Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Beckenbach E.F., Bellman R. — Introduction to Inequalities Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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 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 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020 | | О проекте