| Dewey Class |
512 |
| Title |
Inequalities (EB) : Theorems, Techniques and Selected Problems / by Zdravko Cvetkovski. |
| Author |
Cvetkovski, Zdravko |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Berlin, Heidelberg : Springer , 2012. |
| Physical Details |
X, 444 pages : online resource. |
| ISBN |
9783642237928 |
| Summary Note |
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.: |
| Contents note |
"Basic (elementary) inequalities and their application -- Inequalities between means, (with two and three variables) -- Geometric (triangle) inequalities -- Bernoulliâs inequality, the Cauchy-Schwarz inequality, Chebishevâs inequality, Surányiâs inequality -- Inequalities between means (general case) -- Points of incidence in applications of the AMâGM inequality -- The rearrangement inequality -- Convexity, Jensenâs inequality -- Trigonometric substitutions and their application for proving algebraic inequalities -- The most usual forms of trigonometric substitutions -- Characteristic examples, using trigonometric substitutions -- Hölderâs inequality, Minkowskiâs inequality and their generalizations -- Generalizations of the CauchyâSchwarz inequality, Chebishevâs inequality and the mean inequalities -- Newtonâs inequality, Maclaurinâs inequality -- Schurâs inequality, Muirheadâs 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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
http://dx.doi.org/10.1007/978-3-642-23792-8 |
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