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Inequalities: Theorems, Techniques and Selected Problems de Zdravko Cvetkovski

Inequalities: Theorems, Techniques and Selected Problems

Autor Zdravko Cvetkovski
en Limba Engleză Paperback – 6 ian 2012
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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Specificații

ISBN-13: 9783642237911
ISBN-10: 3642237916
Pagini: 456
Ilustrații: X, 444 p.
Dimensiuni: 155 x 235 x 30 mm
Greutate: 0.69 kg
Ediția:2012
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Popular/general

Cuprins

"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.

Recenzii

From the reviews:
“The book is aimed at the more advanced students about to enter university and is particularly useful to candidates, and their trainers, for mathematical competitions such as the Olympiads. The themes and methods are introduced in 19 chapters of the book, which include exercises and their solutions.” (Peter Shiu, The Mathematical Gazette, Vol. 98 (541), March, 2014)
“This volume collects problems of various degrees of difficulty in the field of elementary inequalities. This book is intended as a valuable source for the training of high-school students in view of mathematical Olympiads. School teachers will also gain benefit from this book. … It would be a particularly valuable resource for those who participate in mathematics competitions at the high school or college level. … this book is a ‘must have’ for a university’s library, and I recommend it highly to its ‘ideal audience’.” (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1233, 2012)

Notă biografică

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

Textul de pe ultima copertă

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.

Caracteristici

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: sn.pub/extras