Analytic Inequalities

Genre: Science
Original Publish Date: Jul 24, 2014
Product Number: EB00796839
Released: Dec 04, 2019
Business Term: Purchase
ISBN: #9780486798172
Publisher: Dover Publications
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Mathematical analysis is largely a systematic study and exploration of inequalities — but for students the study of inequalities often remains a foreign country, difficult of access. This book is a passport to that country, offering a background on inequalities that will prepare undergraduates (and even high school students) to cope with the concepts of continuity, derivative, and integral. Beginning with explanations of the algebra of inequalities and conditional inequalities, the text introduces a pair of ancient theorems and their applications. Explorations of inequalities and calculus cover the number e, examples from the calculus, and approximations by polynomials. The final sections present modern theorems, including Bernstein's proof of the Weierstrass approximation theorem and the Cauchy, Bunyakovskii, HOlder, and Minkowski inequalities. Numerous figures, problems, and examples appear throughout the book, offering students an excellent foundation for further studies of calculus.