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|a 9783642237928
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|a Cvetkovski, Zdravko
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|a Inequalities
|h Elektronische Ressource
|b Theorems, Techniques and Selected Problems
|c by Zdravko Cvetkovski
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| 250 |
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|a 1st ed. 2012
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2012, 2012
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| 300 |
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|a X, 444 p
|b online resource
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|a "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
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| 653 |
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|a Mathematics—Study and teaching
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| 653 |
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|a Mathematics Education
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| 653 |
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|a Popular works
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| 653 |
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|a Popular Science, general
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| 653 |
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|a Algebra
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| 653 |
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|a Algebra
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 856 |
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|u https://doi.org/10.1007/978-3-642-23792-8?nosfx=y
|x Verlag
|3 Volltext
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|a 512
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|a 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 inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book
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