000			03363nam a22004575i 4500
001			978-3-642-23792-8
003			DE-He213
005			20140220083302.0
007			cr nn 008mamaa
008			120104s2012 gw | s |||| 0|eng d
020			_a9783642237928 _9978-3-642-23792-8
024	7		_a10.1007/978-3-642-23792-8 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aCvetkovski, Zdravko. _eauthor.
245	1	0	_aInequalities _h[electronic resource] : _bTheorems, Techniques and Selected Problems / _cby Zdravko Cvetkovski.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
300			_aX, 444p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_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 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.
520			_aThis 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.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aScience (General).
650	1	4	_aMathematics.
650	2	4	_aAlgebra.
650	2	4	_aPopular Science in Mathematics/Computer Science/Natural Science/Technology.
650	2	4	_aMathematics Education.
650	2	4	_aPopular Science, general.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642237911
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-23792-8
912			_aZDB-2-SMA
999			_c102224 _d102224