Differential calculus and equations

IMA Volumes 135: Transport in Transition Regimes and 136: Dispersive Transport Equations and Multiscale Models focus on the modeling of processes for which transport is one of the most complicated components.

The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans- formations.

This is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject.

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999.

This book is the Proceedings of the Second ISAAC Congress.

Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed.

1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics.

During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly.

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati- cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications.

This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October.

Since the seminal work of P.

Harmonic maps are solutions to a natural geometrical variational prob- lem.

Overview Many problems in mathematical physics and applied mathematics can be reduced to boundary value problems for differential, and in some cases, inte- grodifferential equations.

Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994.

Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc.

The main goal of this work is to revisit the proof of the global stability of Minkowski space by D.

We deal in this work with quantitative results in the pointwise approximation of func- tions by positive linear functionals and operators.

As in the case of the two previous volumes published in 1986 and 1997, the purpose of this monograph is to focus the interplay between real (functional) analysis and stochastic analysis show their mutual benefits and advance the subjects.

common feature is that these evolution problems can be formulated as asymptoti- cally small perturbations of certain dynamical systems with better-known behaviour.

Equations of the Ginzburg-Landau vortices have particular applications to a number of problems in physics, including phase transition phenomena in superconductors, superfluids, and liquid crystals.

Differential equations is a subject of wide applicability, and knowledge of dif- Differential equations is a subject of wide applicability, and knowledge of dif- ferential ferential equations equations topics topics permeates permeates all all areas areas of of study study in in engineering engineering and and applied applied mathematics.

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties.

Interactive Operations Research with Maple: Methods and Models has two ob- jectives: to provide an accelerated introduction to the computer algebra system Maple and, more importantly, to demonstrate Maple's usefulness in modeling and solving a wide range of operations research (OR) problems.

As is well known, The Great Divide (a.

Nonlinear partial differential equations has become one of the main tools of mod- ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes.

In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs.

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving.

Now in new trade paper editions, these classic biographies of two of the greatest 20th Century mathematicians are being released under the Copernicus imprint.

I once heard the book by Meyer (1993) described as a "e;vulgarization"e; of wavelets.

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math- ematical questions posed by such equations and the important role they play in many areas of science and technology.

For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE.

tion of fields as a product of coordinate-dependent and time-dependent factors.

Pseudodifferential methods are central to the study of partial differential equations, because they permit an "e;algebraization.

This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications.

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world.

Elliptic boundary problems have enjoyed interest recently, espe- cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary.

During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics.

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.