Integral calculus and equations

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 popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory.

The text contains detailed and complete proofs and includes instructive historical introductions to key chapters.

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

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 book provides a self-contained introduction to convex geometry in Euclidean space.

In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved.

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions.

This book is intended as a manual on modern advanced statistical methods for signal processing.

This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals.

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

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

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

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

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.

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

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

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.

This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects.

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

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

This advanced graduate textbook presents main results and techniques in Functional Analysis and uses them to explore other areas of mathematics and applications.

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis.

This book offers an introduction to a classical problem in ergodic theory and smooth dynamics, namely, the Kolmogorov-Bernoulli (non)equivalence problem, and presents recent results in this field.

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.

This book contains a brief historical introduction and state of the art in fractional calculus.

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

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

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.

This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums.

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 method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells.

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.