Inequality book suggestion for basic level

Question

I don't know if it is the right platform to ask this. (Forgive me if not.) But I need to study about inequalities and inequality solving methods from a very basic level. I can not figure out under which book title (Algebra Or Calculus) inequality chapter comes. That's why it became very much difficult to find right book on google search. Please suggest me some books of inequality for the elementary study.

$\boldsymbol{Very}$ $\boldsymbol{Basic}\boldsymbol{Level}$$\Longrightarrow$I am studying differential calculus for postgraduate entrence exam.I need to find domain and range of given funtion.This is the topic where i need to get acquainted with the methods of sloving inequality equation for x(say)

Here are few problems$\Longrightarrow$1. $\frac{1+(log_{a}x)^{2}}{1+log_{a}x}\succ1$,0$\prec a\prec1$

2. 3sin2x$\succ$sinx + cosx+1

3. log$_{\sqrt{2x^{2}-7x+6}}$($\frac{x}{3})\succ0$

4.log$_{3}\frac{|x^{2}-4x|}{x^{2}+|x-5|}\geq0$

Here i need to find the interval where x may belong.So Please suggest me a book that helps in solving every kind of equation like quadratic,transcedental,exponential,logrithmic etc.

Answer 1

You should try HOW TO LEARN CALCULUS OF ONE VARIABLE BY J.D. GHOSH IT HAS EXACTLY WHAT YOU NEED. It contains very sharp methods of solving inequality

Answer 2

This document may be useful.

I suggest this link of AoPS and the following books:

• The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele.
• Radmila Bulajich Manfrino Inequalities: A Mathematical Olympiad Approach
• Basics of Olympiad Inequalities (Samin Riasat) www.aam.org.in/site/st_material/14.pdf
• Zdravko Cvetkovski Inequalities: Theorems, Techniques and Selected Problems
• Inequalities by Hardy/Littlewood/Pólya
• Introduction to Inequalities by Beckenbach/Bellman
• Geometric Inequalities by Kazarinoff

Answer 3

Try this book:

Secrets of inequalities vol. 1, by Pham Kim Hung

The author was an IMO gold medalist. But it was written when he finished his high school so the writing style is very easy to understand.

Vol 1 is suitable for beginners, you then can go on to vol 2.