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Famous Inequalities

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More Calculus of a Single Variable

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Abstract

In this chapter we meet three very important inequalities: Bernoulli’s Inequality, the Arithmetic Mean–Geometric Mean Inequality, and the Cauchy–Schwarz Inequality. At first we consider only pre-calculus versions of these inequalities, but we shall soon see that a thorough study of inequalities cannot be undertaken without calculus. And really, calculus cannot be thoroughly understood without some knowledge of inequalities. We define Euler’s number \(\mathrm{e}\) by a more systematic method than that of Example 1.32. We’ll see that this method engenders many fine extensions.

I speak not as desiring more, but rather wishing a more strict restraint.

—Isabella, in Measure for Measure, by William Shakespeare

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Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State, Buffalo, NY, USA

    Peter R. Mercer

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  1. Peter R. Mercer
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Mercer, P.R. (2014). Famous Inequalities. In: More Calculus of a Single Variable. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1926-0_2

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