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| Авторизация |
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| Beckenbach E.F., Bellman R. — Introduction to Inequalities |
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| Предметный указатель |
Absolute value 25—45
Absolute value and classical inequalities 73—75
Absolute value and sign function 34—36
Absolute value, algebraic characterization of 40—41
Absolute value, definition of 26
Absolute value, graph of 30 31
Addition of inequalities 17
Algebraic characterization ofabsolute value 40—41
Arithmetic mean 48
Arithmetic-geometric mean 76—78
Arithmetic-mean—geometric-mean inequality 48—61 73—74
Axiom 7
Backward induction 57—59
Bound, upper 12 (footnote)
Buniakowski, V. 63 (footnote)
Cauchy inequality 62—67 73—74
Cauchy inequality, geometric interpretation of 63
Cauchy — Lagrange identity 66
City-block distance 100—102
Classical inequalities 73—75
complex numbers 41
Convex set 107
Cosine inequality 65
Dido, problem of 80—83
Dido, three-dimensional version 86
Directed distance 35
Distance 99—111
Distance, city-block 100—102
Distance, directed 35
Distance, Euclidean 99—100
Distance, homogeneity of 100
Distance, non — Euclidean 100—106
Distance, positivity of 100
Distance, rotation invariance of 100
Distance, symmetry of 99
Distance, translation invariance of 99
Division of inequalities 21
Dual problem 83
Ellipsoid 90
Euclidean distance 99—100
Experimentation, mathematical 48
Fermat’s principle 84
Forward induction 55—57
Gauss’ mean 76—78
Geometric mean 48
Geometry of n dimensions 112
Graustein, W. C. 65 (footnote)
Harmonic mean 52
Holder inequality 68 73—74
Homogeneity 100
Incidence, angle of 85
Induction, mathematical 19
Induction, mathematical for powers 22
Induction, mathematical for roots 22
Induction, mathematical, addition of 17
Induction, mathematical, arithmetic-mean—geometric-mean 48—61 73—74
Induction, mathematical, backward 57—59
Induction, mathematical, Buniakowski 63 (footnote)
Induction, mathematical, Cauchy 62—67 73—74
Induction, mathematical, Cauchy — Schwarz 63 (footnote)
Induction, mathematical, division of 21
Induction, mathematical, for squares 11
Induction, mathematical, forward 55—57
Induction, mathematical, graph of 36—40
Induction, mathematical, HSlder 67 73—74
Induction, mathematical, inequality 5—6 9—10
Induction, mathematical, Minkowski 72 73—74
Induction, mathematical, mixed 9
Induction, mathematical, multiplication of 19
Induction, mathematical, multiplication of, by a number 18
Induction, mathematical, negation of 10
Induction, mathematical, Schwarz 63 (footnote)
Induction, mathematical, strict 9
Induction, mathematical, subtraction of 18
Induction, mathematical, transitivity law for 16
Induction, mathematical, triangle 42—44 69—71 73—74
Kazarinoff, N. D. 81 83
Lagrange, J. L 66
Magnitude 25
Mathematical induction 19
Mathematical induction, backward 57—59
| Mathematical induction, forward 55—57
Maximization 79ff
Maximum function 27
Mean of Gauss 76—78
Mean, arithmetic 48
Mean, arithmetic-geometric 76—78
Mean, geometric 48
Mean, harmonic 52
Mean, root-mean-square 61
Minimization 79ff
Minimum function 28
Minkowski inequality 72 73—74
Mixed inequality 9
Motion, rigid-body 106
Multiplication of inequalities 19
Multiplication of inequality by a number 18
Negation of inequality 10
Negative number 7
Negative number, product involving a 10
Negative of a number 7
Niven, Ivan 12 61
Non — Euclidean distance 100—106
Number, complete 12 (footnote)
Number, negative 10
Number, negative of a 10
Number, negative, product involving a 10
Number, order 12 (footnote)
Number, pairing of 7—8
Number, positive 6
Number, reciprocal of a 22
Ordinate 35
Osgood, W. F 65 (footnote)
Pairing of numbers 7—8
Perimeter 87—88
Point set 106
Positive number 6
Powers 22
PRODUCT 10—11
Product, involving a negative number 10
Pythagorean relationship 40 41
Ray of light 83—86
Reciprocal 22
Reflection, angle of 85
Refraction, Snell’s law of 86
Reverse problem 83
Rigid-body motion 106
Rise 35
Root-mean-square 61
Roots 22
Rotation invariance 100
Run 35
Schwarz, H. A. 63 (footnote)
Set, convex 107
Set, symmetric 107
Sign function 35—36
slope 35
Slope, average 35
Slope, left-hand 35
Slope, right-hand 35
Snell’s law of refraction 86
Specialization 58
Square roots 40—41
Squares, inequality for 11
Strict inequality 9
Subtraction of inequalities 18
Symmetric means 75
Symmetric point set 107
Symmetry 99
Tangent 93—97
Transitivity 16
Translation invariance 99
Triangle inequality 42—44 69—71 73—74
Unit circle 102—106
Unit circle, exterior 106
Unit circle, interior 106
Unit disc 106
Unit disc, boundary of 106
Upper bound 12 (footnote)
Zero 6
“greater than” relationship 5
“less than” relationship 9
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