Integral calculus and equations

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

This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016.

This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure.

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating F-function.

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.

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 has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform.

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

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel.

This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his first devoted to calculus), Resume des lecons sur le calcul infinitesimal, "e;Summary of Lectures on the Infinitesimal Calculus,"e; originally written to benefit his Ecole Polytechnique students in Paris.

This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms.

This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration.

Based on the authors' research experience, this two-volume reference textbook focuses on the theory of generalized locally Toeplitz sequences and its applications.

Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single-variable calculus.

This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus - a major, emerging tool relevant to all areas of scientific inquiry.

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

Intended for a one- or two-semester course, this text applies basic, one-variable calculus to analyze the motion both of planets in their orbits as well as interplanetary spacecraft in their trajectories.

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.

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics.

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective.

What's the point of calculating definite integrals since you can't possibly do them all?

This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language.

In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications.

The present volume contains the transactions of the lOth Oberwolfach Conference on "e;Probability Measures on Groups"e;.

Intended as a self-contained introduction to measure theory, this textbook also includes 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.

The material accumulated and presented in this volume can be ex- plained easily.

This book is intended to serve as introductory and reference material for the application of integral transforms to a range of common mathematical problems.

This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv- ing, primarily, ordinary linear difference equations.

Analytic Extension is a mysteriously beautiful property of analytic functions.

The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997.

The subject of this book stands at the crossroads of ergodic theory and measurable dynamics.

This is a collection of research-oriented monographs, reports, and notes arising from lectures and seminars on the Weil representation, the Maslov index, and the Theta series.

In many scientific or engineering applications, where ordinary differen- tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes.

The calculus has been one ofthe areas of mathematics with a large number of significant applications since its formal development in the seventeenth century.

Trying to make mathematics understandable to the general public is a very difficult task.

In volume I we developed the tools of "e;Multivalued Analysis.

Computational Techniques for the Summation of Series is a text on the representation of series in closed form.

This book considers signal processing and physical modeling meth- ods for sound synthesis.

This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight.

Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus.

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The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada - Azores, from July 4-8, 2011 in honor of Professor Ravi P.

This classroom-tested text is intended for a one-semester course in Lebesgue's theory.

Intended as a self-contained introduction to measure theory, this textbook also includes 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.

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing.

In this book the author presents a new approach to the study of weakly structurable dynamic systems.

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Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator.