Zdravko Cvetkovski
Springer Berlin Heidelberg
2012e druk, 2012
9783642237911
Inequalities
Theorems, Techniques and Selected Problems
Specificaties
Paperback, 444 blz.
|
Engels
Springer Berlin Heidelberg |
2012e druk, 2012
ISBN13: 9783642237911
Rubricering
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9783642237911
Taal:Engels
Bindwijze:paperback
Aantal pagina's:444
Uitgever:Springer Berlin Heidelberg
Druk:2012
Inhoudsopgave
<p>"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.</p>