Michael J. Cloud Livres

This book covers functional analysis and its applications to continuum mechanics. The mathematical material is treated in a non-abstract manner and is fully illuminated by the underlying mechanical ideas. The presentation is concise but complete, and is intended for specialists in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. Exercises and examples are included throughout with detailed solutions provided in the appendix.

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.