Zdravko Cvetkovski: Inequalities

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Cover: 9783642237911 | Inequalities | Theorems, Techniques and Selected Problems | Cvetkovski

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Dipl. Math. Zdravko Cvetkovski, European University-Skopje, R. Macedonia, Informatics Department.

Zusammenfassung

Contains 485 problems on Algebra-Inequalities

Detailed solutions are given

Theoretical background and techniques for proving inequalities are provided

Ideal for participants of national and international mathematical contests

Includes supplementary material: [...]

Inhaltsverzeichnis

"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.

Details

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	456
Inhalt:	x 444 S.
ISBN-13:	9783642237911
ISBN-10:	3642237916
Sprache:	Englisch
Herstellernummer:	80075207
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Cvetkovski, Zdravko
Auflage:	2012
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Maße:	235 x 155 x 25 mm
Von/Mit:	Zdravko Cvetkovski
Erscheinungsdatum:	06.01.2012
Gewicht:	0,686 kg

preigu-id: 106840487