|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Knopp K. — Elements of the Theory of Functions |
|
|
|
| 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте