Integral calculus and equations

This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined.

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering.

This book focuses on solving integral equations with difference kernels on finite intervals.

The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied.

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations.

This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis.

This is the revised and enlarged 2nd edition of the authors' original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory.

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community.

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences.

This is a monograph devoted to recent research and results on dynamic inequalities on time scales.

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields.

Exercises in Analysis will be published in two volumes.

The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book.

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis.

The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields.

Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work.

This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems.

This book provides a comprehensive and timely report in the area of non-additive measures and integrals.

This well-illustrated book, by two established historians of school mathematics, documents Thomas Jefferson's quest, after 1775, to introduce a form of decimal currency to the fledgling United States of America.

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.

This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations.

In this book mathematical techniques for integral transforms are described in detail but concisely.

This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method.

This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians-a textbook for courses in probability for students in mathematical statistics.

This book develops integral identities, mostly involving multidimensional functions and infinite limits of integration, whose evaluations are intractable by common means.

This proceedings volume features selected contributions from the conference Positivity X.

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems.

This textbook introduces readers to the fundamental notions of modern probability theory.

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums.

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball.

This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models.

This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering.

This monograph presents the state of the art of convexity, with an emphasis to integral representation.

In 1903 Fredholm published his famous paper on integral equations.

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis.

This volume presents the proceedings of the Joint German-Israeli Workshop on linear one-dimensional singular integral equations, held in Tel Aviv from March 1-10, 1995.