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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2012, 2012
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| Edition: | 1st ed. 2012 |
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of 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 applicatio