The philosophy of the book, which makes it quite distinct from many existing texts on the subject, is based on treating the concepts of measure and integration starting with the most general abstract setting and then introducing and studying the Lebesgue measure and integration on the real line as an important particular case.　 The book consists of nine chapters and appendix, with the material flowing from the basic set classes, through　measures, outer measures and the general procedure of measure extension, through measurable functions　and　various types of convergence of...

Advanced Materials gives an unique insight into the specialized materials that are required to run our modern society. Provided within are the fundamental theories and applications of advanced materials for metals, glasses, polymers, composites, and nanomaterials. This book is ideal for scientists and engineers of materials science, chemistry, physics, and engineering, and students of these disciplines.

A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications.

The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental...

A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.

This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.

Bioanalytical chemistry plays today a central role in various fields, from healthcare to food and environmental control. This book presents the main methodologies for analyzing biomacromolecules, with a focus on methods based on molecular recognition. The six chapters move from fundamentals to the most recent advances, achieved by a synergetic combination of bio and nanotechnologies. The need for rapid and reliable analytical tools able to perform a large number of quantitative analyses, not only in centralized laboratories and core facilities but also for point-of-care testing, has been...

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

This book is an in-depth and modern presentation of important classical results in complex analysis and is suitable for a first course on the topic, as taught by the authors at several universities. The level of difficulty of the material increases gradually from chapter to chapter, and each chapter contains many exercises with solutions and applications of the results, with the particular goal of showcasing a variety of solution techniques.

Industrial Catalysis provides an excellent introduction to catalytic principles and processes, addressing the applications of inorganic-, organic- and biocatalysts in industrial chemistry. Each chapter is focussed on one catalytic process and discusses its life cycle from source materials, catalyst synthesis, the catalytic process, lifetime and recovery. The book also includes a comprehensive overview on industrial processes employing catalysis.