauchy, criterion      9
Cauchy, inequalities      77 (Prob. 7)
Cauchy, integral formula      71Ч72 170
Cauchy, integral theorem      42Ч43 69Ч70 74
Cauchy, Residue Theorem      102
Change of variable in integrals      45Ч46
Circle of convergence      64 75
Closed poly cylinder      169
Comparison test for series      11
Complete Reinhardt domain      179 183 192 195
Complex conjugate      2
Complex n-dimensional space      166
Complex number infinity      9Ч10 18 94Ч96 107
Complex number system      1Ч4
Conformal mapping      122Ч158
Conjugate harmonic functions      79
Continuity      16Ч18 167
convergence of integrals      119
Convergence of sequences      8Ч9 19
Convergence of series      10Ч12 19
Convergence region of power series      62 176Ч184
Convex      125 181 192
Convex, hull      191 194Ч195 4)
Critical points      133 (Prob.7)
Cross ratio      133Ч134 (Prob.9)
Curl of a vector field      83 146
De lТHopitalТs rule      115
De Moivre theorem      5
Definite integral      116Ч121
Degree of rational function      98Ч99 (Prob.9)
Deleted neighborhood      90
Derivative      22Ч28
Differential      24
Differential equation      68 (Prob.4)
Differentiation of integrals      44Ч45 47 (Prob.4) 85 171
Differentiation of series      66Ч67
Directional derivative      23 39Ч40
Dirichlet problem      135Ч145
Distance      3 166
Divergence of a vector field      83 146
Divergence of sequences, series, integrals      (see Convergence)
Diverges to infinity      9
Domain      14 167
Domain of convergence      62 176
Double series      172 185
Doubly connected      69
Electrostatic potential      143 (Prob.2)
Elementary analytic functions      47Ч51
Entire function      77 (Prob.8)
Envelope of holomorphy      191Ч195
equation      (see Algebraic equation)
Equilibrium      143 (Prob.3)
Equipotential lines      146
Error, estimation of      31 75
Essential singularity      92 95 201
Euler identity      6
Exponential function      6 48 50 58 129Ч130
Exponential function, transformation      129Ч130
Extended z plane      96
Finite z plane      96
Flow past an obstacle      147
Fluid Motion      (see Hydrodynamics)
Fourier, integral      119
Fourier, series      51 64Ч65 83 144 5)
Function      14Ч16 53Ч54 122
Function of several complex variables      165
Functional equation, permanence of      49 161
Fundamental theorem of algebra      115 (Prob.5)
Generalized polycylindrical domain      168
Geometric series      19Ч21 64
Harmonic, conjugate      79
Harmonic, function      iii-iv 22Ч23 33 35 79Ч83 135Ч145
Holomorphic function      167
Hydrodynamics      146Ч148 151 2)
Hyperbolic functions      48Ч51
Imaginary part      2
Incompressible flow      146Ч148 151 2)
Indefinite integral      44 48
Independence of path      43
Indirect analytic continuation      160 190
Inequality      3 31 77
Infinite, sequences      8Ч12 19
Infinite, series      (see also Fourier series Power
Infinity, complex      9Ч10 18 94Ч96 107
Integral, complex      28Ч32
Integral, depending on a parameter      85 (Prob. 9)
Integral, function      77 (Prob. 8)
Integration of series      32
Interior points of a sot      178Ч179
Inverse, functions      53Ч54 84 123 124
Inverse, logarithmic image      191 195
Inverse, points      134 (Prob.10)
Inverse, trigonometric functions      60
Irrotational      146
Isolated, boundary point      91
Isolated, singularity      91 194
Isolation of zeros      93 190 195
Iterated series      173
Jacobian determinant      112
Kronecker integral      111
Laplace equation      (see Harmonic functions)
Laurent series      88Ч121 184Ч189
Leibnitz rule for integrals      47 (Prob. 4) 85 171
Level curves      124 128Ч131
LIMIT      8Ч10 16Ч19 167
Line integral      29
Linear, fractional transformation      126
Linear, integral transformation      126
Linear, transformation      199
LiouvilleТs theorem      77 (Prob.8) 203
Logarithmic, branch point      54
Logarithmic, convexity      181 183 192
Logarithmic, derivative      110
Logarithmic, function      55Ч57
Logarithmic, image      181 184
Logarithmic, potential      86 (Prob. 9)
Logarithmic, residue      110
M-test for series      20
M-uniformly convergent      173 179 185
Mapping      (see Conformal mapping Transformation)
Modulus      2
MoreraТs theorem      44
Multiplication      2Ч7
Multiplication of HorioH      12
Multiplicity of zero      93 95
Multiply connected      69 72
Neighborhood      14 90 167
Nonessential singularity      201 203
Nonessential singularity wth-term test      11
One-to-one transformation      112Ч113 122Ч125 152
Open region      14 167
Order of pole      92 95
Order of zero      93 95
Partial, derivative      167 171
Partial, sum of series      10
Piecewise smooth path      28
Poisson, equation      150
Poisson, integral formula      80Ч86 130Ч137 140 144Ч145
Poisson, summation of series      144Ч145 (Prob.5)
Polar form of complex numbers      4
Pole      92 95 103 201
Polycylindrical domain      108
Polynomial      17Ч18 48 167
Power, function      5Ч7 58Ч59
Power, series      62Ч87 88Ч90 172 176 180
Prime      200 202
Principal, part      92
Principal, value of function      56 58
Principal, value of integral      119
Prob.      11
Pseudoalgebraic equation      196
Pseudopolynomial      196Ч200
Pure imaginary      2
Radius of convergence      62Ч63 75
Ratio Test      11 63Ч64
Rational function      18 48 98 114 4) 126Ч127
Real part      2
Rearrangement of series      172Ч173 176
Reciprocal transformation      126
Reinhardt domain      178 181 184 185 192 195 6)
Removable singularity      91 94 99 194 195 200Ч203
Residues      101Ч121
Riemann, surfaces      162Ч163
Riemann, theorem of      99 (Prob.12) 201
Root test      11
Roots      5Ч7 16 58Ч60 115
Rotation-stretching      125Ч126
Schwarz-Christoffel transformation      154
Sense-preserving      122
Sequences      (see Infinite sequences)
Series      (see Infinite series)
Simply connected      42Ч43 71 80
Singular point      91 200Ч203
Slit domain      147
Smooth path      28
Stationary flow      146Ч148
Stereographic projection      95
Stream function and lines      146
Stress function and tensor      148
Subtraction      2Ч3
Sum of numbers      2
Sum of series      10
Tangent vector      26 (Prob.7) 123 135
Taylor, formula with remainder      75
Taylor, series      35 67 73Ч74 172Ч180
Temperature      143 (Prob. 3) 151
Tensor      148
Transformation      15 112Ч113 122Ч158 199
Translation      125
Triangle inequality      3
Trigonometric, functions      48Ч52
Trigonometric, series      51 64Ч65 83 144 5)
Triply connected      69
Uniform convergence      19Ч21 32 62 173
Uniqueness of analytic continuation      159 190
Vector field      15 83 146
Velocity potential      146
Weierstrass and Casorati, theorem of      99 (Prob. 13)
Weierstrass, M-test      20 173
Weierstrass, preparation theorem      196Ч200
Zeros of functions      16 52 93 95 98Ч99 9 10) 166 195Ч200
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