Inequalities

This book reviews essential facts from algebra and calculus, presents the central inequalities of applied analysis and then illustrates a wide variety of practical applications. The expanded 2nd edition offers new examples, exercise, hints and solutions.

This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the CauchySchwarz inequality, Chebyshev's inequality, Jensen's inequality and the triangle inequality.

The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate students, as well as researchers in engineering, mathematics, physics, chemistry or any other quantitative science.

New edition extensively revised and updated Provides full coverage of the central inequalities of applied analysis: Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the CauchySchwarz inequality, Chebyshev's inequality, Jensen's inequality, the triangle inequality and many more Includes applications to continuum mechanics and an introduction to the powerful field of interval analysis Presents a thorough review of background topics that make the book suitable for undergraduate students and practicing engineers, as well as graduate students and researchers Includes supplementary material: sn.pub/extras

Autorentext

Michael J. Cloud received a Ph.D. in Electrical Engineering from Michigan State University. He has been a faculty member in the Department of Electrical and Computer Engineering at Lawrence Technological University since 1987 and currently holds the rank of Associate Professor.

Byron C. Drachman is Emeritus Professor of Mathematics at Michigan State University. He received a Ph.D. in Mathematics from Brown University in 1966.

Leonid P. Lebedev completed a Ph.D. in Physics and Mathematics at Southern Federal University in Russia. He is a professor of mathematics at the National University of Colombia at Bogota and holds a faculty appointment at Southern Federal University.

Inhalt
Preface.- 1. Basic Review and Elementary Facts.- 2. Methods from the Calculus.- 3. Some Standard Inequalities.- 4. Inequalities in Abstract Spaces.- 5. Some Applications.- 6. Inequalities for Differential Equations.- 7. Brief Introduction to Interval Analysis.- Hints for Selected Problems.- References.- Appendix.