Integral calculus and equations

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based.

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

This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory.

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

In measure theory, a familiar representation theorem due to F.

This textbook offers an extensive list of completely solved problems in mathematical analysis.

This book compiles solutions of linear theory of elasticity problems for isotropic and anisotropic bodies with sharp and rounded notches.

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 first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration.

This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis.

This book discusses the numerical treatment of delay differential equations and their applications in bioscience.

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering.

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

This book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L2-spaces.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations.

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

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.

The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales.

Integrals and sums are not generally considered for evaluation using complex integration.

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry.

This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series.

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

This book explores fractional differential equations with a fixed point approach.

This book explores fractional differential equations with a fixed point approach.

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

This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations.

This volume explains how the recent advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools.

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

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

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

This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017.

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.

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.

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

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization.

This textbook offers an extensive list of completely solved problems in mathematical analysis.

This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017.

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Das Lebesgue-Integral ist ein essentielles Werkzeug für Analysis und Stochastik und damit für viele Bereiche, in denen Mathematik zum Einsatz kommt.

This brief explores the Krasnosel'skii-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

This book features a collection of recent findings in Applied Real and Complex Analysis that were presented at the 3rd International Conference "e;Boundary Value Problems, Functional Equations and Applications"e; (BAF-3), held in Rzeszow, Poland on 20-23 April 2016.

This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields.

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference "e;Dynamical Systems: Theory and Applications"e;, held in Lodz, Poland on December 2-5, 2019.

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory.

When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhauser title by the same author, A Concise Introduction to the Theory of Integration.

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