Inequalities A Mathematical Olympiad Approach /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bulajich Manfrino, Radmila (Autor), Gómez Ortega, José Antonio (Autor), Valdez Delgado, Rogelio (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2009.
Edición:1st ed. 2009.
Temas:
Algebra.
Mathematics.
Mathematical analysis.
Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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