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Knopp K. — Elements of the Theory of Functions
Knopp K. — Elements of the Theory of Functions

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Название: Elements of the Theory of Functions

Автор: Knopp K.

Аннотация:

General background: complex numbers, linear functions, sets and sequences, conformal mapping. Detailed proofs.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1952

Количество страниц: 140

Добавлена в каталог: 15.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute convergence      77ff.
Absolute value      17 31ff.
Addition      3 4 9 20
Addition, geometric      11
Addition, vector      11 20
Addition-theorems      114 120 126
Amplitude      17
Analytic      101
Antipodal      47
Arc sin z      131
Arc tan z      132
Argand, J.R.      15
Argument      17 89
Associative law      4
axes      9 16
Axis of imaginaries      16
Axis of reals      16
Bernoullian numbers      118
Binomial series      133ff.
Binomial theorem      25
Bolzano — Weierstrass theorem      67 69 70f. 73
Bound      67ff.
Bound, greatest lower      68 75
Bound, least upper      69 75
Boundary      33
Boundary point      67
Bounded      67 68 70
Branch-point      108
Cantor — Dedekind axiom      8
Cardan's formulas      14
Cardano, G.      13
Cartesian coordinates      9
Cartesian representation      28
Cauchy      73
Cauchy double-series theorem      82
Cauchy product      81
Cauchy's convergence principle      73 77
Chain rule      95
Circle of convergence      84
Circular mapping      36 48ff.
Closed      67 70
Coinitial      10
Column series      82
Commutative      44
Commutative law      4
Comparison Test      78
Complementary set      67
Completeness theorem      7
components      10
Composite function      88 95
Conditionally convergent      77
conformal      104
Conjugates      18
Connected      101
Continuation into the complex domain      113
Continuity      92 102
Continuity, theorem of      7 8
Convergence criteria      78f.
Convergent      73 77
coordinates      8 9
cos z      119ff.
cosh z      125
cot z      123ff.
Cross ratios      61ff.
de Moivre's formula      29
Dedekind cut      6
Dedekind, fundamental theorem of      7
Derivative      93 95 103
Derivative, formal, of a power series      85
Derivatives of higher order      95
Development in power series      96ff.
Diagonals, arrangement by      80
Diametrically opposite      47
Difference      4 9 21
Differentiability      93
Differential quotient      93 103
Direction factor      28
Distance      21
Distributive law      4
Divergent      74 77
Division      5 9 24 30f.
Division of power series      86
Domain of definition      89
Domain of values      89
Domain of variation      89
Elements      66
Elliptic mapping      58
Empty set      66
Enumerable      72
Equality      3 19
Euler's formulas      119
Euler, L.      14 26 119
Everywhere convergent      84
Expansion in power series      96ff.
Exponential function      84 113ff.
Expression, rational      25
Extension of the number system      25ff.
Exterior of a circle      60
Factor representation      110
Fixed points      47 54
Formal operation      5 13 14 24
Function      42 89
Function, analytic      101
Function, composite      88 95
Function, cyclometric      130ff.
Function, entire      113 119 126
Function, entire linear      42ff.
Function, entire rational      110
Function, even      119
Function, fractional linear      45
Function, hyperbolic      125
Function, linear      42ff.
Function, odd      119
Function, rational      89 111
Function, trigonometric      119ff.
Fundamental domain      116
Fundamental laws of arithmetic      3ff.
Fundamental theorem of algebra      14 110
Gauss, C.F.      15 26
Gaussian plane      16
Geometric series      83
Goniometry      120
Group      54
Grouping terms of series      81
Half-axes      16
Half-planes      16f.
Hamilton, W.R.      15
Hyperbolic functions      125
Hyperbolic mapping      58
i      26
Identically constant      43 92
Identity      43
Identity theorem for power series      97
Image point      102
Imaginary part      16
Improper point      41
Inequalities      31ff.
Inequality      19
infinity      41
Interior of a circle      60
Interior point      67
interval      70
Invariant      61
Inverse      51
inversion      47
Involutoric      47
Isogonal      36 48ff.
Isolated point      67
Isomorphic      26
Joining of vectors      9 10
Lattice points      66
LIMIT      73
Limit point      67 73
Limit, lower      70 75
Limit, upper      70 75
limits of functions      90ff.
Logarithm      127ff.
Loxodromic      58
Mapping      35ff. 42ff. 62ff.
Mapping by reciprocal radii      47
Mapping, conformal      102ff.
Mapping, degenerate      43
Matrix equation      63
Modulus      17
Monotonic law      4
Monotonically decreasing      75
Monotonically increasing      75
Multiple-valued      109
Multiplication      3 4 9 30f.
Nearly all      73
Negative of a complex number      18 22
Neighborhood      34
Nest of intervals      76
Non-real      17
Normal form      57
Nowhere convergent      84
Null sequence      74
Null vector      8 10
Number axis      6 7
Number pairs      16
Number plane      2 16
Number sphere      2 39ff.
Numbers      5 16
Numbers, complex      1 15ff.
Numbers, fractional      3
Numbers, irrational      6
Numbers, natural      3
numbers, negative      3
Numbers, plane of      2 16
Numbers, rational      3
Numbers, real      5 6
Numbers, sequence of      72
Numbers, sequence of real      75
Numbers, set of      see Point set
Numbers, sphere of      2 39ff.
open      67 70
Operations on limits      74 79 91
Operations, rational      25
Order      3
Order of a zero      110
ordered      3 9 10 68
Origin      17
Orthogonal circle      49 50
Parabolic mapping      58
Parallel displacement      43
Parallelogram of forces      10
Partial-fractions decomposition      111
Period-strip      122 124
Plane of numbers      2 16
Point set      66ff.
Point set, real      68
Polar coordinates      11
Polynomial      110
Power      25 106 133 134
Power series      83ff. 96ff.
Preservation of regions      61
Preservation of scale      104
Principal limits      70 75
Principal value      11 17 109 127 131f.
PRODUCT      4 22
Product series      80
Projection, stereographic      35ff.
Proper plane      41
Proper point      41
Pure imaginary      17
Quotient      5 24
Radical test      79
Radius of convergence      84f.
Radius vector      10
Ratio Test      79
REAL      17
Real part      16
Rearrangement      79
Reciprocal      31
Reflection      46 47 50
Region      101
Regions, preservation of      61
Regular      101
Representation by power series      96ff.
Representation, Cartesian      28
Representation, geometric      30
Representation, trigonometric      28
Reversion of angles      47
Riemann surface      108
Riemann, B.      39 108
Root      106 109
Root of a polynomial      110
Rotary stretching      43
Rotation      9 30 44
Row series      82
Rules, derived      5 24
Scale, preservation of      104
Sequence of numbers      72
Sequence of numbers, real      75
Sequence of points      see Sequence of numbers
Series, column      82
Series, infinite      76ff.
Series, row      82
Set of numbers      see Point set
Similarity in the smallest parts      105
Similarity mapping      43
sin z      119ff.
sinh z      126
Sphere of numbers      2 39ff.
Squares, arrangement by      80
Stereographic projection      35ff.
Stretching      9 30 43f.
Subtraction      4 20f.
SUM      3 20 77
Surface of a circle      33
symmetric      18
tan z      123ff.
Taylor series      99
Tending to      73
Terms      72 77
Theory of functions      1
Theory of functions, geometric      2
Transformation, linear      43
Translation      43
Triangle inequality      28 32
Trigonometric representation      28
Two-dimensional      10
Uniqueness theorem      7
Unit circle      33
Value of a series      77
Value, absolute      17 31ff.
Variable      89
Variation, domain of      89
Vector      8ff.
Vector addition      11 20
Vectorial angle      11
w-plane      42
w-sphere      42
Weasel, C.      15
Winding-point      108
z-plane      42
z-sphere      42
Zero      3 22
zeros      110
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