Integral calculus and equations

The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry.

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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes.

This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type.

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications.

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

The first book devoted to ellipsoidal harmonics presents the state of the art in this fascinating subject.

This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications.

It is widely recognized, by the scienti?

This book offers the reader an overview of recent developments of integral equations on time scales.

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature.

This contributed volume contains a collection of articles on the most recent advances in integral methods.

This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations.

This study guide is designed for students taking courses in precalculus.

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

This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory.

This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods.

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.

This study guide is designed for students taking a Calculus II course.

This contributed volume contains a collection of articles on the most recent advances in integral methods.

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research.

Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop- erties of almost all sample paths of the sequences involved (strong limit theorems).

Decomposable sets since T.

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 contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

The authors introduce geomathematics as an active research area to a wider audience.

In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches.

Designed for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration.

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student.

Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals.

Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range.

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications.

Der zweite Teil der Integraltafel, welcher die bestimmten Integrale umfaßt, gleicht in seinem Aufbau dem ersten Teil.

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.

Iteration regularization, i.

This comprehensive textbook explores the topics of vector functions and functions of several variables.

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 textbook introduces readers to real analysis in one and n dimensions.

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations.

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations.

The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces.