Inequalities from complex analysis

✍ Scribed by John P. D'Angelo

Publisher: MAA
Year: 2002
Tongue: English
Leaves: 277
Series: Carus Mathematical Monographs
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author begins by defining the complex number field; he gives a novel presentation of some standard mathematical analysis in the early chapters. The development culminates with some results from recent research literature. The book provides complete yet comprehensible proofs as well as some surprising consequences of the results. One unifying theme is a complex variables analogue of Hilbert's seventeenth problem. Numerous examples, exercises and discussions of geometric reasoning aid the reader. The book is accessible to undergraduate mathematicians, as well as physicists and engineers.

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<p><p>The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology.</p><p>Beginning with the theory of the Riemann integral (and