Differential calculus and equations

In recent years, the study of the Monge-Ampere equation has received consider- able attention and there have been many important advances.

In the field known as "e;the mathematical theory of shock waves,"e; very exciting and unexpected developments have occurred in the last few years.

Disorder is one of the predominant topics in science today.

Surely most geodesists have been occupied by seeking optimal shapes of a net- work.

The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike.

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs).

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences.

This monograph is intended to provide a comprehensive description of the rela- tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain.

The implicit function theorem is part of the bedrock of mathematical analysis and geometry.

In nonlinear problems, essentially new phenomena occur which have no place in the corresponding linear problems.

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry.

Control theory has applications to a number of areas in engineering and communication theory.

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology).

l\lany systems encountered in practice involve a coupling between contin- uous dynamics and discrete events.

The most important thing is to write equations in a beautiful form and their success in applications is ensured.

For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person.

This book is a self-contained introduction to real analysis assuming only basic notions on limits of sequences in ]RN, manipulations of series, their convergence criteria, advanced differential calculus, and basic algebra of sets.

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdos, Fejer, Stieltjes, and Turan.

This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis.

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension.

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations.

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.

Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay.

In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems.

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems.

Extrinsic geometry describes properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves.

"e;Hypernumbers and Extrafunctions"e; presents a rigorous mathematical approach to operate with infinite values.

This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally).

No books dealing with a comprehensive illustration of the fast developing field of nonlinear analysis had been published for the mathematicians interested in this field for more than a half century until D.

This text is intended for an honors calculus course or for an introduction to analysis.

This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations.

On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "e;Mathematical problems"e; at the Second Interna- tional Congress of Mathematicians in Paris.

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics.

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects.

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.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics.

This book introduces the reader to the area of inverse problems.

This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control.

Moving mesh methods are an effective, mesh-adaptation-based approach for the numerical solution of mathematical models of physical phenomena.

Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity).

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly.

A half-century ago, advanced calculus was a well-de?

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces.