Inequalities: With Applications to Engineering

ISBN-13: 9783319307701 / Angielski / Miękka / 2014 / 239 str.

Michael J. Cloud; Byron C. Drachman; Leonid P. Lebedev

Opis

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.

Recenzje

"This second edition of Inequalities with Applications to Engineering is aimed at readers having customary backgrounds in engineering mathematics. ... It is interesting to note that the authors included not only classical inequalities ... but also some discussion of extremum problems and an introduction to interval analysis. ... It should be of interest to both undergraduate and graduate students of mathematics, physics and engineering, as well as to practicing engineers." (Victor A. Eremeyev, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 95 (8), 2015)

"It reads at an undergraduate mathematics level but gives soft introductions and reviews on all topics leaving it possible for those without a formal mathematical or applied mathematical background to follow. ... Any mathematician would enjoy this book and appreciate its clear, concise descriptions. ... It simply is a very nice applied mathematics book." (Anna Heffernan, Irish Mathematical Bulletin, Issue 75, 2015)

"...a remarkable addition to the literature on inequalities, and not only engineers or other applied scientists, but the students of mathematics and researchers will appreciate it." - József Sándor, zbMATH

Spis treści

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.

O autorze

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.

Blurb

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 Cauchy–Schwarz 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.