Inequalities A Mathematical Olympiad Approach /

• Κύριοι συγγραφείς: Manfrino, Radmila Bulajich (Συγγραφέας), Gómez Ortega, José Antonio (Συγγραφέας), Delgado, Rogelio Valdez (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2009.
• Θέματα: Mathematics.; Algebra.; Mathematical analysis.; Analysis (Mathematics).; Mathematics, general.; Analysis.

This book is intended for the Mathematical Olympiad students who wish to prepare 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...

Πίνακας περιεχομένων:

• 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.