Inequalities [electronic resource] Theorems, Techniques and Selected Problems / by Zdravko Cvetkovski.
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...
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| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2012.
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| Edition: | 1st ed. 2012. |
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| Format: | Electronic eBook |
Contents:
- "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.