Titlebook: Inequalities; An Approach Through B. J. Venkatachala Textbook 2018Latest edition Springer Nature Singapore Pte Ltd. and Hindustan Book Age

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n - but this much certainly does. Ideally, an explained occurrence (0) could have been predicted in a connected way - by extrapolation from prior events (e) via the same laws (L). Schematically, 1 Explanation: 0 -Lt, 2, 3-(e e e )‘-AI t 2 3 01 Prediction: (e e e )I-L , 2, 3_ +.11 t 2 3 t Thus Mars‘

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B. J. VenkatachalaDiscusses about the basic topics on inequalities and their applications.Contains over 400 problems with their solutions.Includes a chapter on geometric inequalities.Is useful to students preparing for

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Techniques for proving inequalities,ction. One can also use the known standard inequalities or use ideas from calculus. In some cases trigonometric substitutions simplify the result. We take each of these separately and illustrate them using examples.

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Applications involving inequalities,misation are considered. Inequalities are also useful in solving some Diophantine equations by way of estimating the bounds for solutions. They also help us to determine whether some polynomial equations have real roots. Here we consider several problems whose solutions use inequalities.

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Some basic inequalities, are:.(i) Given any two real numbers . and ., one and only one of the following three relations is true:. < . or . = . or . > .;.(..).(ii) . > 0 and . > 0 imply . + . > 0;.(iii) . > 0 and . > 0 imply . > 0.

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Textbook 2018Latest editionthematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications.?.