Inequalities : Theorems, Techniques and Selected Problems
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving i...
Uloženo v:
| Hlavní autor: | |
|---|---|
| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Vydání: | 1st ed. 2012. |
| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Poznámka: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Inequalities, theorems, techniques and selected problems, Zdravko Cvetkovski, 2012, Berlin, Springer, 1 vol. (X-444p. ), 3-642-23791-6 |
Obsah:
- "Basic (elementary) inequalities and their application Inequalities between means, (with two and three variables) Geometric (triangle) inequalities Bernoulli's inequality, the Cauchy-Schwarz inequality, Chebishev's inequality, Surányi's inequality Inequalities between means (general case) Points of incidence in applications of the AM-GM inequality The rearrangement inequality Convexity, Jensen's inequality Trigonometric substitutions and their application for proving algebraic inequalities The most usual forms of trigonometric substitutions Characteristic examples, using trigonometric substitutions Hölder's inequality, Minkowski's inequality and their generalizations Generalizations of the Cauchy-Schwarz inequality, Chebishev's inequality and the mean inequalities Newton's inequality, Maclaurin's inequality Schur's inequality, Muirhead's inequality Two theorems from differential calculus, and their applications for proving inequalities One method of proving symmetric inequalities with three variables Method for proving symmetric inequalities with three variables defined on set of real numbers Abstract concreteness method (ABC method) Sum of Squares (S.O.S - method) Strong mixing variables method (S.M.V Theorem) Lagrange multipliers method.