Differential calculus and equations

Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory.

The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis.

This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems.

This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work.

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.

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

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).

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.

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 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.

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.

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 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.

The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems.

The subject of complex vector functional equations is a new area in the theory of functional equations.

Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view.

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

Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics.

This monograph derives from familiar economic principles the dynamics of national income, the interest rate, employment, the value of capital stock, prices, and the cumulative balance of payments.

The various types of special functions have become essential tools for scientists and engineers.

This book outlines the modern theory of functional equations and inequalities in several variables.

This book introduces a method of research which can be used in various fields of mathematics.