Differential calculus and equations

The book takes a problem solving approach in presenting the topic of differential equations.

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago.

This monograph proposes a unified theory of the calculus of fractional and standard derivatives by means of an abstract operator-theoretic approach.

This brief investigates the asymptotic behavior of some PDEs on networks.

This study guide is designed for students taking a Calculus I course.

This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations.

The International Conference of Computational Harmonic Analysis, held in Hong Kong during the period of June 4 - 8, 2001, brought together mathematicians and engineers interested in the computational aspects of harmonic analysis.

This textbook is an introduction to the methods needed to solve partial differential equations (PDEs).

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This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book.

Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications.

This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations.

The subject of stability problems for viscoelastic solids and elements of structures, with which this book is concerned, has been the focus of attention in the past three decades.

This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior.

The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit.

This book presents mathematical models and numerical simulations of crowd dynamics.

Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers.

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces.

Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings.

Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences.

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field.

This brief studies recent work conducted on certain exponential type operators and other integral type operators.

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

In this book, expansions of functions in infinite series and infinite product and the asymptotic expansion of functions are discussed.

This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems.

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.

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Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology.

In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications.

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier-Stokes system in bounded domains under sole condition of zero total flux.

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.

This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution.

The aim of this book is to quickly elevate students to a proficiency level where they can solve linear and nonlinear partial differential equations using state-of-the-art numerical methods.

This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons.

This monograph introduces a new mathematical model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility.

It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections.

This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges.

This textbook introduces some basic tools from the theory of monotone operators together with some of their applications.

Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics.

The future of oncology seems to lie in Molecular Medicine (MM).

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine.

This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date.

This book provides an extensive survey on Lyapunov-type inequalities.

The author's approach is one of continuum models of the aerodynamic flow interacting with a flexible structure whose behavior is governed by partial differential equations.