关注微信

推荐商品

    加载中... 正在为您读取数据...
分享到:
  • 不等式(第2版)[平装]
  • 共2个商家     48.10元~53.69
  • 作者:G.Hardy(作者),J.E.Littlewood(作者),G.Polya(作者)
  • 出版社:世界图书出版公司北京公司;第1版(2004年4月1日)
  • 出版时间:
  • 版次 :
  • 印刷时间:
  • 包装:
  • ISBN:9787506266062

  • 商家报价
  • 简介
  • 评价
  • 加载中... 正在为您读取数据...
  • 商品描述

    编辑推荐

    It is often really difficult to trace the origin of a familiar inequality. It is quite likely to occur first as an auxiliary proposition, often without explicit statement, in a memoir on geometry or astronomy; it may have been rediscovered, many years later, by half a dozen different authors; and no accessible statement of it may be quite complete. We have almost always found, even with the most famous inequalities, that we have a little new to add. We have done our best to be accurate and have given all references we can, but we have never undertaken systematic bibliographical research. We follow the common practice, when a particular inequality is habitually associated with a particular mathematician's name; we speak of the inequalities of Schwarz, HSlder, and Jensen, though all these inequalities can be traced further back; and we do not enumerate explicitly all the minor additions which are necessary for absolute completeness. We have received a great deal of assistance from friends. Messrs G. A. Bliss, L. S. Bosanquet, R. Courant, B. Jessen, V. Levin, R. Rado, I. Schur, L. C. Young, and A. Zygmund have all helped us with criticisms or original contributions. Dr Bosanquet, Dr Jessen, and Prof. Zygmund have read tho proofs, and corrected many inaccuracies. In particular, Chapter III has been very largely rewritten as the result of Dr Jessen's suggestions. We hope that the book may now be reasonably free from error, in spite of the mass of detail which it contains.

    媒体推荐

    “20世纪数学经典著作之一……它透彻地介绍了数学分析中的所有标准不等式,并给出了详尽的证明。”
      ——NewTechnicalBooks

    作者简介

    作者:( )G.H.Hardy等[

    目录

    CHAPTER Ⅰ INTRODUCTION
    1.1 Finite,infinite,and integral inequalities
    1.2 Notations
    1.3 Positive inequalities
    1.4 Homogeneous inequalities
    1.5 The axiomatic basis of algebraic inequalities
    1.6 Comparable functions
    1.7 Selection of proofs
    1.8 Selection of subjects
    CHAPTERⅡ ELEMENTARY MEAN VALUES
    2.1 Ordinary means
    2.2 Weighted means
    2.3 Limiting cases of a
    2.4 Cauchy's inequality
    2.5 The theorem of the arithmetic and geometric means
    2.6 Other proofs of the theorem of the means
    2.7 Holder's inequality and its extensions
    2.8 Holder's inequality and its extensions cont
    2.9 General properties of the means a
    2.10 The sums r a
    2.11 Minkowski's inequality
    2.12 A companion to Minkowski's inequality
    2.13 Illustrations and applications of the fundamental inequalities
    2.14 Inductive proofs of the fundamental inequalities
    2.15 Elementary inequalities connected with Theorem 37
    2.16 Elementary proof of Theorem 3
    2.17 Tchebyehef's inequality
    2.18 Muirhead's theorem
    2.19 Proof of Muirhead's theorem
    2.20 An alternative theorem
    2.21 Further theorems on symmetrical means
    2.22 The elementary symmetric functions of n positive numbers
    2.23 A note on definite forms
    2.24 A theorem concerning strictly positive forms Miscellaneous theorems and examples
    CHAPTER Ⅲ MEAN VALUES WITH AN ARBITRARY FUNCTION AND THE THEORY OF CONVEX FUNCTIONS
    3.1 Definitions
    3.2 Equivalent means
    3.3 A characteristic property of the means
    3.4 Comparability
    3.5 Convex functions
    3.6 Continuous convex functions
    3.7 An alternative definition
    3.8 Equality in the fundamental inequalities
    3.9 Restatements and extensions of Theorem 85
    3.10 Twice differentiable convex functions
    3.11 Applieations of the properties of twice differentiable convex functions
    3.12 Convex functions of several variables
    3.13 Generalisations of Holder''''s inequality
    3.14 Some theorems concerning monotonic functions
    3.15 Sums with an arbitrary function: generalisa. tions of Jensen''''s inequality
    3.16 Generalisations of Minkowski''''s inequality
    3.17 Comparison of sets
    3.18 Fur ther general properties of convex functions
    3.19 Further properties of continuous convex functions
    3.20 Discontinuous convex functions Miscellaneous theorems and examples
    ……
    CHAPTERⅣ VARIOUS APPLICATIONS OF THE CALCULUS
    CHAPTERⅤ INFINITE SERIES
    CHAPTERⅥ INTEGRALS
    CHAPTERⅦ SOME APPLICATIONS OF THE CALCULUS OF VARIATIONS
    CHARTERⅧ SOME THEOREMS CONCERNING BILINEAR AND MULTILINEAR FORMS
    CHAPTERⅨ HILBERT'S INEQUALITY AND ITS ANALOGUES AND EXTENSIONS
    CHAPTERⅩ REARRANGEMENTS
    APPENDIXⅠ On strictly positive forms
    APPENDIXⅡ Thorin's proof and extension of Theorem 295
    APPENDIXⅢ On Hilbert's inequality
    BIBLIOGRAPHY

    序言

    本书的三位作者都是数学界,特别是古典分析学界杰出的学者。记得有人说过,英国的数学之为世界同行所重视,是从由Hardy形成的具有世界影响的英国分析学派开始的。其工作涉及解析数论、三角级数、调和分析、发散级数等诸方面,影响深远。在20世纪上半叶,Hardy的文风对数学工作者也有很大的影响。无论是写书,还是写论文,他总能做到像苏轼所说的“如行云流水,初无定质,但常行于所当行,常止于不可不止,文理自然,姿态横生”,将复杂深奥的东西写得明白易懂,使读者在不知不觉之间“轻舟已过万重山”。

    文摘

    插图: