Ekstrēmu uzdevumu risināšanas elementārās metodes
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Latvijas Universitāte
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Abstract
Darba mērķis ar elementārām metodēm atrisināt maksimāli daudz ekstrēmu uzdevumu no mācību līdzekļa Kriķis D., Zariņš P., Ziobrovskis V., Diferencēti uzdevumi matemātikā, 1. daļa, Rīga, Zvaigzne ABC, 1996, 390 lpp. (1. izd. 1991. g.). Bez tam darbā ir atrisināts Heigensa uzdevums n starplodītēm, ja n < 5, kā arī aplūkota sakārtojuma nevienādība un vairāki tās lietojuma piemēri no matemātikas olimpiādēm.
This work deals with extremum problems which can be solved by the elementary methods. The purpose of this work is to solve by elementary means as many problems as possible from the textbook [KZZ] (which would be solved by the differential calculus). Moreover Huygens problem for n balls has been solved if n < 5, tasks and exercises upon the reaarrangement inequality are given as well.
This work deals with extremum problems which can be solved by the elementary methods. The purpose of this work is to solve by elementary means as many problems as possible from the textbook [KZZ] (which would be solved by the differential calculus). Moreover Huygens problem for n balls has been solved if n < 5, tasks and exercises upon the reaarrangement inequality are given as well.