Calculus and mathematical analysis

This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates.

This is a memorial volume in honor of Serguei Kozlov, one of the founders of homogenization, a new branch of mathematical physics.

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations.

Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces.

This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories.

In the past two decades, there has been great progress in the theory of nonlinear partial differential equations.

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders.

This book describes adaptive methods of statistical numerical analysis using evaluation of integrals, solution of integral equations, boundary value problems of the theory of elasticity and heat conduction as examples.

Methods of nonlinear time series analysis are discussed from a dynamical systems perspective on the one hand, and from a statistical perspective on the other.

This book is an introduction to partial differential equations (PDEs) and the relevant functional analysis tools which they require.

This book takes a comprehensive look at mean value theorems and their connection with functional equations.

This book introduces the reader to the general theory of partially ordered sets, i.

The book combines both rigor and intuition to derive most of the classical results of linear and nonlinear filtering and beyond.

This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas.

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs).

Information Theory is studied from the following view points: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels.

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations.

This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials.

This book deals mainly with linear and nonlinear parabolic equations and systems of second order.

New Edition: Lipschitz Algebras (2nd Edition)The Lipschitz algebras Lip(M), for M a complete metric space, are quite analogous to the spaces C(I ) and Linfinity(X), for I a compact Hausdorff space and X a I -finite measure space.

This book deals with the boundary value problems for non-regular partial differential equations in the half-plane.

This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods.

Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description.

This volume collects the articles presented at the Third International Conference on "e;The Navier-Stokes Equations: Theory and Numerical Methods"e;, held in Oberwolfach, Germany.

Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas.

This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion.

This book deals with the new class of one-dimensional variational problems - the problems with branching solutions.

This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent.

This book contains five theses in analysis, by A C Gilbert, N Saito, W Schlag, T Tao and C M Thiele.

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations.

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems.

This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science.

Henstock-Kurzweil (HK) integration, which is based on integral sums, can be obtained by an inconspicuous change in the definition of Riemann integration.

The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-Moon system, as a source of possible nominal orbits for future space missions.

This book studies several problems related to the analysis of planned or possible spacecraft missions.

This book focuses on the interactions between discrete and geometric dynamical systems, and between dynamical systems and theoretical physics and computer science.

This book presents the Henstock/Kurzweil integral and the McShane integral.

Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations.

This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences.

The real world is complicated, as a result of which most mathematical models arising from mechanics, physics, chemistry and biology are nonlinear.

The topics discussed in this book can be classified into three parts:(i) Gaussian processes.

The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation.

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature.

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations.

The third conference on "e;Symmetry and Perturbation Theory"e; (SPT2001) was attended by over 50 mathematicians, physicists and chemists.

This book consists of 20 review articles dedicated to Prof.

This authoritative book provides comprehensive coverage of practical Fourier analysis.

This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions.

This is a reprint of M C Irwin's beautiful book, first published in 1980.

This book provides an overview of recent developments in web theory.