This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations.
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology.
This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa- is in the tradition of the books [GH] and [EW.
Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems.
This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.
Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis.
Written by an engineer and sharply focused on practical matters, Solution of Ordinary Differential Equations by Continuous Groups explores the application of Lie groups to the solution of ordinary differential equations.
Offering in-depth analyses of current theories and approaches related to Sobolev-type equations and systems, this reference is the first to introduce a classification of equations and systems not solvable with respect to the highest order derivative, and it studies boundary value problems for these classes of equations.
Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws.
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators.
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing.
This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations.
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods.
This volume documents the results and presentations relating to the use of wavelet theory and other methods in surface fitting and image reconstruction of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993.
Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave.
This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations.
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.
More than twenty years ago I gave a course on Fourier Integral Op- erators at the Catholic University of Nijmegen (1970-71) from which a set of lecture notes were written up; the Courant Institute of Mathematical Sciences in New York distributed these notes for many years, but they be- came increasingly difficult to obtain.
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.
This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University.
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical SystemsA Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations.
On becoming familiar with difference equations and their close re- lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations.
Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable planar quadratic polynomial differential systems.
