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Inequalities : with applications to engineering / Michael J. Cloud, Byron C. Drachman and Leonid P. Lebedev.

By: Contributor(s): Material type: TextTextPublication details: New York : Springer, 2014.Edition: 2nd edDescription: xiii, 239 p. : illustrations ; 24 cmISBN:
  • 9783319053103
Subject(s): DDC classification:
  • 515.26 23 C647
Contents:
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 -- Appendix A-- References -- Index.
Summary: 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 calculusandproceeds 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 asresearchers in engineering, mathematics, physics, chemistry, or any other quantitative science.
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Includes bibliographical references and index.

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 --
Appendix A--
References --
Index.

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 calculusandproceeds 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 asresearchers in engineering, mathematics, physics, chemistry, or any other quantitative science.

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