.

0 (hodnocen0 x )

BK

Basel : Birkhäuser, c2009

viii, 210 s. : il. ; 24 cm

ISBN 978-3-0346-0049-1 (brož.)

Obsahuje bibliografii na s. [207]-208 a rejstřík

000184404

Contents // Introduction vii // 1 Numerical Inequalities 1 // 1.1 Order in the real numbers... 1 // 1.2 The quadratic function ax2 + 2bx + c... 4 // 1.3 A fundamental inequality, // arithmetic mean-geometric mean... 7 // 1.4 A wonderful inequality: // The rearrangement inequality... 13 // 1.5 Convex functions... 20 // 1.6 A helpful inequality ... 33 // 1.7 The substitution strategy... 39 // 1.8 Muirhead’s theorem... 43 // 2 Geometric Inequalities 51 // 2.1 Two basic inequalities... 51 // 2.2 Inequalities between the sides of a triangle... 54 // 2.3 The use of inequalities in the geometry of the triangle... 59 // 2.4 Euler’s inequality and some applications... 66 // 2.5 Symmetric functions of a, b and c... 70 // 2.6 Inequalities with areas and perimeters... 75 // 2.7 Erdös-Mordell Theorem... 80 // 2.8 Optimization problems... 88 // 3 Recent Inequality Problems 101 // 4 Solutions to Exercises and Problems 117 // 4.1 Solutions to the exercises in Chapter 1...117 // 4.2 Solutions to the exercises in Chapter 2...140 // 4.3 Solutions to the problems in Chapter 3...162 // Notation // 205 // Contents // vili // Bibliography // 207 // Index // 209