Integral calculus and equations

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required.

This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory).

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.

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

The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T.

Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook.

This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "e;max-product"e; type operators.

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces.

This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities.

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities.

This textbook covers the main results and methods of real analysis in a single volume.

The contributions in this volume aim to deepenunderstanding of some of the current research problems and theories inmodern topics such as calculus of variations, optimization theory, complexanalysis, real analysis, differential equations, andgeometry.

This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics.

Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject.

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales.

This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory.

This book covers the material of a one year course in real analysis.

Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena.

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "e;New Trends in Applied Harmonic Analysis:Sparse Representations, Compressed Sensing and Multifractal Analysis"e;.

This book presents the proceedings of Positivity VII, held from 22-26 July 2013, in Leiden, the Netherlands.

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods.

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years.

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation.

This book offers a thoroughand self-contained exposition of the mathematics of time-domain boundaryintegral equations associated to the wave equation, including applications toscattering of acoustic and elastic waves.

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis.

This book provides an introduction to the basic ideas and tools used in mathematical analysis.

The basic mathematics of computerized tomography, the CT scan, are aptly presented for an audience of undergraduates in mathematics and engineering.

This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems.

Classical in its approach, this textbook is thoughtfully designed and composed in two parts.

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes.

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations.

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.

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

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014.

Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces.

Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems.

This book describes mathematical techniques for integral transforms in a detailed but concise manner.

This monograph is an annotated translation of what is considered to be the world's first calculus textbook, originally published in French in 1696.

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.