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Beckenbach E.F., Bellman R. — Introduction to Inequalities
Beckenbach E.F., Bellman R. — Introduction to Inequalities

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Название: Introduction to Inequalities

Авторы: Beckenbach E.F., Bellman R.

Аннотация:

Most people, when they think of mathematics, think first of numbers and equations-this number (x) = that number (y). But professional mathematicians, in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that areequal. This book provides an introduction to the fascinating world of inequalities, beginning with a systematic discussion of the relation "greater than" and the meaning of "absolute values" of numbers, and ending with descriptions of some unusual geometries. In the course of the book, the reader wil encounter some of the most famous inequalities in mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 133

Добавлена в каталог: 09.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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