Differential calculus and equations

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations.

An enormous array of problems encountered by scientists and engineers are based on the design of mathematical models using many different types of ordinary differential, partial differential, integral, and integro-differential equations.

This book presents the general theory of categorical closure operators to- gether with a number of examples, mostly drawn from topology and alge- bra, which illustrate the general concepts in several concrete situations.

The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam.

Algebraic, differential, and integral equations are used in the applied sciences, en- gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time.

First posed by Hermann Weyl in 1910, the limit-point/limit-circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations.

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an intro- duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl].

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences.

It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana- lytic Functions.

Optimal control of partial differential equations (PDEs) is a well-established discipline in mathematics with many interfaces to science and engineering.

The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass.

Here is a book that will be a joy to the mathematician or graduate student of mathematics or even the well-prepared undergraduate who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis.

This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen-Cahn PDE model of phase transitions.

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems.

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.

Combining two important and growing areas of applied mathematics-control theory and modeling-this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences.

With each methodology treated in its own chapter, this monograph is a thorough exploration of several theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators.

Mathematical modeling using dynamical systems and partial differential equations is now playing an increasing role in the understanding of complex multi-scale phenomena.

Many problems in science and engineering involve the solution of differential equations or systems.

TheinternationalconferencesonIntegralMethodsinScienceandEngineering (IMSE) are biennial opportunities for academics and other researchers whose work makes essential use of analytic or numerical integration methods to discuss their latest results and exchange views on the development of novel techniques of this type.

TheinternationalconferencesonIntegralMethodsinScienceandEngineering (IMSE) are biennial opportunities for academics and other researchers whose work makes essential use of analytic or numerical integration methods to discuss their latest results and exchange views on the development of novel techniques of this type.

Some of the most common dynamic phenomena that arise in engineering practice-actuator and sensor delays-fall outside the scope of standard finite-dimensional system theory.

The present volume is a collection of papers mainly concerning Phase Space Analysis,alsoknownasMicrolocal Analysis,anditsapplicationstothetheory of Partial Di?

During the past decade, the mathematics of superconductivity has been the subject of intense activity.

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging.

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, "e;Fractals and Related Fields II,"e; held in June 2011.

This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition.

An outgrowth of The Seventh International Conference on Integral Methods in Science and Engineering, this book focuses on applications of integration-based analytic and numerical techniques.

This second edition of Generalized Functions has been strengthened in many ways.

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems.

Since the ?

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity.

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

Harmonic analysis is a venerable part of modern mathematics.

I am sure that something must be found.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade.

The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games.

The purpose of the book is to summarize Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance.

The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di?

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.

A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis.

This book provides an introduction to the theory of dynamical systems with the (R) aid of the Mathematica computer algebra system.