Differential calculus and equations

The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations.

The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived.

Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type.

This text provides the first comprehensive treatment of the discrete fractional calculus.

This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations.

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice.

This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations.

The Inverse Scattering Transformation and The Theory of Solitons

This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed.

In honour of Noel Baker, a leading exponent of transcendental complex dynamics, this book describes the state of the art in this subject.

In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.

The conference Operator Theory, Analysis and Mathematical Physics - OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics.

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory.

This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field.

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.

CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field.

Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance.

This book covers applications of fractional calculus used for medical and health science.

This book gathers original research papers and survey articles presented at the "e;International Conference on Class Groups of Number Fields and Related Topics,"e; held at Harish-Chandra Research Institute, Allahabad, India, on September 4-7, 2017.

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself.

This monograph extends well-known facts to new classes of problems and works out novel approaches to the solution of these problems.

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory.

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes.

This reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators.

Approximation methods are vital in many challenging applications of computational science and engineering.

This handbook is the sixth and last volume in the series devoted to stationary partial differential equations.

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book.

This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences.

Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena.

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models.

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory.

Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences.

In the field known as "e;the mathematical theory of shock waves,"e; very exciting and unexpected developments have occurred in the last few years.

This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators.

The papers contained in this book address problems in one and several complex variables.

First published in 1990.

This book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements.

The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics.

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.