Synopses & Reviews
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, Hölder, and Minkowski inequalities. Numerous figures, problems, and examples appear throughout the book, offering students an excellent foundation for further studies of calculus.
Synopsis
Appropriate for undergraduates and even high school students, this text introduces a pair of ancient theorems, explores inequalities and calculus, and covers modern theorems, including Bernstein's proof of the Weierstrass approximation theorem and the Cauchy, Bunyakovskii, Hölder, and Minkowski inequalities. 1961 edition. Includes 28 figures.
Synopsis
In order to reach conclusions and prove theorems, mathematicians rely upon a form of analysis that allows approximations for integrals, infinite sums, and solutions of differential equations; these approximations are expressed in terms of inequalities. This text addresses a difficult subject — one that is usually treated only in works for advanced students — at a level appropriate for undergraduates and even high school students, offering a background on inequalities that will prepare students to cope with the concepts of continuity, derivative, and integral.
About the Author
Nicholas D. Kazarinoff was Professor of Mathematics at the University of Michigan and the State University of New York at Buffalo.