Inequalities : a Mathematical Olympiad approach
This book is intended for the Mathematical Olympiad students who wish to p- pare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2009. |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Description d'après consultation du 26 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Inequalities, a Mathematical Olympiad approach, Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado, Basel, Birkhäuser, 2009, 1 vol. (VIII-210 p.), 978-3-0346-0049-1 |
Inhaltsangabe:
- Introduction 1 Numerical Inequalities 1.1 Order in the real numbers 1.2 The quadratic function ax2 + 2bx + c 1.3 A fundamental inequality, arithmetic mean-geometric mean 1.4. A wonderful inequality: the rearrangement inequality 1.5 Convex functions 1.6 A helpful inequality 1.7 The substitutions strategy 1.8 Muirhead's theorem 2 Geometric Inequalities 2.1 Two basic inequalities 2.2 Inequalities between the sides of a triangle 2.3 The use of inequalities in the geometry of the triangle 2.4 Euler's inequality and some applications 2.5 Symmetric functions of a, b and c 2.6 Inequalities with areas and perimeters. 2.7 Erdös-Mordell theorem 2.8 Optimization problems 3 Recent Inequality Problems 4 Solutions to Exercises and Problems Bibliography Index