Kategoria BISAC: Mathematics >> Calculus

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.

Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics,...

Building on the author s previous book in the series, Complex Analysis with Applications to Flows and Fields (CRC Press, 2010), Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. This book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible...

This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration no generalized Riemann integrals of Henstock Kurzweil variety are involved.

In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy Riemann, Laplace, and minimal surface equations.

Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis - often with different definitions and under different names. Among the synonyms are Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called Pick functions', Nevanlinna functions' or operator monotone functions'.

This monograph - now in its second revised and extended edition - offers a self-contained and unified approach to Bernstein functions and closely related function...

Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and C^r macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C¹ splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C² splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the...

Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science.

This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its...

Intended as a self-contained introduction to measure theory, this textbook provides a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition provides the reader with a broad perspective on measure theory through additional topics such as the Kurzweil-Henstock integral, the Banach-Tarski paradox, a proof of the existence of liftings, the Daniell integral. In addition, applications and introductions to other related areas such as measure-theoretic probability...

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace...

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought...

This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable efficient methods of applied mathematics and computer-based modeling can be to enhancing the quality of interdisciplinary...

Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising...

Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms "Hardy spaces" and "Bergman spaces" are by now standard and well established. But the term "Fock spaces" is a different story.

Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author's, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void,...